Structural Dynamics and Loads
Spacecraft Structural Dynamics & Loads
An Overview
Adriano Calvi, PhD
ESA / ESTEC, Noordwijk, The Netherlands
This presentation is distributed to the students of the University of Liege
Satellite Engineering Class – November 29, 2010)
This presentation is not for further distribution
Spacecraft Structural Dynamics & Loads - A. Calvi
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Foreword
• This half-day course on “Structural Dynamics and Loads” intends to
present the subject within the broad context of the development of
spacecraft structures. Basic notions as well as some “advanced”
concepts are explained with minimum mathematics
• The content is the result of the author’s experience acquired
through his involvement with research and industrial activities
mainly at the European Space Agency and Alenia Spazio
• The course is specifically tailored for university students
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Specific Objectives of the Presentation
• To provide a short overview about structural dynamics and its
importance in the development of the spacecraft structures (design,
analysis & test)
– To introduce the students to the “logic and criteria” as regards
“dynamics and loads”
• To point out the importance of some topics such as “modal
effective mass”, “dynamic testing” and “model validation” often not
addressed in the University Courses
• To show results of some applications (satellites, launchers, etc.)
• To testify the importance of structural dynamics analysis (and
specifically of some numerical methods)
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Spacecraft Structural Dynamics & Loads (1)
• Introduction
– Preliminary concepts: the launch mechanical environment
– Requirements for spacecraft structures
– The role of structural dynamics in a space project
• Dynamic analysis types
– Real eigenvalue
– Frequency response
– Transient response
– Shock response
– Random vibration
• The effective mass concept
• Preliminary design, design load cycles & verification loads cycle
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Spacecraft Structural Dynamics & Loads (2)
• Payload-launcher Coupled Loads Analysis (CLA)
• Mechanical tests
– Modal survey test
– Sinusoidal vibration test
– Acoustic noise test
– Shock test
– Random vibration test
• Overtesting, “notching” and sine vibration testing
• Mathematical model updating and validation
• Summary and conclusive remarks
– Bibliography
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Preliminary concepts (1)
Structural dynamics is the study of structures subjected to a
mechanical environment which depends on time and leading to a
movement
•
•
•
•
•
Excitation transmission types (mechanical & acoustic)
Type of time functions (sinusoidal, transient, random)
Type of frequencies involved (low frequency, broadband)
Domain of analysis (time domain, frequency domain)
Structure representation with a mathematical model (continuous or
discrete)
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Preliminary concepts (2)
• The parameter most commonly used (in the industry) to “define the motion
of a mechanical system” is the acceleration
• Typical ranges of acceleration of concern in aerospace structures are from
0.01 g to 10,000 g.
• Frequency (Hz or rad/s) and “octave”
• Vibroacoustics, pressure (N/m2) and Sound Pressure Level (dB)
• Random vibration and (acceleration) Power Spectral Density (g2/Hz)
• Shock Response Spectrum
• Root mean square (rms) = square root of the mean of the sum of all the
squares
– Note 1: the decibel is a tenth of a bel, the logarithm (base 10) of a power ratio (it
is accepted that power is proportional to the square of the rms of acceleration,
velocity, pressure, etc.)
– Note 2: it must be emphasized that dB in acoustics is not an unit of acoustic
pressure but simply a power ratio with respect to a reference pressure which
must be stated or clearly implicit
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Example of satellite structural design concept
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Accelerations… some remarks
• The parameter most commonly used (in the industry) to “define the
motion of a mechanical system” is the acceleration
• Good reasons: accelerations are directly related to forces/stresses and
“easy” to specify and measure
• Some “hidden” assumptions
– Criteria for equivalent structural damage (e.g. shock response spectra)
Note: failures usually happen in the largest stress areas, regardless if they
are the largest acceleration areas!
– Rigid or static determinate junction (e.g. quasi-static loads)
• Important consequences
– Need for considering the “actual” (e.g. “test” or “ flight”) boundary conditions
(e.g. for the purpose of “notching”)
– Need for a “valid” F.E. model (e.g. to be used for force and stress recovery)
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Mechanical loads are caused by:
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•
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•
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Transportation
Rocket Motor Ignition Overpressure
Lift-off Loads
Engine/Motor Generated Acoustic Loads
Engine/Motor Generated Structure-borne Vibration Loads
Engine/Motor Thrust Transients
Pogo Instability, Solid Motor Pressure Oscillations
Wind and Turbulence, Aerodynamic Sources
Liquid Sloshing in Tanks
Stage and Fairing Separation Loads
Pyrotechnic Induced Loads
Manoeuvring Loads
Flight Operations, Onboard Equipment Operation
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Launch mechanical environment
• Steady state accelerations
• Low frequency vibrations
• Broad band vibrations
– Random vibrations
– Acoustic loads
• Shocks
• Loads (vibrations) are transmitted to the payload (e.g. satellite)
through its mechanical interface
• Acoustic loads also directly excite payload surfaces
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“Steady-state” and low-frequency transient accelerations
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Acoustic Loads
• During the lift off and the early phases of
the launch an extremely high level of
acoustic noise surrounds the payload
• The principal sources of noise are:
– Engine functioning
– Aerodynamic turbulence
• Acoustic noise (as pressure waves)
impinging on light weight panel-like
structures produce high response
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Broadband and high frequency vibrations
Broad band random vibrations are produce by:
• Engines functioning
• Structural response to broad-band acoustic loads
• Aerodynamic turbulent boundary layer
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Shocks
Mainly caused by the actuation of pyrotechnic devices:
• Release mechanisms for stage and satellite separation
• Deployable mechanisms for solar arrays etc.
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Static and dynamic environment specification (typical ranges)
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Quasi-Static Loads (accelerations)
