Table of Contents
Journal of Structures
Volume 2014, Article ID 234085, 13 pages
http://dx.doi.org/10.1155/2014/234085
Research Article

Static, Vibration Analysis and Sensitivity Analysis of Stepped Beams Using Singularity Functions

Department of Mechanical and Aerospace Engineering, Old Dominion University, Norfolk, VA 23529, USA

Received 30 September 2013; Accepted 5 December 2013; Published 20 January 2014

Academic Editor: Yiyang Li

Copyright © 2014 Peng Cheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A systematic approach is presented in this paper to derive the analytical deflection function of a stepped beam using singularity functions. The discontinuities considered in this development are associated with the jumps in the flexural rigidity and the applied loads. This approach is applied to static and vibration analyses of stepped beams. The same approach is later extended to perform sensitivity analysis of stepped beams. This is done by directly differentiating the analytical deflection function with respect to any beam-related design variable. The particular design variable considered here is the location of discontinuity in flexural rigidity. Example problems are presented in this paper to demonstrate and verify the derivation process.