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Calculation of higher frequencies of beams by the simultaneous iteration technique

22 Oct 1978-Journal of Sound and Vibration (Elsevier BV)-Vol. 60, Iss: 4, pp 599-601
About: This article is published in Journal of Sound and Vibration.The article was published on 1978-10-22.
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Journal ArticleDOI
Abstract: A FORTRAN IV algorithm is presented for determining sets of dominant eigenvalues and corresponding eigenvectors of symmetric matrices. It is also extended to the solution of the equations of natural vibration of a structure for which symmetric stiffness and mass matrices are available. The matrices are stored and processed in variable bandwidth form, thus enabling advantage to be gained from sparseness in the equations. Some of the procedures may also be used to solve symmetric positive definite equations such as those arising from the static analysis of structures loaded within the elastic range.

154 citations


Journal ArticleDOI
Abstract: The simultaneous iteration method of obtaining eigenvalues and eigenvectors is employed for the solution of undamped vibration problems. This method is of significance when a few of the dominant eigenvalues and eigenvectors are required from a large matrix, and hence is particularly suitable for vibration problems involving a large number of degrees of freedom. It is shown that advantage may be taken of both the symmetry and the band form of the mass and stiffness matrices, thus making it feasible to process on a computer larger order vibration problems than can be processed using transformation methods. A method of allowing for body freedom is given and some numerical tests are discussed.

69 citations


Journal ArticleDOI

21 citations


Journal ArticleDOI
TL;DR: This paper discusses the use of these for finding the first few modes of vibration of a large undamped structural system by computer by using a Sturm sequence procedure together with Chebyshev acceleration of the simultaneous iteration.
Abstract: There are several ways in which simultaneous iteration may be carried out for symmetric eigen value problems. This paper discusses the use of these for finding the first few modes of vibration of a large undamped structural system by computer. Two alternative methods are advocated. The first is a simple method adopting an approximate interaction analysis. The second achieves a controlled rate of convergence and improved efficiency by using a Sturm sequence procedure together with Chebyshev acceleration of the simultaneous iteration and accurate eigensolution of the interaction matrix.

12 citations


Journal ArticleDOI
Abstract: Prismatic shells find wide application in mechanical, civil and aeronautical engineering. The object of this paper is to propose a method of analysing such shells having different internal ribbing for their torsional vibrations. The governing equations of motion are derived by using a finite difference method and solved by the simultaneous iteration technique. The accuracy of the method is ascertained by comparing the results for some wellknown boundary conditions with the results obtained by classical methods. Shells of square cross-section and rectangular shells of variable and constant cross-section have been analysed. The effects of introduction of diaphragms on the eignefrequencies have been analysed. The effects of variations in shell thickness and length on the dynamic behaviour also have been studied.

11 citations