• “Loads independent of time or which vary slowly, so that the dynamic
response of the structure is not significant” (ECSS-E-ST-32). Note: this is
the definition of a quasi-static event!
• “Combination of static and low frequency loads into an equivalent static
load specified for design purposes as C.o.G. acceleration” (e.g. NASA RP1403, NASA-HDBK-7004). Note: this definition is fully adequate for the
design of the spacecraft primary structure. For the design of components
the contribution of the high frequency loads, if relevant, is included as well!
• CONCLUSION: quasi static loading means under steady-state
accelerations (unchanging applied force balanced by inertia loads). For
design purposes (e.g. derivation of design limit loads, selection of the
fasteners, etc.), the quasi-static loads are normally calculated by
combining both static and dynamic load contributions. In this context the
quasi static loads are equivalent to (or interpreted by the designer as)
static loads, typically expressed as equivalent accelerations at the C.o.G.
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Typical Requirements for Spacecraft Structures
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Strength
Structural life
Structural response
Stiffness
Damping
Mass Properties
Dynamic Envelope
Positional Stability
Mechanical Interface
• Basic requirement: the structure shall support the payload and
spacecraft subsystems with enough strength and stiffness to
preclude any failure (rupture, collapse, or detrimental deformation)
that may keep them from working successfully.
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Requirements evolution
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Design requirements and verification
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Examples of (Mechanical) Requirements (1)
• The satellite shall be compatible with 2 launchers (potential candidates:
VEGA, Soyuz in CSG, Rockot, Dnepr)...
• The satellite and all its units shall withstand applied loads due to the
mechanical environments to which they are exposed during the service-life…
• Design Loads shall be derived by multiplication of the Limit Loads by a design
factor equal to 1.25 (i.e. DL= 1.25 x LL)
• The structure shall withstand the worst design loads without failing or
exhibiting permanent deformations.
• Buckling is not allowed.
• The natural frequencies of the structure shall be within adequate bandwidths
to prevent dynamic coupling with major excitation frequencies…
• The spacecraft structure shall provide the mounting interface to the launch
vehicle and comply with the launcher interface requirements.
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Examples of (Mechanical) Requirements (2)
• All the Finite Element Models (FEM) prepared to support the mechanical
verification activities at subsystem and satellite level shall be delivered in
NASTRAN format
• The FEM of the spacecraft in its launch configuration shall be detailed enough to
ensure an appropriate derivation and verification of the design loads and of the
modal response of the various structural elements of the satellite up to 140 Hz
• A reduced FEM of the entire spacecraft correlated with the detailed FEM shall be
delivered for the Launcher Coupled Loads Analysis (CLA)…
• The satellite FEMs shall be correlated against the results of modal survey tests
carried out at complete spacecraft level, and at component level for units above
50 kg…
• The structural model of the satellite shall pass successfully qualification sine
vibration Test.
• The flight satellite shall pass successfully acceptance sine vibration test.
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Spacecraft stiffness requirements for different launchers
Launch vehicle manuals specify minimum values for the payload natural
(fundamental) frequency of vibration in order to avoid dynamic coupling between
low frequency dynamics of the launch vehicle and payload modes
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The Role of Structural Dynamics in a Space Project
• Mechanical environment definition (structural response and loads
identification by analysis and test)
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–
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–
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–
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Launcher/Payload coupled loads analysis
Random vibration and vibroacoustic analyses
Jitter analysis
Test predictions (e.g. sine test by frequency response analysis)
Test evaluations (sine, acoustic noise…)
Input to structural life analysis (e.g. generation of the loading spectrum)
…
• Structural identification (by analysis and test)
– Modal analysis
– Modal survey test and experimental modal analysis
– Mathematical model updating and validation
• Design qualification and flight product acceptance
– Qualification and Acceptance tests (sine, random, acoustic noise, shock)
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Spacecraft Structural Dynamics & Loads (1)
• Introduction
– Preliminary concepts: the launch mechanical environment
– Requirements for spacecraft structures
– The role of structural dynamics in a space project
• Dynamic analysis types
– Real eigenvalue
– Frequency response
– Transient response
– Shock response
– Random vibration
• The effective mass concept
• Preliminary design, design load cycles & verification loads cycle
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Dynamic analysis types
• Real eigenvalue analysis (undamped free vibrations)
– Modal parameter identification, etc.
• Linear frequency response analysis (steady-state response of
linear structures to loads that vary as a function of frequency)
– Sine test prediction, transfer functions calculation, LV/SC CLA etc.
• Linear transient response analysis (response of linear structures to
loads that vary as a function of time).
– LV/SC CLA, base drive analysis, jitter analysis, etc.
• “Shock” response spectrum analysis
– Specification of equivalent environments (e.g. equivalent sine input),
– Shock test specifications, etc.
• Vibro-acoustics (FEM/BEM, SEA) & Random vibration analysis
– Vibro-acoustic test prediction & random vibration environment definition
– Loads analysis for base-driven random vibration
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Reasons to compute normal modes (real eigenvalue analysis)
• To verify stiffness requirements
• To assess the dynamic interaction between a component and its
supporting structure
• To guide experiments (e.g. modal survey test)
• To validate computational models (e.g. test/analysis correlation)
• As pre-requisite for subsequent dynamic analyses
• To evaluate design changes
• Mathematical model quality check (model verification)
• Numerical methods: Lanczos,…
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Real eigenvalue analysis
Note: mode shape normalization
Scaling is arbitrary
Convention: “Mass”, “Max” or “Point”

