33 Structural Dynamic Modification and Sensitivity Analysis

Back

Su Huan Chen

Jilin University

33.1 Introduction ........................................................................ 33-2

33.2 Structural Dynamic Modification of Finite

Element Model .................................................................... 33-2

33.3 Perturbation Method of Vibration Modes ....................... 33-4

First-Order Perturbation of Distinct Modes † Second-Order

Perturbation of Distinct Modes † Numerical Examples

33.4 Design Sensitivity Analysis of Structural

Vibration Modes ................................................................. 33-8

Direct Differential Method for Sensitivity Analysis †

Perturbation Sensitivity Analysis † Numerical

Example † Concluding Remarks

33.5 High-Accuracy Modal Superposition for Sensitivity

Analysis of Modes ............................................................... 33-11

Method One † Method Two

33.6 Sensitivity of Eigenvectors for Free – Free

Structures ............................................................................. 33-13

33.7 Matrix Perturbation Theory for Repeated Modes ........... 33-14

Basic Equations † The First-Order Perturbation of

Eigensolutions † High-Accuracy Modal Superposition for

the First-Order Perturbation of Repeated Modes

33.8 Matrix Perturbation Method for Closely Spaced

Eigenvalues .......................................................................... 33-16

Method One of Perturbation Analysis for Close Eigenvalues †

Method Two of Perturbation Analysis for Close Eigenvalues †

Concluding Remarks

33.9 Matrix Perturbation Theory for Complex Modes ........... 33-22

Basic Equations † Matrix Perturbation Method for Distinct

Modes † High-Accuracy Modal Superposition for Eigenvector

Derivatives † Matrix Perturbation for Repeated Eigenvalues

of Nondefective Systems † Matrix Perturbation for Close

Eigenvalues of Unsymmetric Matrices

Summary

The matrix perturbation theory for structural dynamic modification and sensitivity analysis is presented in this

chapter. The theory covers a broad spectrum of subjects, specifically, matrix perturbation of real modes of complex

structures and matrix perturbation of complex modes. The contents include nine sections. Section 33.2 provides the

preliminaries to matrix perturbation and sensitivity analysis. Section 33.3 presents the matrix perturbation

method including first-order and second-order perturbation. Section 33.4 presents methods for design sensitivity

33-1

© 2005 by Taylor & Francis Group, LLC

analysis. In Section 33.5, high-accuracy modal superposition for sensitivity analysis of modes is given. Section 33.6

presents the sensitivity analysis of eigenvectors for free – free structures. In Section 33.7 and Section 33.8, matrix

perturbations for repeated modes and closely spaced modes are discussed. In Section 33.9, the matrix perturbation

approach for complex modes is presented.

Навигация