Date of Award

Spring 1971

Document Type


Degree Name

Doctor of Engineering Science in Mechanical Engineering


Mechanical Engineering

First Advisor

Benedict C. Sun

Second Advisor

P. A. Fox

Third Advisor

Harry Herman

Fourth Advisor

James L. Martin

Fifth Advisor

Arnold Allentuch


This study determines the eigenvalues, eigenvectors, and nodal patterns of a class of orthotropic plates whose geometry is governed by the equation

(x/a)α + (y/b)β = 1,

where the parameters a, b, a, and a permit the plate geometry to vary over a range which includes the rhombus, circle, ellipse, square, and rectangle.

Variable thickness, inplane forces, and mixed or discontinuous boundary conditions are also considered. The following assumptions have been employed:

i). plate is thin with respect to other dimensions,

ii). deflections are small,

iii). rotary inertia and shear are neglected.

The method of analysis employed is the Rayleigh-Ritz energy technique using xy-polynomials as the approximated deflection. Eigenvalues and eigenvectors were computed by the method of reductions, and the evaluation of double integrals was achieved by the numerical procedure of Gauss-Legendre quadratures.

The validity of the analysis was checked by comparison with known solutions for rectangular orthotropic plates, and isotropic plates with variable thickness, in-plane forces, and mixed or discontinuous boundary conditions. It was found that the calculated frequencies and nodal patterns were in good agreement with existing data.