Date of Award

Spring 1972

Document Type

Dissertation

Degree Name

Doctor of Engineering Science in Mechanical Engineering

Department

Mechanical Engineering

First Advisor

Benedict C. Sun

Second Advisor

Harry Herman

Third Advisor

James L. Martin

Fourth Advisor

P. A. Fox

Fifth Advisor

Charles E. Wilson

Abstract

The effects of shear, rotatory inertia and inplane forces on the transverse vibration of thin plates are studied. In addition, the effect of shear on the buckling of thin plates is examined. A general differential equation of motion is derived for an isotropic thin plate subjected to normal and inplane forces with the consideration of shear and rotatory inertia. The method of internal constraints and Hamilton's principle are utilized.

The resulting fourth order differential equation is solved for simply supported plates of various shapes by employing a finite difference technique. The shapes examined are a square, a circle, a circular annulus, and an elliptic annulus. The differential equation is written in its finite difference form and finally as a matrix. The value of the matrix is determined using the lower and upper decomposition method. The first few natural frequencies and the critical buckling loads are obtained using an iterative technique.

The numerical results for the several shapes examined show that the inclusion of shear, rotatory inertia, and inplane forces result in substantially lower natural frequencies. The inclusion of shear effect in the buckling analysis also results in significantly lowering the critical buckling load.

As a check on the numerical technique employed in the study, natural frequencies and critical buckling loads neglecting the effects of shear and rotatory inertia were also determined. Excellent agreement between these numerical results and analytical data obtained from classical theories is obtained.

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