文章基本信息

标题：Rayleigh Quotient Algorithm for Modal Analysis of Structural Models
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作者：José A. Inaudi
期刊名称：Mecánica Computacional
印刷版ISSN：2591-3522
出版年度：2016
卷号：34
期号：22
页码：1459-1477
语种：English
出版社：CIMEC-INTEC-CONICET-UNL
其他摘要：An algorithm for the computation of natural frequencies in continuum models based on classical separation of variables and the Rayleigh quotient is presented. The iterative method uses frequency-dependent shape functions derived from conventional modal analysis to assemble the boundary condition matrix resulting from the application of separation of variables for modal analysis, and the corresponding mass and stiffness matrices. An order reduction to a single generalized coordinate allows the application of the Rayleigh quotient for the estimation of a particular natural frequency. An iterative procedure is followed which starts from an initial estimate of a desired natural frequency. The evaluation of the Rayleigh quotient provides an improved estimate of the squared natural frequency and the corresponding improvement of the shape functions that estimate a mode shape. The recursive application of the proposed algorithm allows the estimation of any natural frequency and mode shape of the continuum model. The application of the proposed technique is illustrated using continuum-parameter rod and beam elements in longitudinal and flexural vibrations, respectively. Some characteristics of the speed of convergence and regions of convergence are explored. The algorithm shows excellent convergence characteristics.