Experimentele Modale Analyse

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Presentation transcript:

Experimentele Modale Analyse LES 1 – THEORETISCHE INLEIDING Patrick Guillaume E-mail: patrick.guillaume@vub.ac.be Tel.: 02/6293566 4/6/2019 EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

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” EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Frequency Response of MDOF System EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

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) x(t) f(t) EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Poles of SDOF System Poles : Generalized eigenvalue problem EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

The SDOF Modal-Parameter Model Pole p Re - Decay rate Im - Modal frequency Residue R Strength of the mode EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Poles and Residues Amplitude of mode is not given by the residue alone Hi-Fi turntable Car Same pole Different residues EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Basic Equations for a 2-DOF System Forces acting on mass 1 Sum forces = 0 x1(t) x2(t) f1(t) f2(t) m2 k1 c1 m1 c2 k2 EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Basic Equations for a 2-DOF System Time domain Frequency domain (Laplace) Matrix notations Dynamic stiffness matrix Transfer function matrix EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

FRF of 2-DOF System f2(t) m2 x2(t) f1(t) k2 c2 m1 x1(t) k1 c1 0° -180° -360° EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Multiple Degree of Freedom (MDOF) Dynamic stiffness matrix Transfer function matrix EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

FREQUENCY RESPONSE FUNCTION IMPULSE RESPONSE FUNCTION Poles of MDOF System Poles: FREQUENCY RESPONSE FUNCTION IMPULSE RESPONSE FUNCTION EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Eigenvalues and Eigenvectors No Damping EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Weighted Orthogonality of Modal Vectors Pre-multiply with Transpose the equation EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Weighted Orthogonality of Modal Vectors Substracting From eq. 1: (eq. 1) EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Modal Mass and Stiffness No Damping Modal mass and stiffness are not unique ! EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Modal Coordinates EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Modal Model EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Modal Decomposition IRF FRF EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Scaling of the Mode Shapes EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Proportional Damping Eigenvalues EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Proportional Damping Complex system poles and normal modal vectors Modal mass, stiffness and damping EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

General Viscous Damping EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

General Viscous Damping Eigenvalues and vectors Complex system poles and complex modal vectors Orthogonality EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

General Viscous Damping Poles: FREQUENCY RESPONSE FUNCTION IMPULSE RESPONSE FUNCTION EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

General Viscous Damping EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Operational Deflection Shapes (ODS) Resonant frequencies (peaks) Mode shapes (ODS) EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Operational Deflection Shapes (ODS) Uncoupled modes (SDOF) EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

Operational Deflection Shapes (ODS) Coupled modes + = EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

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 EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

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 EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005

MatLab Oefening modal_model.m SDOF MDOF Eigenwaarden en vectoren Schaling van de eigenvectoren EXPERIMENTELE MODALE ANALYSIS, LES 1, 2005