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PERTURBATION METHOD FOR DETERMINING EIGENSOLUTIONS OF WEAKLY DAMPED SYSTEMS

โœ Scribed by J. Tang; W.L. Wang

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
474 KB
Volume
187
Category
Article
ISSN
0022-460X

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โœฆ Synopsis

A perturbation method is developed for computation of eigensolutions of weakly damped systems. The eigenvalues and eigenvectors of the corresponding undamped system are regarded as the zero order approximations of the damped eigensolutions, while the damping effect is obtained by the higher order modifications. Based upon strict mathematical derivations, a complete set of equations governing the higher order unknowns of the damped eigensolution is established. Unlike other algorithms, the present method can deal with the case in which the undamped system has repeated eigenvalues. The method does not require the complete eigenvector set of the undamped system, but rather knowledge of only the undamped eigenpairs from which the interesting damped ones stem. This enables one to predict the damped dynamic property for practical complex structures. Numerical examples are given to show the validity of the method.

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