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.
Rights
In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
DOI
10.25777/m1zw-0539
Recommended Citation
Jackson, Cheryl C..
"The Effects of Nonlinearities on the Optimal Design of Forced Vibrating Beams"
(1989). Thesis, Old Dominion University, DOI: 10.25777/m1zw-0539
https://digitalcommons.odu.edu/mae_etds/545