Inverse Problems in Vibration

1986 ◽  
Vol 39 (7) ◽  
pp. 1013-1018 ◽  
Author(s):  
Graham M. L. Gladwell
Keyword(s):  
Inverse Problems ◽  
Eigenvalue Problems ◽  
Discrete Systems ◽  
Free Vibrations ◽  
Continuous Systems ◽  
Thin Beam ◽  
Inverse Eigenvalue Problems ◽  
Elastic Systems ◽  
Inverse Eigenvalue ◽  
Sturm Liouville

This article concerns infinitesimal free vibrations of undamped elastic systems of finite extent. A review is made of the literature relating to the unique reconstruction of a vibrating system from natural frequency data. The literature is divided into two groups—those papers concerning discrete systems, for which the inverse problems are closely related to matrix inverse eigenvalue problems, and those concerning continuous systems governed either by one or the other of the Sturm–Liouville equations or by the Euler–Bernoulli equation for flexural vibrations of a thin beam.

scholarly journals Inverse Eigenvalue Problems for Singular Rank One Perturbations of a Sturm-Liouville Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Xuewen Wu
Keyword(s):  
Eigenvalue Problem ◽  
Potential Function ◽  
Liouville Operator ◽  
Eigenvalue Problems ◽  
Inverse Eigenvalue Problem ◽  
Inverse Eigenvalue Problems ◽  
Rank One ◽  
Inverse Eigenvalue ◽  
Sturm Liouville

This paper is concerned with the inverse eigenvalue problem for singular rank one perturbations of a Sturm-Liouville operator. We determine uniquely the potential function from the spectra of the Sturm-Liouville operator and its rank one perturbations.

scholarly journals A Generalized Inexact Newton Method for Inverse Eigenvalue Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Weiping Shen
Keyword(s):  
Newton Method ◽  
Quadratic Convergence ◽  
Eigenvalue Problems ◽  
Generalized Newton Method ◽  
Inexact Newton Method ◽  
Numerical Tests ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue ◽  
Generalized Newton ◽  
Special Case

We propose a generalized inexact Newton method for solving the inverse eigenvalue problems, which includes the generalized Newton method as a special case. Under the nonsingularity assumption of the Jacobian matrices at the solutionc*, a convergence analysis covering both the distinct and multiple eigenvalue cases is provided and the quadratic convergence property is proved. Moreover, numerical tests are given in the last section and comparisons with the generalized Newton method are made.

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