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Mode shapes

Cantilever beam
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
Simply supported beam
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Satellite Normal Modes Analysis
Mode 1: 16.2 Hz
Mode 2: 18.3 Hz
INTEGRAL Satellite (FEM size 120000 DOF’s)
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Frequency Response Analysis
• Used to compute structural response to steady-state harmonic
excitation
• The excitation is explicitly defined in the frequency domain
• Forces can be in the form of applied forces and/or enforced
motions
• Two different numerical methods: direct and modal
• Damped forced vibration equation of motion with harmonic
excitation:
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Frequency response considerations
• If the maximum excitation frequency is much less than the lowest
resonant frequency of the system, a static analysis is probably
sufficient
• Undamped or very lightly damped structures exhibit large dynamic
responses for excitation frequencies near natural frequencies
(resonant frequencies)
• Use a fine enough frequency step size (Δf) to adequately predict
peak response.
• Smaller frequency spacing should be used in regions near resonant
frequencies, and larger frequency step sizes should be used in
regions away from resonant frequencies
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Harmonic forced response with damping
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Transient Response Analysis
• Purpose is to compute the behaviour of a structure subjected to timevarying excitation
• The transient excitation is explicitly defined in the time domain
• Forces can be in the form of applied forces and/or enforced motions
• The important results obtained from a transient analysis are typically
displacements, velocities, and accelerations of grid points, and
forces and stresses in elements
• Two different numerical methods: direct (e.g. Newmark) and modal
(e.g. Lanczos + Duhamel’s integral or Newmark)
• Dynamic equation of motion:
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Modal Transient Response Analysis
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Transient response considerations
• The integration time step must be small enough to represent accurately
the variation in the loading
• The integration time step must also be small enough to represent the
maximum frequency of interest (“cut-off frequency”)
• The cost of integration is directly proportional to the number of time steps
• Very sharp spikes in a loading function induce a high-frequency transient
response. If the high-frequency transient response is of primary
importance in an analysis, a very small integration time step must be
used
• The loading function must accurately describe the spatial and temporal
distribution of the dynamic load
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“Shock” response spectrum (and analysis)
• Response spectrum analysis is an approximate method of
computing the peak response of a transient excitation applied to a
structure or component
• There are two parts to response spectrum analysis: (1) generation
of the spectrum and (2) use of the spectrum for dynamic response
such as stress analysis
• Note 1: the “part (2)” of the response spectrum analysis has a
limited use in structural dynamics of spacecraft (e.g. preliminary
design) since the accuracy of the method may be questionable
• Note 2: the term “shock” can be misleading (not always a “physical
shock”, i.e. an environment of a “short duration”, is involved. It
would be better to use “response spectrum”)
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Generation of a response spectrum (1)
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Generation of a response spectrum (2)
• the peak response for one oscillator does not necessarily occur at the
same time as the peak response for another oscillator
• there is no phase information since only the magnitude of peak response is
computed
• It is assumed in this process that each oscillator mass is very small relative
to the base structural mass so that the oscillator does not influence the
dynamic behaviour of the base structure
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Shock Response Spectrum. Some remarks
• The 1-DOF system is used as reference structure (since the
simplest) for the characterization of environments (i.e.
quantification of the severity → equivalent environments can be
specified)
• In practice, the criterion used for the severity is the maximum
response which occurs on the structure (note: another criterion
relates to the concept of fatigue damage…)
• A risk in comparing two excitations of different nature is in the
influence of damping on the results (e.g. maxima are proportional
to Q for sine excitation and variable for transient excitation!)
• The absolute acceleration spectrum is used, which provides
information about the maximum internal forces and stresses
• The shock spectrum is a transformation of the time history which is
not reversible (contrary to Fourier transform)
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Shock Response Spectrum
(A) is the shock spectrum
of a terminal peak
sawtooth (B) of 500 G
peak amplitude and 0.4
millisecond duration
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Random vibration (analysis)
• Random vibration is vibration that can be described only in a
statistical sense
• The instantaneous magnitude is not known at any given time;
rather, the magnitude is expressed in terms of its statistical
properties (such as mean value, standard deviation, and probability
of exceeding a certain value)
• Examples of random vibration include earthquake ground motion,
wind pressure fluctuations on aircraft, and acoustic excitation due
to rocket and jet engine noise
• These random excitations are usually described in terms of a
power spectral density (PSD) function
• Note: in structural dynamics of spacecraft, the random vibration
analysis is often performed with simplified techniques (e.g. based
on “Miles’ equation” + effective modal mass models)
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Random noise with normal amplitude distribution
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Power Spectral Density (conceptual model)
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Sound Pressure Level (conceptual model)
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Spacecraft Structural Dynamics & Loads (1)
• Introduction
– Preliminary concepts: the launch mechanical environment
– Requirements for spacecraft structures
– The role of structural dynamics in a space project
• Dynamic analysis types
– Real eigenvalue
– Frequency response
– Transient response
– Shock response
– Random vibration
• The effective mass concept
• Preliminary design, design load cycles & verification loads cycle
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Modal effective mass (1)
• It may be defined as the mass terms in a modal expansion of the
drive point apparent mass of a kinematically supported system
– Note: driving-point FRF: the DOF response is the same as the excitation
• This concept applies to structure with base excitation
• Important particular case: rigid or statically determinate junction
• It provides an estimate of the participation of a vibration mode, in
terms of the load it will cause in the structure, when excited
• Note: avoid using: “it is the mass which participates to the mode”!
Modal reaction forces
Dynamic amplification factor
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Base (junction) excitation
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Modal effective mass (2)
Resultant of modal interface forces
Effective mass
Gen. mass
Modal participation factors
i-th mode
Rigid body modes
Eigenvector max value
• The effective mass matrix can be calculated either by the “modal
participation factors” or by using the modal interface forces
• Normally only the values on the leading diagonal of the modal
effective mass matrix are considered and expressed in percentage
of the structure rigid body properties (total mass and second
moments of inertia)
• The effective mass characterises the mode and it is independent
from the eigenvector normalisation
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Modal effective mass (3)
• For the complete set of modes the summation of the modal
effective mass is equal to the rigid body mass
• Contributions of each individual mode to the total effective mass
can be used as a criterion to classify the modes (global or local)
and an indicator of the importance of that mode, i.e. an indication of
the magnitude of participation in the loads analysis
• It can be used to construct a list of important modes for the
