Date of Award

Fall 1987

Document Type

Thesis

Department

Mechanical & Aerospace Engineering

Program/Concentration

Engineering Mechanics

Committee Director

Jean W. Hou

Committee Member

Chuh Mei

Committee Member

Thomas E. Alberts

Call Number for Print

Special Collections; LD4331.E57X83

Abstract

A finite element method is developed in this thesis for analyzing stepped beams under nonlinear free and forced vibrations. A new assumption is made to improve an existing finite element procedure for treating beams of nonuniform cross sections. The geometric nonlinearity results from the nonlinear, strain-displacement relation due to large deflection of a beam.

Based on an improved finite element procedure a computational method is then established for design sensitivity analyses of nonlinear eigenproblems pertaining to the free and forced nonlinear vibrations of beams. It is found that the equation for computing the design sensitivity of eigenvector is linear and nonsymmetric. A prior knowledge of the eigenvector design sensitivity is needed for the calculation of the eigenvalue sensitivity.

Numerical results show that the proposed computational methods are valid and efficient.

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DOI

10.25777/7064-yv56

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