0
Research Papers

Nonlinear Free Vibration of a Symmetrically Conservative Two-Mass System With Cubic Nonlinearity

[+] Author and Article Information
T. Pirbodaghi1

School of Mechanical Engineering, Sharif University of Technology, 11365-9567 Tehran, Iranpirbodaghi@mech.sharif.edu

S. Hoseini

School of Mechanical Engineering, Sharif University of Technology, 11365-9567 Tehran, Iran

1

Corresponding author.

J. Comput. Nonlinear Dynam 5(1), 011006 (Nov 18, 2009) (6 pages) doi:10.1115/1.4000315 History: Received September 20, 2008; Revised May 12, 2009; Published November 18, 2009; Online November 18, 2009

In this study, the nonlinear free vibration of conservative two degrees of freedom systems is analyzed using the homotopy analysis method (HAM). The mathematical model of such systems is described by two second-order coupled differential equations with cubic nonlinearities. First, novel approximate analytical solutions for displacements and frequencies are established using HAM. Then, the homotopy Padé technique is applied to accelerate the convergence rate of the solutions. Comparison between the obtained results and those available in the literature shows that the first-order approximation of homotopy Padé technique leads to accurate solutions with a maximum relative error less than 0.068 percent for all the considered cases.

FIGURES IN THIS ARTICLE
<>
Copyright © 2010 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 conservative two degree of freedom system

Grahic Jump Location
Figure 2

The effect of auxiliary parameter ℏ on the frequency (m=k=k1=k2=1, a=5, b=1)

Grahic Jump Location
Figure 3

Displacement x1(t) for k=0, m=k1=k2=1, a=5, and b=1

Grahic Jump Location
Figure 4

Displacement x2(t) for k=0, m=k1=k2=1, a=5, and b=1

Grahic Jump Location
Figure 5

Displacement x1(t) for m=k=k1=k2=1, a=3, and b=1

Grahic Jump Location
Figure 6

Displacement x2(t) for m=k=k1=k2=1, a=3, and b=1

Grahic Jump Location
Figure 7

Displacement x1(t) for m=k=k1=1, k2=5, a=5, and b=1

Grahic Jump Location
Figure 8

Displacement x2(t) for m=k=k1=1, k2=5, a=5, and b=1

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