test/analysis correlation and it is a significant correlation parameter
• It can be used to create simplified mathematical models (equivalent
models with respect to the junction)
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Example of Effective Mass table
(MPLM test and FE model)
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Spacecraft Structural Dynamics & Loads (1)
• Introduction
– Preliminary concepts: the launch mechanical environment
– Requirements for spacecraft structures
– The role of structural dynamics in a space project
• Dynamic analysis types
– Real eigenvalue
– Frequency response
– Transient response
– Shock response
– Random vibration
• The effective mass concept
• Preliminary design, design load cycles & verification loads cycle
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A5 Typical Sequence of events
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A5 Typical Longitudinal Static Acceleration
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Sources of Structural Loadings (Launch)
80
g
70
60
8
acceleration [m/s2]
50
7
40
30
20
10
6
0
-10
5
-20
0
0.1
0.2
0.3
0.4
0.5
t [s]
0.6
0.7
0.8
0.9
1
4
3
2
1
0
0
50
100
150
200
250
300
t, s
Axial-Acceleration Profile for the Rockot Launch Vehicle
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80
70
60
acceleration [m/s2]
50
40
30
20
10
0
-10
-20
0
0.1
0.2
0.3
0.4
0.5
t [s]
0.6
0.7
0.8
0.9
1
Axial Acceleration at Launcher/Satellite Interface (Engines Cut-off)
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Load Factors for Preliminary Design (Ariane 5)
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Quasi-static loads for different launchers
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Quasi-Static Flight Limit loads for Dnepr and Soyuz
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Dynamic Response Acceleration, g
100
Physical
Modal
10
1
1
10
100
1000
Effective Mass, kg
Example of Physical (and Modal) Mass Acceleration Curve
for preliminary design of payload hardware or equipment items
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Load Combination Criteria for Components
(International Space Station Program)
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Loads and Factors
ECSS E-ST-32-10
Satellites
Test Logic
Common Design Logic
Expendable launch vehicles,
pressurized hardware and
manned system Test Logic
Limit Loads - LL
Increasing Load Level
x KQ
QL
x KA
x Coef. A
AL
Design Limit Loads
DLL
x Coef. B
x Coef. C
x KQ
x KA
AL
DYL
DUL
QL
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Some definitions
• Design:
– The process used to generate the set information describing the
essential characteristics of a product (ECSS-P-001A)
– Design means developing requirements, identifying options, doing
analyses and trade studies, and defining a product in enough detail so
it can be built (T. P. Sarafin)
• Verification:
– Confirmation by examination and provision of objective evidence that
specified requirements have been fulfilled (ISO 8402:1994)
– Verification means providing confidence through disciplined steps that
a product will do what it is supposed to do (T. P. Sarafin)
• Note: we can “prove” that the spacecraft satisfies the measurable criteria
we have defined, but we cannot “prove” a space mission will be successful
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Design Loads Cycles
A load cycle is the process of:
• Generating and combining math models for a proposed design
• Assembling and developing forcing functions, load factors, etc. to
simulate the critical loading environment
• Calculating design loads and displacements for all significant
ground, launch and mission events
• Assessing the results to identify design modifications or risks
• Then, if necessary, modifying the design accordingly or choosing to
accept the risk
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Design loads cycle process
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Final Verification
Consist of:
• Making sure all requirements are satisfied (“compliance”)
• Validating the methods and assumptions used to satisfy
requirements
• Assessing risks
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Final Verification (crucial points)
• To perform a Verification Loads Cycle for structures designed
and tested to predicted loads
– Finite element models correlation with the results of modal and
static testing
– Loads prediction with the current forcing functions
– Compliance with analysis criteria (e.g. MOS>0)
• To make sure the random-vibration environments used to
qualify components were high enough (based on data
collected during the spacecraft acoustic test)
Note: in the verification loads cycle instead of identifying required
design changes (design loads cycle) the adequacy of the structure
that has already been built and tested is assessed
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Criteria for Assessing Verification Loads (strength)
• Analysis: margins of safety must me greater that or equal to zero
• Test: Structures qualified by static or sinusoidal testing
– Test loads or stresses “as predicted” (test-verified math model and test
conditions) are compared with the total predicted loads during the
mission (including flying transients, acoustics, random vibration,
pressure, thermal effects and preloads)
• Test: Structures qualified by acoustic or random vibration testing
– Test environments are compared with random-vibration environments
derived from system-level acoustic testing
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Spacecraft Structural Dynamics & Loads (2)
• Payload-launcher Coupled Loads Analysis (CLA)
• Mechanical tests
– Modal survey test
– Sinusoidal vibration test
– Acoustic noise test
– Shock test
– Random vibration test
• Overtesting, “notching” and sine vibration testing
• Mathematical model updating and validation
• Summary and conclusive remarks
– Bibliography
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Launcher / Satellite C.L.A.
A5 / Satellite Recovered System Mode shapes
• CLA: simulation of the structural response to
low frequency mechanical environment
• Main Objective: to calculate the loads on the
satellite caused by the launch transients (liftoff, transonic, aerodynamic gust, separation of
SRBs…)
• Loads (in this context): set of internal forces,
displacements and accelerations that
characterise structural response to the applied
forces
• Effects included in the forcing functions :
thrust built-up, engine shut-down/burnout,
gravity, aerodynamic loads (gust), separation
of boosters, etc.
Mode 18: 2.93 Hz
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Mode 53: 16.9 Hz
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UPPER
COMPOSITE
Ariane-5 Dynamic Mathematical Model
PAYLOAD
– Dynamic effects up to about 100 Hz
– 3D FE models of EPC, EAP, UC
– Dynamic Reduction using Craig-Bampton formulation
– Incompressible or compressible fluids models for liquid
propellants
– Structure/fluid interaction
– Nearly incompressible SRB solid propellant modeling
– Pressure and stress effects on launcher stiffness
– SRB propellant and DIAS structural damping
– Non-linear launch table effects
EAP-
EAP+
EPC
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Sizing flight events (CLA with VEGA Launcher)
6. Z9 Ignition
5. Z23 Pressure Oscillations
4. Z23 Ignition
3. P80 Pressure Oscillations
2. Mach1/QMAX Gust
1. Lift-off (P80 Ignition and Blastwave)
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CLA Output
• LV-SC interface accelerations
– Equivalent sine spectrum
• LV-SC interface forces
– Equivalent accelerations at CoG
• Internal responses
–
–
–
–
–
Accelerations,
Displacements
Forces
Stresses
…
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Payload / STS CLA
Lift-off
Main Fitting
I/F Force
X Dir. [N]
Lift-off
Main Fitting
I/F Force
Z Dir. [N]
Lift-off
Keel Fitting
I/F Force
Y Dir. [N]
Lift-off Force Resultant in X [lbf]
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Spacecraft Structural Dynamics & Loads (2)
• Payload-launcher Coupled Loads Analysis (CLA)
• Mechanical tests
– Modal survey test
– Sinusoidal vibration test
– Acoustic noise test
– Shock test
– Random vibration test
• Overtesting, “notching” and sine vibration testing
• Mathematical model updating and validation
• Summary and conclusive remarks
– Bibliography
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Testing techniques – Introduction (1)
• Without testing, an analysis can give completely incorrect results
• Without the analysis, the tests can represent only a very limited reality
• Two types of tests according to the objectives to be reached:
– Simulation tests for structure qualification or acceptance
– Identification tests (a.k.a. analysis-validation tests) for structure
