Inverse problems in vibration
The last thing one settles in writing a book is what one should put in first. Pascal's Pensees Classical vibration theory is concerned, in large part, with the infinitesimal (i. e. , linear) undamped free vibration of various discrete or continuous bodies. One of the basic problems in this theo...
Main Author: | |
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Format: | eBook |
Language: | English |
Published: |
Dordrecht
Springer Netherlands
1986, 1986
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Edition: | 1st ed. 1986 |
Series: | Mechanics: Dynamical Systems
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Subjects: | |
Online Access: | |
Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 — Elementary Matrix Analysis
- 1.1 Introduction
- 1.2 Basic definitions and notations
- 1.3 Matrix inversion and determinants
- 1.4 Eigenvalues and eigenvectors
- 2 — Vibration of Discrete Systems
- 2.1 Introduction
- 2.2 Vibration of some simple systems
- 2.3 Transverse vibration of a beam
- 2.4 Generalized coordinates and Lagrange’s equations
- 2.5 Natural frequencies and normal modes
- 2.6 Principal coordinates and receptances
- 2.7 Rayleigh’s Principle
- 2.8 Vibration under constraint
- 2.9 Iterative and independent definitions of eigenvalues
- 3 — Jacobian Matrices
- 3.1 Sturm sequences
- 3.2 Orthogonal polynomials
- 3.3 Eigenvectors of Jacobian matrices
- 4 — Inversion of Discrete Second-Order Systems
- 4.1 Introduction
- 4.2 An inverse problem for a Jacobian matrix
- 4.3 Variants of the inverse problem for a Jacobian matrix
- 4.4 Inverse eigenvalue problems for spring-mass system
- 5 — Further Properties of Matrices
- 8 — Green’s Functions and Integral Equations
- 8.1 Introduction
- 8.2 Sturm-Liouville systems
- 8.3 Green’s functions
- 8.4 Symmetric kernels and their eigenvalues
- 8.5 Oscillatory properties of Sturm-Liouville kernels
- 8.6 Completeness
- 8.7 Nodes and zeros
- 8.8 Oscillatory systems of functions
- 8.9 Perron’s theorem and associated kernels
- 8.10 The interlacing of eigenvalues
- 8.11 Asymptotic behaviour of eigenvalues and eigenfunctions
- 8.12 Impulse responses
- 9 — Inversion of Continuous Second-Order Systems
- 9.1 Introduction
- 9.2 A historical overview
- 9.3 The reconstruction procedure
- 9.4 The Gel’fand-Levitan integral equation
- 9.5 Reconstruction of the differential equation
- 9.6 The inverse problem for the vibrating rod
- 9.7 Reconstruction from the impulse response
- 10 — The Euler-Bernoulli Beam
- 10.1 Introduction
- 10.2 Oscillatory properties of Euler-BernouUi kernels
- 10.3 The eigenfunctions of the cantilever beam
- 10.4 The spectra of the beam
- 10.5 Statement of the inverse problem
- 10.6 The reconstruction procedure
- 10.7 The positivity of matrix P is sufficient
- 10.8 Determination of feasible data
- 5.1 Introduction
- 5.2 Minors
- 5.3 Further properties of symmetric matrices
- 5.4 Perron’s theorem and associated matrices
- 5.5 Oscillatory matrices
- 5.6 Oscillatory systems of vectors
- 5.7 Eigenvalues of oscillatory matrices
- 5.8 u-Line analysis
- 6 — Some Applications of the Theory of Oscillatory Matrices
- 6.1 The inverse mode problem for a Jacobian matrix
- 6.2 The inverse problem for a single mode of a spring-mass system
- 6.3 The reconstruction of a spring-mass system from two modes
- 6.4 A note on the matrices appearing in a finite element model of a rod
- 7 — The Inverse Problem for the Discrete Vibrating Beam
- 7.1 Introduction
- 7.2 The eigenanalysis of the clamped-free beam
- 7.3 The forced response of the beam
- 7.4 The spectra of the beam
- 7.5 Conditions of the data
- 7.6 Inversion by using orthogonality.-7.7 The block-Lanczos algorithm
- 7.8 A numerical procedure for the beam inverse problem