Exact Solutions for the Analysis of General Elastically Restrained Nonuniform Beams

[+] Author and Article Information
Sen Yung Lee

Mechanical Engineering Department, National Cheng Kung University, Tainan, Taiwan 700

Yee Hsiung Kuo

Aeronautical Research Laboratory, Taichung, Taiwan 400

J. Appl. Mech 59(2S), S205-S212 (Jun 01, 1992) doi:10.1115/1.2899490 History: Received September 09, 1990; Revised January 18, 1991; Online March 31, 2008


The exact solutions for the problems governed by a general self-adjoint fourth-order nonhomogeneous ordinary differential equation with arbitrarily polynomial varying coefficients and general elastic boundary conditions are derived in Green’s function form. To illustrate the analysis, the static deflection and dynamic analysis of a general eiastically end restrained Bernoulli-Euler beam with polynomial varying bending rigidity, applied axial and force, and elastic foundation modulus along the beam, subjected to an arbitrary transverse force are presented. The Green’s function is concisely expressed in terms of the four normalized fundamental solutions of the system and these fundamental solutions are given in power series forms. The characteristic equations for elastic stability and free vibrational analysis of the beam can be obtained by setting the denominator of the corresponding Green’s function equal to zero. Finally, examples are given to illustrate the accuracy and efficiency of the analysis.

Copyright © 1992 by The American Society of Mechanical Engineers
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