identification (the objective is to determine the dynamic characteristics of
the tested structure in order to “update” the mathematical model)
• Note: identification and simulation tests are generally completely
dissociated. In certain cases (e.g. spacecraft sine test) it is technically
possible to perform them using the same test facility
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Testing techniques – Introduction (2)
• Generation of mechanical environment
– Small shakers (with flexible rod; electrodynamic)
– Large shakers (generally used to impose motion at the base)
• Electrodynamic shaker
• Hydraulic jack shaker
– Shock machines (pyrotechnic generators and impact machines)
– Noise generators + reverberant acoustic chamber (homogeneous and
diffuse field)
• Measurements
– Force sensors, calibrated strain gauges
– Accelerometers, velocity or displacement sensors
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Classes of tests used to verify requirements (purposes)
• Development test
– Demonstrate design concepts and acquire necessary information for
design
• Qualification test
– Show a design is adequate by testing a single article
• Acceptance test
– Show a product is adequate (test each flight article)
• Analysis validation test
– Provide data which enable to confirm critical analyses or to change
(“update/validate”) mathematical models and redo analyses
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Tests for verifying mechanical requirements (purposes)
• Acoustic test
– Verify strength and structural life by introducing random vibration
through acoustic pressure (vibrating air molecules)
– Note: acoustic tests at spacecraft level are used to verify adequacy of
electrical connections and validate the random vibration environments
used to qualify components
• (Pyrotechnic) shock test
– Verify resistance to high-frequency shock waves caused by separation
explosives (introduction of high-energy vibration up to 10,000 Hz)
– System-level tests are used to verify levels used for component testing
• Random vibration test
– Verify strength and structural life by introducing random vibration
through the mechanical interface (typically up to 2000 Hz )
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Tests for verifying mechanical requirements (purposes)
• Sinusoidal vibration test
– Verify strength for structures that would not be adequately tested in
random vibration or acoustic testing
– Note 1: cyclic loads at varying frequencies are applied to excite the
structure modes of vibration
– Note 2: sinusoidal vibration testing at low levels are performed to verify
natural frequencies
– Note 3: the acquired data can be used for further processing (e.g.
experimental modal analysis)
– Note 4: this may seem like an environmental test, but it is not.
Responses are monitored and input forces are reduced as necessary
(“notching”) to make sure the target responses or member loads are
not exceeded.
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Marketed by: Eurockot
Manufactured by: Khrunichev
Actually flight qualified
Capability: 950 kg @ 500 km
Environment
Sine vibration
Acoustic
Shock
Launch site: Plesetsk
Level
Longitudinal= 1 g on [5-10] Hz
Lateral = 0.625 g on [5-100] Hz
1.5 g at 20 Hz
1 g on [40-100] Hz
31.5 Hz = 130.5 dB
63 Hz = 133.5 dB
125 Hz = 135.5 dB
250 Hz = 135.7 dB
500 Hz = 130.8 dB
1000 Hz = 126.4 dB
2000 Hz = 120.3 dB
100 Hz = 50 g
700 Hz = 800 g
1000 Hz  1500 Hz = 2000 g
4000 Hz  5000 Hz = 4000 g
10000 Hz = 2000 g
Rockot Dynamic Specification
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Modal survey test (identification test)
Purpose: provide data for dynamic mathematical model validation
Note: the normal modes are the most appropriate dynamic
characteristics for the identification of the structure
• Usually performed on structural models (SM or STM) in flight
representative configurations
• Modal parameters (natural frequencies, mode shapes, damping,
effective masses…) can be determined in two ways:
– by a method with appropriation of modes, sometimes called phase
resonance, which consists of successively isolating each mode by an
appropriate excitation and measuring its parameters directly
– by a method without appropriation of modes, sometimes called phase
separation, which consists of exciting a group of modes whose
parameters are then determined by processing the measurements
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Data consistency
Increasing effort
Different ways to get modal data from tests
• Hammer test
• Vibration test data analysis
• Dedicated FRF measurement & modal analysis
• Full scale modal survey with mode tuning
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Modal Survey Test vs. Modal Data extracted from the Sine Vibration Test
• Modal Survey:
– requires more effort (financial and time)
– provides results with higher quality
• Modal Data from Sine Vibration:
– easy access / no additional test necessary
– less quality due to negative effects from vibration
• fixtures / facility tables not indefinitely stiff
• higher sweep rate (brings along effects like beating or control instabilities)
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Ariane 5 - Sine excitation at spacecraft base (sine-equivalent
dynamics)
(
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Sine vibration for different launchers (longitudinal)
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Sine vibration for different launchers (lateral)
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Test Set-up for Satellite Vibration Tests
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Herschel on Hydra
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Acoustic test (objectives)
• Demonstrate the ability of a specimen to
withstand the acoustic environment during
launch
• Validation of analytical models
• System level tests verify equipment
qualification loads
• Acceptance test for S/C flight models
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Ariane 5 – Acoustic noise spectrum under the fairing
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Acoustic spectra for different launchers
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Shock test. Objectives and remarks
• Demonstrate the ability of a specimen to
withstand the shock loads during launch
and operation
• Verify equipment qualification loads
during system level tests
• System level shock tests are generally
performed with the actual shock
generating equipment (e.g. clamp band
release)
• or by using of a sophisticated pyroshock generating system (SHOGUN for
ARIANE 5 payloads)
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Shock response spectra for different launchers (spacecraft separation)
Note: for a consistent
comparison, data
should refer to
the same adapter.
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Shock machine (metal-metal pendulum impact machine)
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Random Vibration Test (vs. Acoustic Test)
Purpose: verify strength and structural life by introducing random
vibration through the mechanical interface
• Random Vibration
– base driven excitation
– better suited for Subsystem / Equipment tests
– limited for large shaker systems
• Acoustic
– air pressure excitation
– better suited for S/C and large Subsystems with low mass / area
density
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Random vibration test with slide table
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Random vibration test: data-processing bandwidth
• The figures show how the data-processing bandwidth can affect a
calculated power spectral density. Whether a PSD satisfies criteria
for level and tolerance depends on the frequency bandwidth used
to process the measured acceleration time history.
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Spacecraft Structural Dynamics & Loads (2)
• Payload-launcher Coupled Loads Analysis (CLA)
• Mechanical tests
– Modal survey test
– Sinusoidal vibration test
– Acoustic noise test
– Shock test
– Random vibration test
• Overtesting, “notching” and sine vibration testing
• Mathematical model updating and validation
• Summary and conclusive remarks
– Bibliography
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Overtesting:
an introduction
(vibration absorber effect)
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Introduction to overtesting and notching
• The qualification of the satellite to low
frequency transient is normally
achieved by a base-shake test
• The input spectrum specifies the
acceleration input that should excite
the satellite, for each axis
• This input is definitively different from
the mission loads, which are transient
• Notching: “Reduction of acceleration
