Asymmetric Solutions of SDOF System with Wire Rope Vibration Isolator Subjected to Harmonic Excitation

A new modification of homotopy analysis method (HAM) is proposed for capturing asymmetric solutions of wire rope isolation systems. Analytical expressions of asymmetric solutions to wire rope isolation systems are obtained. A dynamic system with quadratic polynomial restoring force is investigated specifically. Then the analytical results are applied to a single-degree-of-freedom (SDOF) system with wire rope vibration isolator to investigate the response curve and other dynamic characteristics. The analytical approximations match satisfactorily with the numerical results. The presented analytical approximation is a useful method to derive the response curves and examine limit cycles without resorting to numerical simulations.

[1]  S. Abbasbandy,et al.  Soliton solutions for the fifth-order KdV equation with the homotopy analysis method , 2007 .

[2]  A. Rashid,et al.  The One Step Optimal Homotopy Analysis Method to Circular Porous Slider , 2012 .

[3]  Subrata K. Chakrabarti,et al.  Nonlinear progressive waves in water of finite depth — an analytic approximation , 2007 .

[4]  P. Hilton.  An Introduction to Homotopy Theory , 1953 .

[7]  F. Santonja,et al.  Solving a model for the evolution of smoking habit in Spain with homotopy analysis method , 2013 .

[8]  K. Shankar,et al.  PARAMETRIC IDENTIFICATION OF NONLINEAR DYNAMIC SYSTEMS USING COMBINED LEVENBERG–MARQUARDT AND GENETIC ALGORITHM , 2007 .

[9]  Andrew Y. T. Leung,et al.  Nonlinear Vibrations of Viscoelastic Plane Truss Under Harmonic Excitation , 2014 .

[10]  Michael L. Tinker,et al.  Damping phenomena in a wire rope vibration isolation system , 1992 .

[11]  Michael C. Constantinou,et al.  Study of wire rope systems for seismic protection of equipment in buildings , 1992 .

[12]  S. Abbasbandy.  Homotopy analysis method for the Kawahara equation , 2010 .

[13]  Shijun Liao,et al.  An analytic approach to solve multiple solutions of a strongly nonlinear problem , 2005, Appl. Math. Comput..

[14]  Yi-Qing Ni,et al.  IDENTIFICATION OF NON-LINEAR HYSTERETIC ISOLATORS FROM PERIODIC VIBRATION TESTS , 1998 .

[15]  S. Liao,et al.  Beyond Perturbation: Introduction to the Homotopy Analysis Method , 2003 .

[16]  A. Molabahrami,et al.  THE HOMOTOPY ANALYSIS METHOD TO SOLVE THE BURGERS–HUXLEY EQUATION , 2009 .

[17]  J. Jing,et al.  Homotopy Analysis Method for Nonlinear Dynamical System of an Electrostatically Actuated Microcantilever , 2011 .