A Solution Procedure Combining Analytical and Numerical Approaches to Investigate a Two-Degree-of-Freedom Vibro-Impact Oscillator

In this paper, a new approach is proposed to analyze the behavior of a nonlinear two-degree-of-freedom vibro-impact oscillator subject to a harmonic perturbing force, based on a combination of analytical and numerical approaches. The nonlinear governing equations are analytically solved by means of a new analytical technique, namely the Optimal Auxiliary Functions Method (OAFM), which provided highly accurate explicit analytical solutions. Benefiting from these results, the application of Schur principle made it possible to analyze the stability conditions for the considered system. Various types of possible motions were emphasized, taking into account possible initial conditions and different parameters, and the explicit analytical solutions were found to be very useful to analyze the kinetic energy loss, the contact force, and the stability of periodic motions.

[1]  On the dynamics of vibro-impact systems with ideal and non-ideal excitation , 2021 .

[2]  N. Herisanu,et al.  An effective analytical approach to nonlinear free vibration of elastically actuated microtubes , 2020, Meccanica.

[3]  N. Herisanu,et al.  Optimal Auxiliary Functions Method for a Pendulum Wrapping on Two Cylinders , 2020, Mathematics.

[4]  Nicolae Herisanu,et al.  Construction of Analytic Solution to Axisymmetric Flow and Heat Transfer on a Moving Cylinder , 2020, Symmetry.

[5]  Nicolae Herisanu,et al.  An Efficient Analytical Approach to Investigate the Dynamics of a Misaligned Multirotor System , 2020 .

[6]  On Leonov’s Method for Computing the Linearization of Transverse Dynamics and Analyzing Zhukovsky Stability , 2019, Vestnik St. Petersburg University, Mathematics.

[7]  Nicolae Herisanu,et al.  Application of the Optimal Auxiliary Functions Method to a Permanent Magnet Synchronous Generator , 2019 .

[8]  Ilmar F. Santos,et al.  Unilateral vibro-impact systems — Experimental observations against theoretical predictions based on the coefficient of restitution , 2019, Journal of Sound and Vibration.

[9]  R. B. Davis,et al.  Nonlinear dynamics and triboelectric energy harvesting from a three-degree-of-freedom vibro-impact oscillator , 2018 .

[10]  N. Herisanu,et al.  The nonlinear thermomechanical vibration of a functionally graded beam on Winkler-Pasternak foundation , 2018 .

[11]  Shaopu Yang,et al.  Dynamical analysis of a single degree-of-freedom impact oscillator with impulse excitation , 2017 .

[12]  Nikolay V. Kuznetsov,et al.  Hidden Oscillations in Electromechanical Systems , 2017 .

[13]  Mei-Yan Lin,et al.  Dynamic behavior analysis of Vibro-impact System with Two Motion Limited Constraints , 2016 .

[14]  G. Leonov,et al.  Hidden attractors in dynamical systems , 2016 .

[15]  Masoud Tahani,et al.  An alternative reduced order model for electrically actuated micro-beams under mechanical shock , 2014 .

[16]  Y. S. Hamed,et al.  Analytical, numerical solutions and study of stability, resonance for nonlinear vibro-impact system under different excitation , 2014 .

[17]  Srdjan Jovic,et al.  Vibro-Impact System Based on Forced Oscillations of Heavy Mass Particle along a Rough Parabolic Line , 2012 .

[18]  Valery N. Pilipchuk,et al.  Inelastic impact dynamics of ships with one-sided barriers. Part I: analytical and numerical investigations , 2011 .

[19]  M. Belhaq,et al.  Control of vibroimpact dynamics of a single-sided Hertzian contact forced oscillator , 2011 .

[20]  Tomasz Kapitaniak,et al.  Dynamics of a two-degree-of-freedom cantilever beam with impacts , 2009 .

[21]  K. V. Avramov.  Application of nonsmooth transformations to analyze a vibroimpact duffing system , 2008 .

[22]  Alexander Fidlin,et al.  Near-elastic vibro-impact analysis by discontinuous transformations and averaging , 2008 .

[23]  Brian P. Mann,et al.  Experimental study of an impact oscillator with viscoelastic and Hertzian contact , 2007 .

[24]  Marian Wiercigroch,et al.  Cumulative effect of structural nonlinearities: chaotic dynamics of cantilever beam system with impacts , 2005 .

[25]  Iberê L. Caldas,et al.  Controlling chaotic orbits in mechanical systems with impacts , 2004 .

[26]  Albert C. J. Luo,et al.  An Unsymmetrical Motion in a Horizontal Impact Oscillator , 2002 .

[27]  L. Brindeu.  Stability of the periodic motions of the vibro-impact systems , 2000 .

[28]  V. Babitsky.  Theory of Vibro-Impact Systems and Applications , 2013 .

[29]  J. Awrejcewicz,et al.  CONTROLLING SYSTEMS WITH IMPACTS , 1999 .

[30]  A. Vakakis,et al.  Exact solutions of the problem of the vibro-impact oscillations of a discrete system with two degrees of freedom , 1999 .

[31]  A. P. Ivanov.  Analytical methods in the theory of vibro-impact systems , 1993 .

[32]  Pi-Cheng Tung,et al.  The Dynamics of a Nonharmonically Excited System Having Rigid Amplitude Constraints , 1992 .

[33]  D. L. Cronin,et al.  Substitute for the Impact Damper , 1975 .

[34]  Sami Faiz Masri,et al.  Analytical and experimental studies of impact dampers , 1965 .