input spectrum in narrow frequency
bands, usually where test item has
resonances” (NASA-HDBK-7004)
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GOCE on ESTEC Large Slip Table
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Herschel on ESTEC Large Slip Table
101
The overtesting problem (causes)
• Difference in boundary conditions between test and flight
configurations
– during a vibration test, the structure is excited with a specified input
acceleration that is the envelope of the flight interface acceleration,
despite the amplitude at certain frequencies drops in the flight
configuration (there is a feedback from the launcher to the spacecraft in
the main modes of the spacecraft)
• The excitation during the flight is not a steady-state sine function and
neither a sine sweep but a transient excitation with some cycles in a
few significant resonance frequencies
• The objective of notching of the specified input levels is to take into
account the real dynamic response for the different flight events. In
practice the notching simulates the antiresonances in the coupled
configuration
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Shock Response Spectrum and Equivalent Sine Input
• A shock response spectrum is a
plot of maximum “response” (e.g.
displacement, stress, acceleration)
of single degree-of-freedom
(SDOF) systems to a given input
versus some system parameter,
generally the undamped natural
frequency.
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SRS/ESI of the following transient acceleration:
ESI 
SRS
Q
ESI
ESI
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ESI for Spacecraft
CLA (Coupled Load Analysis)
Difference is negligible for small damping ratios
250
SRS
ESI 
SRS [m/s2]
200
SRS
Q
ESI 
150
100
SRS
Q2 1
SRS
50
ESI
0
0
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10
20
30
40
50
frequency [Hz]
60
70
80
105
SDOF
[m / s ]
2DOF
  0.01
natural frequency  23 Hz
[m / s
2.41
Transient response
Transient response
[s ]
[s ]
[m / s ]
1.97
  0.01
natural frequency  23 Hz
Frequency response at ESI level
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[Hz
[m / s ]
2.46
Frequency response at ESI level
106
[Hz
The effects of the sine sweep rate on the structural response
5
accelaration [m/s2]
• The acceleration enforced by the shaker
is a swept frequency function
• The sweep is amplitude modulated
• Acceleration transient response can be
significantly lower that the steady-state
frequency response
4 oct/min
0
-5
0
10
20
30
time [s]
40
50
60
2 oct/min
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Effect of sweep rate on isolated peak for increasing and decreasing
frequency sweeps
The sweep rate V has 3
effects:
• a variation (sign of V) of
the frequency of the peak:
Δf
• A decrease of the peak
amplitude: ΔA
• An increase of the peak
width (with loss of
symmetry): Δζ
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Notching
ESI
(equivalent sine)
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Sine-burst load test
• The sine-burst test is used to apply a quasi-static load to a test item in
order to strength qualify the item and its design for flight
• A secondary objective is to minimize potential fatigue damage to the
test item
• For components and subsystems, the fixture used for vibration testing
often can also be used for sine-burst strength testing. For this reason,
strength qualification and random vibration qualification can often be
performed during the same test session which saves time and money
• Since the test is intended to impart a quasi-static load to the test item,
the test frequency “must be” (in principle) below the fundamental
resonant frequency of the test item
• The sine-burst test is a cost effective alternative to either static loads
or to centrifuge testing
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“(Sine) quasi static load test” (sine burst)
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Random vibration test: notching of test specification
Illustration of notching of random vibration test specification,
at the frequencies of strong test item resonances
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Spacecraft Structural Dynamics & Loads (2)
• Payload-launcher Coupled Loads Analysis (CLA)
• Mechanical tests
– Modal survey test
– Sinusoidal vibration test
– Acoustic noise test
– Shock test
– Random vibration test
• Overtesting, “notching” and sine vibration testing
• Mathematical model updating and validation
• Summary and conclusive remarks
– Bibliography
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Validation of Finite Element Models
(with emphasis on Structural Dynamics)
“Everyone believes the test data except for the
experimentalist, and no one believes the finite
element model except for the analyst”
“All models are wrong, but some are still useful”
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Verification and Validation Definitions
(ASME Standards Committee: “V & V in Computational Solid Mechanics”)
• Verification (of codes, calculations): Process of determining that a
model implementation accurately represents the developer’s
conceptual description of the model and the solution to the model
– Math issue: “Solving the equations right”
• Validation: Process of determining the degree to which a model is
an accurate representation of the real world from the perspective of
the intended uses of the model
– Physics issue: “Solving the right equations”
Note: objective of the validation is to maximise confidence in
the predictive capability of the model
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Terminology: Correlation, Updating and Validation
• Correlation:
– the process of quantifying the degree of similarity and dissimilarity between
two models (e.g. FE analysis vs. test)
• Error Localization:
– the process of determining which areas of the model need to be modified
• Updating:
– mathematical model improvement using data obtained from an associated
experimental model (it can be “consistent” or “inconsistent”)
• Valid model :
– model which predicts the required dynamic behaviour of the subject
structure with an acceptable degree of accuracy, or “correctness”
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Some remarks on the validation of “critical analyses”
• Loads analysis is probably the single most influential task in
designing a space structure
• Loads analysis is doubly important because it is the basis for static
test loads as well as the basis for identifying the target responses
and “notching criteria” in sine tests
• A single mistake in the loads analysis can mean that we design and
test the structure to the wrong loads
• We must be very confident in our loads analysis, which means we
must check the sensitivity of our assumptions and validate the
loads analysis that will be the basis of strength analysis and static
testing
• Note: Vibro-acoustic, random and shock analyses are usually “not
critical” in the sense that we normally use environmental tests to
verify mechanical requirements
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ASME V&V Guide vs. Validation of FEM for CLA
• Reality of interest: satellite / low frequency transient environment
• Intended use of the model: launcher/satellite CLA (to predict system
behaviour for cases that will not be tested)
• Response features of interest: “CLA loads” (forces, accelerations, etc.)
• Validation testing: modal survey test or base-drive sine test
• Experimental data: accelerations (and forces) (time histories)
• Experimental features of interest: natural frequencies, mode shapes…
• Metrics: relative errors (e.g. natural frequencies), MAC, etc.
• Accuracy requirements: e.g. ECSS-E-ST-32-11
• Computational model: NASTRAN F.E. model (eigenmodes analysis)
• Validation documentation: ECSS-E-ST-32 (DRD Test/analysis
correlation)
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Targets of the correlation
(features of interest for quantitative comparison)
Characteristics that most affect the structure response to applied forces
•
•
•
•
•
•
•
•
•
•
Natural frequencies
Mode shapes
Modal effective masses
Modal damping
…
Total mass, mass distribution
Centre of Gravity, inertia
Static stiffness
Interface forces
…
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Correlation of mode shapes
• Spacehab FEM coupled to the test rig model & Silhouette
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GOCE modal analysis and survey test
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123
Cross-Orthogonality Check (COC) and Modal Assurance Criterion (MAC)
• The cross-orthogonality between the analysis and test mode
shapes with respect to the mass matrix is given by:
C 
T
mM
a
• The MAC between a measured mode and an analytical mode is
defined as:


