Date of Award

Fall 1985

Document Type

Thesis

Department

Mechanical & Aerospace Engineering

Program/Concentration

Engineering Mechanics

Committee Director

Jean W. Hou

Committee Member

Chuh Mei

Committee Member

Duc T. Nguyen

Call Number for Print

Special Collections; LD4331.E57Y82

Abstract

A beam with immovable ends under large amplitude oscillations is axially subjected to an amplitude-dependent stretching force which is induced by the geometrical nonlinearity. The design sensitivity analysis for such a beam is investigated in this study.

Two variational formulations based on different approximations of nonlinear stretching force are studied firstly. The analytical equations of design sensitivity analysis for these nonlinear eigenproblems are then derived. Finally, a computational scheme using finite element method is developed to calculate the design sensitivity derivatives of the eigenvalue and eigenvector numerically. Numerical examples associated with the nonlinear eigenvalue and eigenvector analysis, as well as the design sensitivity analysis, are also presented. The interdependence of design derivatives of eigenvalues and the corresponding eigenvectors, which is an important feature of nonlinear vibration, is recognized theoretically and is verified through numerical computation. The numerical results show that the proposed algorithm for calculating design derivatives of nonlinear eigenvalues and eigenvectors are very accurate and efficient.

Further study is necessary to perform the design sensitivity analysis of the nonlinear vibration problems based on the newly developed formulations such as vibration including axial inertia, forced vibration, random vibration, etc. With this information, optimal design can then be pursued systematically for most of nonlinear structural components.

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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

10.25777/65mr-3s74

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