0
TECHNICAL PAPERS

A Transfer-Matrix-Perturbation Approach to the Dynamics of Chains of Nonlinear Sliding Beams

[+] Author and Article Information
Angelo Luongo

Dipartimento di Ingegneria delle Strutture, delle Acque e del Terreno, Università di L’Aquila, 67040 Monteluco di Roio (L’Aquila), Italyluongo@ing.univaq.it

Francesco Romeo1

Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma “La Sapienza,” Via Gramsci 53, 00197 Rome, Italyfrancesco.romeo@uniroma1.it

1

Corresponding author.

J. Vib. Acoust 128(2), 190-196 (Nov 08, 2005) (7 pages) doi:10.1115/1.2159034 History: Received September 04, 2004; Revised November 08, 2005

Chains of nonlinear shear indeformable beams with distributed mass, resting on movable supports, are considered. To determine the dynamic response of the system, the transfer-matrix approach is merged with the harmonic balance method and a perturbation method, thereby transforming the original space-temporal continuous problem into a discrete one-dimensional map xk+1=F(xk) expressed in terms of the state variables xk at the interface between adjacent beams. Such transformation does not imply any discretization, because it is obtained by integrating the single-element field equations. The state variables consist of both first-order variables, namely, transversal displacement and couples, and second-order variables, which are longitudinal displacement and axial forces. Therefore, while the linear problem is monocoupled, the nonlinear one becomes multicoupled. The procedure is applied to determine frequency-response relationship under free and forced vibrations.

FIGURES IN THIS ARTICLE
<>
Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

(a) Chain of nonlinear beams and (b) inextensible and shear indeformable single beam

Grahic Jump Location
Figure 2

First four natural frequencies-amplitude relationship for a four four-bay beam: thick lines, nonlinear; thin lines, linear

Grahic Jump Location
Figure 3

Second four natural frequencies-amplitude relationship for a four-bay beam: thick lines, nonlinear; thin lines, linear

Grahic Jump Location
Figure 4

First natural frequencies-amplitude relationship for a chain with number of beams increasing from 1 to 4 (Ω, ω: nonlinear and linear frequency)

Grahic Jump Location
Figure 5

First and second mode of a four-bay beam: (a) first mode (β=π)a=0.04π, (b) first mode (β=π)a=0.08π, (c) second mode (β=3.393)a=0.04π, and (d) second mode (β=3.393)a=0.08π; thick lines, nonlinear; thin lines, linear

Grahic Jump Location
Figure 6

Third and fourth mode of a 4-bay beam: (a) third mode (β=3.926)a=0.04π, (b) third mode (β=3.926)a=0.06π, (c) fourth mode (β=4.464)a=0.02π, and (d) fourth mode (β=4.464)a=0.035π; thick lines, nonlinear; thin lines, linear

Grahic Jump Location
Figure 7

Frequency-response relationship for a four-bay beam with m0=0.0,0.001,0.005,0.01: (a) first mode, (b) second mode, (c) third mode, and (d) fourth mode (Ω, ω: nonlinear and linear frequency)

Grahic Jump Location
Figure 8

Frequency-response relationship in the first linear pass band for a four-bay beam; m0=0.01

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In