Accession Number : AD0622482

Title :   BOUNDS TO EIGENVALUES OF RHOMBICAL MEMBRANES,

Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB

Personal Author(s) : Stadter,James T.

Report Date : 12 MAY 1964

Pagination or Media Count : 43

Abstract : Upper and lower bounds to eigenvalues are obtained for vibrating rhombical membranes. Two specific problems are treated: the membrane which has all edges fixed and the membrane which has two opposite edges fixed, the other two edges free. These problems have been studied as part of a systematic program for the development of rigorous methods for the estimation of frequencies of elastic structures. The techniques used are applicable to a substantial class of plate problems of interest in guided missile technology, but, since the analysis for membranes is in general easier than for plates, the problems treated here form an ideal vehicle for the acquisition of experience in applying the methods (actually, the fixed membrane problem considered here is essentially identical with the problem for simply supported plates. The method used consists of the following steps: (1) map the rhombus to the unit square using an affine transformation; (2) obtain the quadratic form, J, of the transformed membrane operator; (3) introduce two quadratic forms, one smaller than J, one larger, for which the corresponding eigenvalue problems can be solved; and (4) apply the B*B method to obtain the desired bounds.

Descriptors :   (*MEMBRANES, VIBRATION), (*BOUNDARY VALUE PROBLEMS, MEMBRANES), ELASTIC PROPERTIES, MAPPING(TRANSFORMATIONS), MATRICES(MATHEMATICS), OPERATORS(MATHEMATICS)

Distribution Statement : APPROVED FOR PUBLIC RELEASE