Experimentele Modale Analyse

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Experimentele Modale Analyse

• LES 1 THEORETISCHE INLEIDING

Patrick Guillaume E-mail patrick.guillaume_at_vub.
ac.be Tel. [phone]
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Overzicht cursus

• Theoretische basisbegrippen
• Meettechnieken
• Niet-parametrische schattingen
• Parametrische schattingen
• Toepassingen
• Gevoeligheidsanalyse
• FE Model updating
• Substructuring
• Operationele modale analyse
• Structural Health Monitoring
• Flight Flutter Testing

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Frequency Response of MDOF System
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Basic Equations of Motion for SDOF System

• Time domain
• Frequency domain (Laplace)
• Dynamic Stiffness Z(s) ? (static) stiffness k
• Transfer function
• Frequency response function (FRF)

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Poles of SDOF System

• Poles
• Generalized eigenvalue problem

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The SDOF Modal-Parameter Model

• Pole p
• Re - Decay rate
• Im - Modal frequency
• Residue R
• Strength of the mode

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Poles and Residues

• Amplitude of mode is not given by the residue
  alone
• Hi-Fi turntable
• Car
• Same pole
• Different residues

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Basic Equations for a 2-DOF System

• Forces acting on mass 1
• Sum forces 0

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Basic Equations for a 2-DOF System

• Time domain
• Frequency domain (Laplace)
• Matrix notations
• Dynamic stiffness matrix
• Transfer function matrix

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FRF of 2-DOF System
0
-180
-360
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Multiple Degree of Freedom (MDOF)

• Dynamic stiffness matrix
• Transfer function matrix

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Poles of MDOF System

• Poles

IMPULSE RESPONSE FUNCTION
FREQUENCY RESPONSE FUNCTION
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Eigenvalues and Eigenvectors

• No Damping

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Weighted Orthogonality of Modal Vectors

• Pre-multiply with
• Transpose the equation

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Weighted Orthogonality of Modal Vectors

• Substracting
• From eq. 1

(eq. 1)
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Modal Mass and Stiffness

• No Damping
• Modal mass and stiffness are not unique !

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Modal Coordinates
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Modal Model
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Modal Decomposition
FRF
IRF
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Scaling of the Mode Shapes
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Proportional Damping

• Eigenvalues

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Proportional Damping

• Complex system poles and normal modal vectors
• Modal mass, stiffness and damping

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General Viscous Damping
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General Viscous Damping

• Eigenvalues and vectors
• Complex system poles and complex modal vectors
• Orthogonality

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General Viscous Damping

• Poles

IMPULSE RESPONSE FUNCTION
FREQUENCY RESPONSE FUNCTION
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General Viscous Damping
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Operational Deflection Shapes (ODS)

• Resonant frequencies (peaks)
• Mode shapes (ODS)

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Operational Deflection Shapes (ODS)

• Uncoupled modes (SDOF)

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Operational Deflection Shapes (ODS)

• Coupled modes

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Force Appropriation Method

• Also called
• Normal Mode Testing
• Phase Resonance Testing
• Traditionally used for Ground Vibration Testing
  (GVT) of airplanes (large structures)
• First method to use multiple inputs
• Find (mono-phased) forced vector to obtain a
  (mono-phased) response vector with a 90 degree
  phase

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Force Appropriation Method

• Real/imaginary part
• Find (mono-phased) forced vector to obtain a
  (mono-phased) response vector with a 90 degree
  phase
• Verification of normal mode tuning by turning off
  the excitations

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MatLab Oefening

• modal_model.m
• SDOF
• MDOF
• Eigenwaarden en vectoren
• Schaling van de eigenvectoren