Nonlinear Vibrations of Aerospace Structures A Second Test Case: an F-16 Fighter Aircraft F16...

download Nonlinear Vibrations of Aerospace Structures A Second Test Case: an F-16 Fighter Aircraft F16 aircraft,

of 53

  • date post

    09-Aug-2020
  • Category

    Documents

  • view

    0
  • download

    0

Embed Size (px)

Transcript of Nonlinear Vibrations of Aerospace Structures A Second Test Case: an F-16 Fighter Aircraft F16...

  • Nonlinear Vibrations of

    Aerospace Structures

    Jean-Philippe NoΓ«l | jp.noel@uliege.be 22 October 2018

    Detecting Nonlinearity

    Lecture

  • 2

    System Identification in Structural Dynamics?

    Construction of an accurate mathematical model of the dynamics

    of a real structure based on input and output measurements.

    𝑦 = β„±(𝑒) β„± is a dynamic input-

    output mapping

    Input

    𝑒(𝑑)

    Output

    𝑦(𝑑)

  • 3

    System Identification: 3 Basis Ingredients and User-choices

    Data + Model + Distance

    𝑦 = β„±(𝑒) β„± is a dynamic input-

    output mapping

    Input

    𝑒(𝑑)

    Output

    𝑦(𝑑)

  • 4

    Linear System Identification (= Modal Analysis) Is Mature

    AIRBUS A350XWB Govers et al., ISMA 2014.

    Theoretical modal

    analysis for design

    Experimental modal

    analysis for certification

    (eigenvalue solver in all

    commercial FE packages).

    (stochastic subspace

    identification, PolyMAX, …).

  • 5

    But Every Modern Mechanical System Is Nonlinear …

    Force amplitude (N)

    0 5 10 15 20 25 30

    0.58

    0.55

    0.56

    0.57

    5

    2

    3

    4

    Natural

    freq. (Hz)

    Damping

    ratio (%)

    > 5 % shift

    > 180 % shift

    A350 ground vibration testing, Spring 2013,

    Suspected nonlinearity sources:

    clearance in actuators, wing slenderness,

    engine mounts, fuselage composite, …

    β€œLinearity” plot!

  • 6

    An example from SONACA: the Piccolo tube.

    Stress underestimated by more than to 200 % led to cracks in a weld.

    … and FE Models Fail to Capture Most Nonlinearities

    Forcing frequency (Hz)

    1e-1

    100 1000

    Stress Power Spectral

    Density (daN/mmΒ²/Hz)

    1e-3

    1e-5

    1e-7

    Experimental test

    Nonlinear FEM in

    Samcef Mecano

    Linear FEM

    10

  • 7

    … and Commercial Testing Software Fail to Identify Them

    FRF (dB)

    Frequency (Hz)

    6.6

    F16 Fighter Peeters et al., IMAC 2011.

    7

    2 poles around

    1 nonlinear mode

    6.8 7.2

  • 8

    NSI in the Design Cycle of Eng. Structures = Troubleshooting!

    MEASURE MODELIDENTIFY UNDERSTD

    UNCOVER DESIGN

    Computer-aided

    modelling (FEM, …)

  • 9

    Where Do We Stand?

    1980s 1990s 2000s Today

    First analyses of

    SDOF systems.

    MDOF systems and

    continuous structures with

    localised nonlinearities.

    Real-life structures

    with strong nonlinearities,

    nonlinear modal analysis,

    numerical model updating.

  • 10

    Outline of this Lecture

    What are the challenges in nonlinear system identification?

    How to build a nonlinear experimental model?

    Nonlinearity detection in sine conditions: SmallSat spacecraft.

    Nonlinearity detection in broadband conditions: F-16 aircraft.

  • 11

    Outline of this Lecture

    What are the challenges in nonlinear system identification?

    How to build a nonlinear experimental model?

    Nonlinearity detection in sine conditions: SmallSat spacecraft.

    Nonlinearity detection in broadband conditions: F-16 aircraft.

  • 12

    Why Is Nonlinear System Identification Difficult?

    Challenge #1: Sensitivity to the type of input signal.

    Distorted resonance

    under random excitation.

    Distorted resonance

    under sine excitation.

    Time (s) Frequency (Hz)

    Amplitude (m) Amplitude (dB)

  • 13

    Why Is Nonlinear System Identification Difficult?

    Challenge #2: Specific and demanding test campaigns.

    Increase the sampling frequency.

    Record throughput time histories.

    Measure the force signal.

    Instrument potential nonlinearities with sensors on both sides.

    Consider multiple levels of excitations/types of excitations.

    Study multiple sets of initial conditions, and reverse the sweep.

  • 14

    Why Is Nonlinear System Identification Difficult?

    Challenge #3: Inapplicability of linear concepts.

    FRFs are not invariant.Modal properties are not invariant.