2
T
mr as
T
T
mr mr as as

MACrs 
   
Note: COC and MAC do not give a “useful” measure of the error!

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Columbus: Cross-Orthogonality Check up to 35 Hz (target modes)
TEST
1
FEM Err.% [Hz]
2
3
4
5
6
7
8
9
10
11
12
13
-2.94 13.37
2
-0.95 15.65
3
-1.73 16.90
4
-3.26 23.03
0.93
0.35
5
-1.16 23.95
0.34
0.93
6
-2.00 24.16
7
-1.98 24.86
8
-0.12 25.56
0.86
9
-0.95 26.34
0.22
10
-2.65 26.47
11
-0.40 27.42
12
-3.65 27.82
0.82
0.27
13
-6.00 28.38
0.46
0.89
15
1.19 30.91
17
1.63 33.26
-
-4.72 34.45
20
1.21 34.99
16
17
18
19
20
1.00
1.00
0.99
0.95
33.71
19
15
13.78 15.80 17.20 23.81 24.23 24.65 25.36 25.59 26.59 27.19 27.53 28.87 30.19 30.55 32.73 33.15 33.86 34.57 35.21 36.16
1
18
14
Spacecraft Structural Dynamics & Loads - A. Calvi
0.95
0.27
0.90
0.95
0.26
0.96
0.26
0.95
0.94
0.21
0.32
0.64
0.34
0.62
0.95
0.57
0.81
125
MPLM Modal Correlation
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126
MPLM
Modal
Effective
Masses
(Final Correlation)
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127
Soho SVM – Cross-Orthogonality Check
TEST
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Err. % Freq. Hz
35.86
2.87
37.24
0.00
45.99
4.17
4.78
47.46
-3.39
49.82
0.96
53.19
56.65
2.10
58.67
60.24
3.30
64.30
66.40
67.50
68.73
69.68
71.69
72.71
3.30
73.34
74.78
75.63
78.77
82.12
7.72
84.51
5.54
86.31
88.64
7.21
89.29
5.45
94.44
97.15
99.56
F.E.M.
1
2
34.83 37.24
0.87
0.46
0.87
0.47
3
44.07
4
45.19
8
51.51
0.77
-0.33
0.24
0.76
9
52.68
10
55.46
15
62.18
21
70.92
26
77.99
29
81.53
30
82.25
31
84.42
0.87
0.22
0.75
0.21
-0.35
0.46
0.79
-0.28
-0.30
0.21
0.45
Spacecraft Structural Dynamics & Loads - A. Calvi
-0.22
-0.22
0.46
0.61
0.32
-0.43
-0.38
0.37
0.21
-0.33
0.85
-0.24
0.76
-0.23
0.87
0.64
-0.33
0.63
128
GOCE - MAC and Effective Mass
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129
Aeolus STM: comparison of transfer functions
Sine test response, FEM predicted response and post-test (updated FEM) response
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130
Lack of Matching between F.E. Model and Test
• Modelling uncertainties and errors (model is not completely physically
representative)
–
–
–
–
–
Approximation of boundary conditions
Inadequate modelling of joints and couplings
Lack or inappropriate damping representation
The linear assumption of the model versus test non-linearities
Mistakes (input errors, oversights, etc.)
• Scatter in manufacturing
– Uncertainties in physical properties (geometry, tolerances, material properties)
• Uncertainties and errors in testing
– Measured data or parameters contain levels of errors
– Uncertainties in the test set-up, input loads, boundary conditions etc.
– Mistakes (oversights, cabling errors, etc.)
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131
Test-Analysis Correlation Criteria
The degree of similarity or dissimilarity establishing that the correlation
between measured and predicted values is acceptable
ECSS-E-ST-32-11 Proposed Test / Analysis Correlation Criteria
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132
Model Updating Using Design Sensitivity and Optimisation
(traditional basic assumptions)
• Some appropriate objective functions, within design optimisation
codes, can be used to drive a F.E.M. to behave in the same
manner as the real structure portrayed by a set of numerical test
results
• The test results accurately depict the true behaviour of the structure
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133
Example of Optimisation
Find the set of design variables X that
• Minimise
  aj   mj 

