Isolated response curves in a base-excited, two-degree-of-freedom, nonlinear system

In the present paper, isolated response curves in a nonlinear system consisting of two masses sliding on a horizontal guide are examined. Transverse springs are attached to one mass to provide the nonlinear restoring force, and a harmonic motion of the complete system is imposed by prescribing the displacement of their supports. Numerical simulations are carried out to study the conditions of existence of isolated solutions, their bifurcations, their merging with the main response branch and their basins of attraction. This is achieved using tools including nonlinear normal modes, energy balance, harmonic balance-based continuation and bifurcation tracking, and global analysis.Copyright © 2015 by ASME

[1]  R. M. Rosenberg,et al.  On Nonlinear Vibrations of Systems with Many Degrees of Freedom , 1966 .

[2]  Gaëtan Kerschen,et al.  Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques , 2009 .

[3]  Gianluca Gatti,et al.  On the interaction of the responses at the resonance frequencies of a nonlinear two degrees-of-freedom system , 2010 .

[4]  Lawrence N. Virgin,et al.  Measuring the Stability of Periodic Attractors Using Perturbation-Induced Transients: Applications to Two Non-Linear Oscillators , 1994 .

[5]  Frank Schilder,et al.  Exploring the performance of a nonlinear tuned mass damper , 2009 .

[6]  Gaëtan Kerschen,et al.  Modal testing of nonlinear vibrating structures based on nonlinear normal modes: Experimental demonstration , 2011 .

[7]  Matthew S. Allen,et al.  Nonlinear normal modes modal interactions and isolated resonance curves , 2015, 1604.05567.

[8]  R. M. Rosenberg,et al.  The Normal Modes of Nonlinear n-Degree-of-Freedom Systems , 1962 .

[9]  Chengwu Duan,et al.  Isolated sub-harmonic resonance branch in the frequency response of an oscillator with slight asymmetry in the clearance , 2008 .

[10]  Alexander F. Vakakis,et al.  Nonlinear normal modes, Part I: A useful framework for the structural dynamicist , 2009 .

[11]  R. Seydel.  Practical Bifurcation and Stability Analysis , 1994 .

[12]  Christophe Pierre,et al.  Normal Modes for Non-Linear Vibratory Systems , 1993 .

[13]  Gaëtan Kerschen,et al.  The Harmonic Balance Method for Advanced Analysis and Design of Nonlinear Mechanical Systems , 2014 .

[14]  L. Virgin.  Introduction to Experimental Nonlinear Dynamics: A Case Study In Mechanical Vibration , 2000 .

[15]  G. Kerschen,et al.  Dynamic testing of nonlinear vibrating structures using nonlinear normal modes , 2011 .

[16]  G. Kerschen,et al.  The Harmonic Balance Method for Bifurcation Analysis of Nonlinear Mechanical Systems , 2016 .