    Energy (J) Frequency (Hz)

    Frequency (Hz) Amplitude (dB)

  • 15

    Why Is Nonlinear System Identification Difficult?

    Challenge #4a: Individualistic nature of structural nonlinearities.

    Disp.

    Disp.

    Vel.

    Disp.R e

    s t.

    f o

    rc e

    R e

    s t.

    f o

    rc e

    R e

    s t.

    f o

    rc e

    R e

    s t.

    f o

    rc e

  • 16

    Why Is Nonlinear System Identification Difficult?

    Challenge #4b: Limited amount of prior knowledge.

    𝑀 αˆ·π‘ž + 𝐢𝑣 αˆΆπ‘ž + 𝐾 π‘ž + 𝑔(π‘ž, αˆΆπ‘ž) = 𝑝

    Determining nonlinear functional forms is an integral part of

    nonlinear system identification (and arguably the most difficult).

    ?

  • 17

    Why Is Nonlinear System Identification Difficult?

    Challenge #5: True system may be (is!) outside the model class.

    Selected model class

    Tested system

  • 18

    Outline of this Lecture

    What are the challenges in nonlinear system identification?

    How to build a nonlinear experimental model?

    Nonlinearity detection in sine conditions: SmallSat spacecraft.

    Nonlinearity detection in broadband conditions: F-16 aircraft.

  • 19

    Three-Step NL System ID Process in Structural Dynamics

    Do I observe nonlinear effects? Yes.

    Should I build a nonlinear model? Yes.

    3

    2

    1

    Detection

    Characterisation

    Estimation

    Information

    vs. complexity

    Where is the nonlinearity located? At the joint.

    What is the underlying physics? Dry friction.

    How to model its effects? 𝑓𝑛𝑙 π‘ž, αˆΆπ‘ž = 𝑐 𝑠𝑖𝑔𝑛 αˆΆπ‘ž .

    Model parameters?

    How uncertain are they?

    𝑐 = 5.47.

    𝑐 = 𝒩(5.47,1).

  • 20

    Nonlinearity Detection

    Evidence nonlinear behaviour in experimental data.

    This is not particularly challenging:

    This is crucial:

    A wide variety of techniques exists in the literature.

    Sine and broadband excitations can be addressed.

    A single excitation level is generally sufficient.

    Detection supports an important decision as building a nonlinear model

    demands more time, capabilities and efforts than a linear model.

  • 21

    Nonlinearity Characterisation

    Infer a suitable nonlinearity model from experimental data.

    This is challenging:

    This is crucial:

    Prior knowledge is most often very limited.

    Physical mechanisms resulting in nonlinearity are extremely diverse.

    Nonlinearity may translate into a plethora of dynamic phenomena.

    The success of the parameter estimation step is conditional upon an

    accurate characterisation of all observed nonlinearities.

  • 22

    Nonlinear Parameter Estimation

    Fit a mathematical model to experimental data.

    This is challenging:

    This is crucial:

    If characterisation was not successfully completed.

    If nonlinearities were not instrumented.

    If the input signals were not measured.

    Quantitative models are required to carry out response prediction,

    numerical model updating and validation, design optimisation, …

  • 23

    Outline of this Lecture

    What are the challenges in nonlinear system identification?

    How to build a nonlinear experimental model?

    Nonlinearity detection in sine conditions: SmallSat spacecraft.

    Nonlinearity detection in broadband conditions: F-16 aircraft.

  • 24

    A First Test Case: the SmallSat Spacecraft from Airbus DS

    NL WEMS device

    Challenges:

    β–Ί Nonsmooth nonlinearities

    β–Ί High damping

    β–Ί Gravity-induced asymmetry

    β–Ί Viscoelastic components

  • 25

    WEMS Device: Piecewise-linear Behaviour

    Elastomer plots

    Isolation and

    protection device.

    Mechanical stops

    Experimental

    stiffness curve.

    Displacement

    R e s to

    ri n g f

    o rc

    e

  • 26

    A β€œGood” Excitation: the Sine-sweep Signal

    Linear sine sweep:

    𝑒(𝑑) = 𝐴 𝑠𝑖𝑛 2πœ‹π‘“0 𝑑 βˆ’ 𝑑0 + 2πœ‹ π‘Ÿ

    2 𝑑 βˆ’ 𝑑0

    2 + πœ‘0

    Time (s) Time (s)

    Force (N) Forcing frequency (Hz)

  • 27

    A β€œGood” Excitation: the Sine-sweep Signal

    Linear sine sweep:

    Fully deterministic signal, so easy to interpret data visually.

    Strongly activates nonlinearities, as energy is concentrated.

    Very useful in nonlinearity characterisation.

    Logarithmic sweep may be used to focus on low frequencies.

    𝑒(𝑑) = 𝐴 𝑠𝑖𝑛 2πœ‹π‘“0