E X   w g  w j 
 

j 1
mj


2
P
• Subject to bounds on the design variables X
xil  xi  xiu
where  m and  a are the test and analysis eigenvalues, P is the
number of paired modes, w j and wg are weighting factors
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134
Model updating: example of “objective functions”
Natural Frequency:
f f
df  a e
fe
d 
Mode Shape:
a  e
e
~
Effective Transmissibilities:
Effective Masses:
~ 
dM
(: modal scale factor)
~
T T
~  a~ e
dT
Te
~
~
Ma  Me
~
Me
Objective Function
F  bT W b
with
 df 
d 

b 
 d~ 
 T
~
dM 
Spacecraft Structural Dynamics & Loads - A. Calvi
and
w f

W





w

~

wT

~
wM

135
Location of Modelling Errors and Selection of the Design
Variables Based on Sensitivity Analysis
Criterion (selection of design variables):
The design variables should be selected for those elements or element groups
which have an influence on the eigenfrequencies and mode shapes which are
targeted during the correlation/updating process (in addition to analyst’s knowledge
of uncertain modelled regions of the structure and/or results of other error
localisation analyses)
Two basic approaches are possible:
• Initial model sensitivities (e.g. initial derivative approach)
• “A Posteriori” Approach (at the end of a preliminary optimisation process)
Criterion (error localisation):
To determine how effective certain physical properties changes might be in reducing
the difference between measured and calculated data (however high sensitivity is
not generally a sufficient reason for the selection of a candidate parameter!)
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136
Limitations of the “sensitivity and optimisation” approach
• Largest changes can be in the most sensitive parameters rather
than those in error (→ inconsistent updating and misleading error
localization)
• Errors of insensitive regions cannot be detected
• The success of the updating procedure can strongly depend on the
selection of the design parameters to be updated (it could be
necessary to consider several sets of design parameters to detect
erroneous regions of the structure)
• The approach could be “short-sighted” (possible convergence to
local minima)
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137
Exercise
• Calculate natural frequencies and mode
shapes of the 2-DOF satellite represented
in the figure
• Consider a perturbed model, representing
the real (tested) structure, having
– k1= 60 E5 N/m
– k2= 130 E5 N/m
• Calculate natural frequencies and mode
shapes for the perturbed (test) model
• Correlate the 2 models, i.e. calculate:
– Natural frequency deviations
– Mode shapes cross-orthogonality check
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138
Solutions of the exercise
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139
Exercise… part 2
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140
Summary and Conclusive Remarks
• The role of structural dynamics in a space project
• Dynamic analysis types
• The effective mass concept
• Design load cycles & verification loads cycle
• Payload-launcher Coupled Loads Analysis
• Mechanical tests
• Overtesting & “notching”
• Mathematical model updating and validation
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141
Bibliography
• Sarafin T.P. Spacecraft Structures and Mechanisms, Kluwer, 1995
• Craig R.R., Structural Dynamics – An introduction to computer methods, J. Wiley
and Sons, 1981
• Clough R.W., Penzien J., Dynamics of Structures, McGraw-Hill, 1993
• Ewins D.J., Modal Testing – Theory, practice and applications, Research Studies
Press, Second Edition, 2000
• Wijker J., Mechanical Vibrations in Spacecraft Design, Springer, 2004
• Girard A., Roy N., Structural Dynamics in Industry, J. Wiley and Sons, 2008
• Steinberg D.S., Vibration Analysis for Electronic Equipment, J. Wiley and Sons,
2000
• Friswell M.I., Mottershead J.E., Finite Element Model Updating in Structural
Dynamics, Kluwer 1995
• Ariane 5 User’s Manual, Arianespace, http://www.arianespace.com/
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Bibliography - ECSS Documents
• ECSS-E-ST-32
• ECSS-E-ST-32-03
• ECSS-E-ST-32-10
• ECSS-E-ST-32-11
• ECSS-E-ST-32-01
Space Project Engineering - Structural
Structural finite element models
Structural factors of safety for spaceflight
hardware
Structural design and verification of
pressurized hardware
Modal survey assessment
Fracture control
• ECSS-E-10-02
• ECSS-E-10-03
Space Engineering - Verification
Space Engineering - Testing
• ECSS-E-ST-32-02
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THE END!
Acknowledgements:
ALENIA SPAZIO, Italy, for the data concerning the projects GOCE, COLUMBUS,
MPLM and SOHO
EADS ASTRIUM, UK, for the data concerning the project AEOLUS and
EarthCARE
ESA/ESTEC, Structures Section, NL, for the data concerning ARIANE 5 FE
model and LV/SC CLA
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