Nonlinear Vibrations of a Hinged Beam Including Nonlinear Inertia Effects

[+] Author and Article Information
S. Atluri

Department of Aeronautics and Astronautics, University of Washington, Seattle, Wash.

J. Appl. Mech 40(1), 121-126 (Mar 01, 1973) (6 pages) doi:10.1115/1.3422909 History: Received November 01, 1971; Revised March 01, 1972; Online July 12, 2010


This investigation treats the large amplitude transverse vibration of a hinged beam with no axial restraints and which has arbitrary initial conditions of motion. Nonlinear elasticity terms arising from moderately large curvatures, and nonlinear inertia terms arising from longitudinal and rotary inertia of the beam are included in the nonlinear equation of motion. Using a Galerkin variational method and a modal expansion, the problem is reduced to a system of coupled nonlinear ordinary differential equations which are solved for arbitrary initial conditions, using the perturbation procedure of multiple-time scales. The general response and frequency-amplitude relations are derived theoretically. Comparison with previously published results is made.

Copyright © 1973 by ASME
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