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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Main Author: Gladwell, G.M.L.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1986, 1986
Edition:1st ed. 1986
Series:Mechanics: Dynamical Systems
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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100 1 |a Gladwell, G.M.L. 
245 0 0 |a Inverse problems in vibration  |h Elektronische Ressource  |c by G.M.L. Gladwell 
250 |a 1st ed. 1986 
260 |a Dordrecht  |b Springer Netherlands  |c 1986, 1986 
300 |a 284 p  |b online resource 
505 0 |a 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 --  
505 0 |a 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 --  
505 0 |a 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 --  
505 0 |a 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 
653 |a Mathematical analysis 
653 |a Classical Mechanics 
653 |a Vibration 
653 |a Vibration, Dynamical Systems, Control 
653 |a Analysis (Mathematics) 
653 |a Mechanics 
653 |a Dynamical systems 
653 |a Analysis 
653 |a Dynamics 
710 2 |a SpringerLink (Online service) 
041 0 7 |a eng  |2 ISO 639-2 
989 |b SBA  |a Springer Book Archives -2004 
490 0 |a Mechanics: Dynamical Systems 
856 |u https://doi.org/10.1007/978-94-015-1178-0?nosfx=y  |x Verlag  |3 Volltext 
082 0 |a 620 
520 |a 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 theory is the determination of the natural frequencies (eigen­ frequencies or simply eigenvalues) and normal modes of the vibrating body. A body which is modelled as a discrete system' of rigid masses, rigid rods, massless springs, etc. , will be governed by an ordinary matrix differential equation in time t. It will have a finite number of eigenvalues, and the normal modes will be vectors, called eigenvectors. A body which is modelled as a continuous system will be governed by a partial differential equation in time and one or more spatial variables. It will have an infinite number of eigenvalues, and the normal modes will be functions (eigen­ functions) of the space variables. In the context of this classical theory, inverse problems are concerned with the construction of a model of a given type; e. g. , a mass-spring system, a string, etc. , which has given eigenvalues and/or eigenvectors or eigenfunctions; i. e. , given spec­ tral data. In general, if some such spectral data is given, there can be no system, a unique system, or many systems, having these properties