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On the natural vibrations of linear structures with constraints

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Author

Summary, in English

The undamped natural vibrations of a constrained linear structure are given by the solutions to a generalized eigenvalue problem derived from the equations of motion for the constrained system involving Lagrangian multipliers. The eigenvalue problem derived is defined by the mass matrix of the unconstrained structure and a non-symmetric and singular stiffness matrix for the constrained system. The character of the solution of the eigenvalue problem of the constrained system is stated and proved in a Theorem. Applications of the constrained eigenvalue problem to some simple structures are demonstrated. Finally a condition for the calculation of the damped natural vibrations for the constrained structure in terms of the undamped mode shapes is formulated. (c) 2006 Elsevier Ltd. All rights reserved.

Department/s

Publishing year

2007

Language

English

Pages

341-354

Publication/Series

Journal of Sound and Vibration

Volume

301

Issue

1-2

Document type

Journal article

Publisher

Elsevier

Topic

  • Applied Mechanics

Status

Published

ISBN/ISSN/Other

  • ISSN: 0022-460X