Forced Vibration of Timoshenko Beams Made of Multimodular Materials

[+] Author and Article Information
C. W. Bert, F. Gordaninejad

School of Aerospace, Mechanical and Nuclear Engineering, The University of Oklahoma, Norman, Okla.

J. Vib., Acoust., Stress, and Reliab 107(1), 98-105 (Jan 01, 1985) (8 pages) doi:10.1115/1.3274723 History: Received June 10, 1983; Online December 08, 2009


This paper presents a transfer-matrix analysis for determining the sinusoidal vibration response of thick, rectangular cross-section beams made of “multimodular materials” (i.e., materials which have different elastic behavior in tension and compression, with nonlinear stress-strain curves approximated as piecewise linear). An experimentally determined stress-strain curve for aramid-cord rubber is approximated by four straight-line segments (two segments in tension and two segments in compression). To validate the transfer-matrix results, a closed-form solution is also presented for the special case in which the neutral-surface location is uniform along the length of the beam. Also, comparisons are made among multimodular, bimodular (two line segments), and unimodular models. Numerical results for axial displacement, transverse deflection, bending slope, bending moment, transverse shear and axial forces, and the location of the neutral surface are presented for the multimodular model. Effects of translatory and rotatory inertia coefficients on axial force are investigated for a clamped-clamped beam. Moreover, natural frequencies associated with the first three modes of a clamped-free beam are presented. Transfer-matrix results agree very well with the closed-form results for the corresponding material model (one, two, or four segments).

Copyright © 1985 by ASME
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