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...
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Format:  eBook 
Language:  English 
Published: 
Dordrecht
Springer Netherlands
1986, 1986

Edition:  1st ed. 1986 
Series:  Mechanics: Dynamical Systems

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Online Access:  
Collection:  Springer Book Archives 2004  Collection details see MPG.ReNa 
Table of Contents:
 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 uLine 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 springmass system
 6.3 The reconstruction of a springmass 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 clampedfree 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 blockLanczos algorithm
 7.8 A numerical procedure for the beam inverse problem
 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 SecondOrder 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 springmass system
 5 — Further Properties of Matrices
 8 — Green’s Functions and Integral Equations
 8.1 Introduction
 8.2 SturmLiouville systems
 8.3 Green’s functions
 8.4 Symmetric kernels and their eigenvalues
 8.5 Oscillatory properties of SturmLiouville 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 SecondOrder Systems
 9.1 Introduction
 9.2 A historical overview
 9.3 The reconstruction procedure
 9.4 The Gel’fandLevitan 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 EulerBernoulli Beam
 10.1 Introduction
 10.2 Oscillatory properties of EulerBernouUi 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