Novel equivalent function for deadzone nonlinearity: applied to analytical solution of beam vibration using He's Parameter Expanding Method

This study intends to introduce the novel and efficient exact equivalent function (EF) for well-known deadzone nonlinearity. To indicate the effectiveness of this EF, the nonlinear vibration of cantilever beam in presence of deadzone nonlinear boundary condition is studied. The powerful analytical method, called He's Parameter Expanding Method (HPEM) is used to obtain the exact solution of dynamic behavior of mentioned system. It is shown that one term in series expansions is sufficient to obtain a highly accurate solution. Comparison of the obtained solutions using numerical method shows the soundness of this analytical EF.

[1]  Mahdi Bayat,et al.  Analytical study on the vibration frequencies of tapered beams , 2011 .

[2]  Kourosh H. Shirazi,et al.  Accurate modeling of preload discontinuity in the analytical approach of the nonlinear free vibration of beams , 2012 .

[3]  Yuwaraj M. Ghugal,et al.  A refined shear deformation theory for flexure of thick beams , 2011 .

[4]  Amin Barari,et al.  Non-linear vibration of Euler-Bernoulli beams , 2011 .

[5]  José Carlos M. Bermudez,et al.  Statistical analysis of the LMS adaptive algorithm subjected to a symmetric dead-zone nonlinearity at the adaptive filter output , 2008, Signal Process..

[6]  Massood Mofid,et al.  Exact solution to free vibration of beams partially supported by an elastic foundation , 2011 .

[7]  Amin Barari,et al.  DYNAMIC RESPONSE OF AXIALLY LOADED EULER-BERNOULLI BEAMS , 2011 .

[8]  Hongan Xu,et al.  An Exact Fourier Series Method for the Vibration Analysis of Multispan Beam Systems , 2009 .

[9]  Zhao-ling Tao.  Frequency–amplitude relationship of nonlinear oscillators by He’s parameter-expanding method , 2009 .

[10]  Ali H. Nayfeh,et al.  Problems in Perturbation , 1985 .

[11]  Mohammad Reza Khedmati,et al.  An extension of coupled beam method and its application to study ship's hull-superstructure interaction problems , 2011 .

[12]  Mahmoud Bayat,et al.  ANALYSIS OF NONLINEAR VIBRATION OF COUPLED SYSTEMS WITH CUBIC NONLINEARITY , 2012 .

[13]  Kourosh H. Shirazi,et al.  A New Approach to Analytical Solution of Cantilever Beam Vibration With Nonlinear Boundary Condition , 2012 .

[14]  A. Yildirim,et al.  ASYMPTOTIC INVESTIGATION OF BUCKLED BEAM NONLINEAR VIBRATION , 2012 .

[15]  Shapour Moradi,et al.  Drillstring vibration analysis using differential quadrature method , 2010 .

[16]  F Daneshmand,et al.  MESHLESS ANALYSIS OF BACKWARD EXTRUSION BY NATURAL ELEMENT METHOD , 2011 .

[17]  Marco Amabili,et al.  Nonlinear Vibrations and Stability of Shells and Plates , 2008 .

[18]  P. Ogbobe,et al.  FORMULATION AND EVALUATION OF COUPLING EFFECTS BETWEEN DOF MOTIONS OF HYDRAULICALLY DRIVEN 6 DOF PARALLEL MANIPULATOR , 2011 .

[19]  H. Sedighi.  Study on the frequency – amplitude relation of beam vibration , 2011 .

[20]  Vitalijus Volkovas,et al.  INVESTIGATION OF INTERACTION BETWEEN ACOUSTIC FIELD AND NONHOMOGENEOUS BUILDING STRUCTURES , 2011 .

[21]  Livija Cveticanin,et al.  The homotopy-perturbation method applied for solving complex-valued differential equations with strong cubic nonlinearity , 2005 .

[22]  Chengwu Duan,et al.  Dynamic analysis of preload nonlinearity in a mechanical oscillator , 2007 .

[23]  G. Vossoughi,et al.  A periodic solution for friction drive microrobots based on the iteration perturbation method , 2011 .

[24]  M. Ahmadian,et al.  Dynamic pull-in instability of electrostatically actuated beams incorporating Casimir and van der Waals forces , 2010 .

[25]  M. Nikkhah Bahrami,et al.  Modified wave approach for calculation of natural frequencies and mode shapes in arbitrary non-uniform beams , 2011 .

[26]  M. Z. Nejad,et al.  DETERMINATION OF DISPLACEMENTS AND STRESSES IN PRESSURIZED THICK CYLINDRICAL SHELLS WITH VARIABLE THICKNESS USING PERTURBATION TECHNIQUE , 2012 .