Date of Award

Spring 1989

Document Type

Thesis

Department

Mechanical & Aerospace Engineering

Program/Concentration

Engineering Mechanics

Committee Director

Jean W. Hou

Committee Director

Chuh Mei

Committee Member

Thomas E. Alberts

Call Number for Print

Special Collections; LD4331.E57J33

Abstract

The optimal design of a beam under harmonic excitations is formulated and solved numerically for linear and nonlinear forced vibration theories. The beam has a nonuniform cross-sect ion, whose thickness can change during the optimization procedure. Based on the numerical results, for the given input frequency range, the linear vibration theory produces a more conservative design than the nonlinear vibration theory.

The analytical formulation for both theories is presented. For the linear case, a mean case is defined for the self-weight on a beam, and an alternating case is defined for input forcing frequencies which cause fatigue variations on a beam. For the nonlinear vibration theory, the geometric nonlinearities are from the nonlinear strain-displacement relation induced by large deflections in the beam. The design sensitivity analyses are also presented for both theories.

Finally, an optimization routine using a predefined subroutine, LINRM, is used to define the optimal design for the beam satisfying the prescribed stress requirements. A comparative analysis between the two vibration theories is detailed in this study. Additionally, the modified Goodman theory is used as a stress constraint, and the results for this case are compared with the results obtained in the linear case.

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DOI

10.25777/m1zw-0539

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