ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
A quadratic method is presented for solving the eigenvalue problem of a structural system having a large number of degrees-of-freedom. The eigenproblem is reduced to a smaller problem by condensing the system stiffness and mass using Guyan reduction. Application of a set of corrective displacements to the reduced system subsequently leads to an eigenproblem of quadratic form involving an additional mass term. To obtain the solution to the reduced problem, inverse iteration with spectrum shifts based on the eigenvalues of the Guyan problem is used. The resulting eigenvalues and mode shapes represent a corrected Guyan approximation to the solution of the unreduced system. In addition, it is shown that the amount of improvement over the Guyan solution can be approximated by employing a first-order error analysis procedure. Numerical examples of vibrations of a bar, a beam and a plate demonstrate that the solutions obtained from the quadratic reduction procedure are very accurate and require relatively little additional computational effort in comparison with the solutions of the corresponding linear eigen-problem. The relationship of the present method to that proposed by Przemieniecki is illustrated by an example.
Additional Material:
4 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620150609
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