HMSC chap2

Modeling Components

• Study of Load model,Component model
• Useful in
  • assessing the change in component response when components are damaged
  • predicting the response of component to loads
• Models : Raw data -> information of health of component
• Two kinds
  • Physical law(Physics based)
  • Measurement data(Data-driven)
• Inertia, damping,, stiffness are included in these dynamic models
• Nonlinear damping and stiffness restoring forces are common
• Free vibration response : sum of the modes of vibration
• mode of vibration : natural frequency + mode shape
• Impulsive(transient) type of exitation excite the free vibration response
• Damage nearly always behave in a nonlinear manner
• Matlab can be used to analyze dynamic response and Simulink can be used to simulate dynamic response of onlinear system.2

  Vibration Model

• describe the dynamic response of structural components to dynamic loads
• Resonant frequencies,, mode shapes = Free response
  • Free response whanges with damage

    Lumped parameter/Continuous model

• model Vibration and wave propagation
• Vibration : standing wave pattern setup by interference between propagating waves
  • Lumped parameter model
    • ordinary differential equation
  • Continuous model
    • partial differential equation

Frequency response functions(FRFs)

• Ratio between the response exitation as a function of frequency
• Describe relative amplitude and phrase of the dynamic response with respect to excitation forcing amplitude and phase
• can combined with impedance model for different configurations to describe dynamic response of the combined system

Wave equation

• Describes the propagation of elastic waves
• Used to identify damage due to change in speed of propagation
• Separation of variablesmethod decomposes the solution of the wave equation into temporal and spatial pieces
• speed of sound is function of modulus and density
  • Equal to the product of frequency in Hz and wavelength
• Wave number is the ratio of requency to speed of sound
  • Represents of spatial frequency
• Group velocity can be get by differentiating the frequency with respect to wave number
  • Describes the speed of a group of waves in a certain frequency bandwith
• Smaller defect detection : Wavelength is small, frequency is high
  • Smaller wavelengths also results in more relfections from rough surfaces and boundaries
• Dispersion : occurs when the propagation energy of a wave front decreases due to motions in other directions
  • Causes the wave front to change shape. Because higher frequencies travel faster than low frequencies
  • Makes it more difficult to identify damage.

Finite elemnt models(FEMs)

• Used to model structure components with discontinuous mass, damping and stiffness properties due to damage or variations in the healthy structural component and geometrical parameters.

Direct parameter models

• Used to estimate mass, damping ,and stiffness parameters from the measured exitation and response data
• Estimated using least squares solution techniques

  Restoring force models

• Relate the internal forces within a component due to stiffness and damping to mass $\times$ acceleration of the components
• Acceleration is used to construct models, Restoring force projections are obtainedㅁㄴㅇㄻㄴㅇㄻㄴㅇㄻㄴㅇㄹ
• Phase-plane trajectories relating the velocity to the displacement response of a components are also useful model for health monitoring

Discrete time models(difference equation models)

• Model can be estimated from the measurement data
• Advantageous for all response variables are not needed to estimated the parameters.

  Experimental frequency response models(embedded sensitivity functions

• Can be utilized to estimated the change in frequency response function with changes to the mass, damping or stiffness parameters without requiring the starting values of these parameters
• Change in the parameters can be estimated

  Virtual force models

• Describe the damged components as a sum of the healthy structural components and forces applied locally to represent the damage.

  Experimental modal vibration models

• can be developed from measured data using various modal parameter estimation methods

  Load models

• Different mechanical exitations : exercise component and damage differently
  • Impulses
  • Narrow band cyclic
  • Broadband random
• Load due to other environmental factors : also important to consider in health monitoring
  • Acoustic pressure
  • Temperature