On Nonlinear Dynamics of Planar Shear Indeformable Beams

[+] Author and Article Information
A. Luongo

Istituto di Scienza delle Costruzioni, University of Rome, Roma, Italy 00184

G. Rega, F. Vestroni

Istituto di Scienza delle Costruzioni, University of L’Aquila, L’Aquila, Italy 67100

J. Appl. Mech 53(3), 619-624 (Sep 01, 1986) (6 pages) doi:10.1115/1.3171821 History: Received January 10, 1985; Revised July 19, 1985; Online July 21, 2009


The planar forced oscillations of shear indeformabie beams with either movable or immovable supports are studied through a unified approach. An exact nonlinear beam model is referred to and a consistent procedure up to order three nonlinearities is followed. By eliminating the longitudinal displacement component through a constraint condition and assuming one mode, the problem is reduced to one nonlinear differential equation. A perturbational solution in the neighborhood of the resonant frequency is determined and the stability of the steady-state solutions is studied. The dependence of the phenomenon on the geometrical and mechanical characteristics of the system is put into light and the frequency-response curves for different boundary conditions are furnished.

Copyright © 1986 by ASME
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