Frequency response characteristics of a multi-degree-of-freedom system with clearances

Abstract In an earlier study, the frequency response characteristics of a single-degree-of-freedom system with a clearance non-linearity were studied. The current study, an extension of the earlier work, is concerned with the frequency response characteristics of a multi-degree-of-freedom system with clearances. The method of harmonic balance is used to develop approximate analytical solutions of the undamped equations of motion of a multi-degree-of-freedom system composed of three coupled non-linear oscillators. For primary resonances and a harmonic excitation, general formulations are presented which can be used to study both the existence and the stability of the solutions. These general formulations are used to discuss a number of modal spacing and modal coupling issues. An analysis methodology for multi-degree-of-freedom systems is introduced and illustrated by two special but practical cases: a strongly non-linear system and a weakly non-linear system. The results of the analysis of the special cases are validated by using analog simulation. It is shown that an analysis of the special cases of the general multi-degree-of-freedom non-linear formulation can provide not only an improved understanding of the dynamic behavior of non-linear systems, but also can be used as the basis for the development of simplified approximate solutions. The limitations of the current study and areas for further research are discussed.

[1]  C. Bapat.  Impact-pair under periodic excitation , 1988 .

[2]  K. Watanabe,et al.  Development of Nonlinear Building Block Approach , 1988 .

[3]  Arthur Gelb,et al.  Multiple-Input Describing Functions and Nonlinear System Design , 1968 .

[4]  N. Popplewell,et al.  Stable periodic motions of an impact-pair , 1983 .

[5]  Steven W. Shaw,et al.  The Dynamics of a Harmonically Excited System Having Rigid Amplitude Constraints, Part 2: Chaotic Motions and Global Bifurcations , 1985 .

[6]  Robert Joseph Comparin.  A study of the frequency response of impact pairs with application to automotive gear rattle , 1988 .

[7]  T. S. Sankar,et al.  Vibro-Impact Analysis of Control Systems With Mechanical Clearance and Its Application to Robotic Actuators , 1986 .

[8]  R. J. Comparin,et al.  Non-linear frequency response characteristics of an impact pair , 1989 .

[9]  G. S. Whiston,et al.  Global dynamics of a vibro-impacting linear oscillator , 1987 .

[10]  N. Popplewell,et al.  Several similar vibroimpact systems , 1987 .

[11]  G. S. Whiston,et al.  The vibro-impact response of a harmonically excited and preloaded one-dimensional linear oscillator , 1987 .

[12]  Geoffrey R. Tomlinson,et al.  Frequency response characteristics of structures with single and multiple clearance-type non-linearity , 1984 .

[13]  Steven W. Shaw,et al.  A Periodically Forced Impact Oscillator With Large Dissipation , 1983 .

[14]  Ferdinand Freudenstein,et al.  Dynamic Analysis of Mechanical Systems With Clearances—Part 2: Dynamic Response , 1971 .

[15]  R. Palej,et al.  On a direct method of analyzing impacting mechanical systems , 1986 .

[16]  G. S. Whiston.  Impacting under harmonic excitation , 1979 .

[17]  F. R. E. Crossley,et al.  Multiple Impacts of a Ball Between Two Plates—Part 1: Some Experimental Observations , 1975 .

[18]  N. Popplewell,et al.  Stable periodic vibroimpacts of an oscillator , 1983 .

[19]  P. Holmes,et al.  A periodically forced piecewise linear oscillator , 1983 .

[20]  S. T. Noah,et al.  Forced periodic vibration of unsymmetric piecewise-linear systems , 1988 .

[21]  K. P. Byrne,et al.  Impact statistics for a simple random rattling system , 1987 .