Optimization of secondary suspension of piecewise linear vibration isolation systems

A comprehensive optimal design solution is presented for piecewise-linear vibration isolation systems. First, primary suspension optimum parameters are established, followed by an investigation of jump-avoidance conditions for the secondary suspension. Within the no-jump zones, an optimal design solution is then obtained for the secondary system and overall results are discussed. Averaging method is employed to obtain an implicit function for frequency response of a bilinear system under steady-state conditions. This function is examined for jump-avoidance and a condition is derived which when met ensures that the undesirable phenomenon of 'jump' does not occur and the system response is functional and unique. Optimal stiffness and damping parameters for the primary suspension are extracted from a recently established work for passive linear vibration systems. For each point of the primary suspension optimal curve, jump-free zones are identified. Iterating this process, a boundary surface between no-jump (unique response) and jump (multiple-response) areas is established. Keeping optimal parameters for the primary suspension system fixed, the secondary suspension stiffness and damping parameters are varied inside the no-jump zones to explore optimum solutions for the secondary. The root mean square (RMS) of the absolute acceleration is minimized against the RMS of the relative displacement (η). It is observed that there is a certain band of parameters defined by primary damping, within which a valid frequency response can be obtained. An optimum numerical solution is sought within this band of parameters. Optimal solution curves are achieved for the secondary suspension. These can be used in conjunction with the optimal curve for the primary suspension to select design parameter values for the best possible vibration isolation performance in a given application.

[1]  Amir Khajepour,et al.  Optimization of Engine Mount Characteristics Using Experimental/Numerical Analysis , 2003 .

[2]  S. Narayanan,et al.  Periodic and chaotic responses of an sdf system with piecewise linear stiffness subjected to combined harmonic and flow induced excitations , 1995 .

[3]  Colin H. Hansen,et al.  Analytical approximation of the primary resonance response of a periodically excited piecewise non-linear–linear oscillator , 2004 .

[4]  Matthew Cartmell,et al.  Introduction to Linear, Parametric and Non-Linear Vibrations , 1990 .

[5]  Ivan Jordanov,et al.  Optimal design of linear and non-linear dynamic vibration absorbers , 1988 .

[6]  Anita C. Faul,et al.  Non-linear systems , 2006 .

[7]  E. Chicurel-Uziel.  EXACT, SINGLE EQUATION, CLOSED-FORM SOLUTION OF VIBRATING SYSTEMS WITH PIECEWISE LINEAR SPRINGS , 2001 .

[8]  Sotirios Natsiavas,et al.  ON VIBRATION ISOLATION OF MECHANICAL SYSTEMS WITH NON-LINEAR FOUNDATIONS , 1996 .

[9]  S. T. Noah,et al.  Impact behaviour of an oscillator with limiting stops, part I: A parametric study , 1986 .

[10]  B. Schmalhorst,et al.  Optimization of a non-linear dynamic vibration absorber , 1985 .

[11]  Sotirios Natsiavas.  STABILITY OF PIECEWISE LINEAR OSCILLATORS WITH VISCOUS AND DRY FRICTION DAMPING , 1998 .

[12]  Yao Zhang,et al.  Suspension optimization by a frequency domain equivalent optimal control algorithm , 1989 .

[13]  W. S. Loud.  Branching phenomena for periodic solutions of non-autonomous piecewise linear systems , 1968 .

[14]  S. Natsiavas,et al.  Periodic response and stability of oscillators with symmetric trilinear restoring force , 1989 .

[15]  M. Nakai,et al.  Analysis of Piecewise Linear Systems With Boundaries in Displacement and Time , 2002 .

[16]  S. W. Shaw,et al.  DYNAMICS OF A PIECEWISE NON-LINEAR SYSTEM SUBJECT TO DUAL HARMONIC EXCITATION USING PARAMETRIC CONTINUATION , 2022 .

[17]  J. Ji,et al.  Periodic and chaotic motions of a harmonically forced piecewise linear system , 2004 .

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

[19]  Walter D. Pilkey,et al.  Optimization of Shock Isolation Systems , 1968 .

[20]  S. F. Masri,et al.  Random Excitation of a Nonlinear Vibration Neutralizer , 1978 .

[21]  A. H. Nayfeh,et al.  Calculation of the jump frequencies in the response of s.d.o.f. non-linear systems , 2002 .

[22]  M. F. Golnaraghi,et al.  Practical Frequency and Time Optimal Design of Passive Linear Vibration Isolation Mounts , 2003 .

[23]  R. Jazar,et al.  Comparison of Exact and Approximate Frequency Response of a Piecewise Linear Vibration Isolator , 2005 .

[24]  Yu Wang,et al.  Dynamics of unsymmetric piecewise-linear/non-linear systems using finite elements in time , 1995 .

[25]  A. K. Mallik,et al.  Periodic response of piecewise non-linear oscillators under harmonic excitation , 1996 .

[26]  R T.J.,et al.  OPTIMIZATION OF PASSIVE AND ACTIVE NON-LINEAR VIBRATION MOUNTING SYSTEMS BASED ON VIBRATORY POWER TRANSMISSION , 2022 .

[27]  Albert C. J. Luo,et al.  The mapping dynamics of periodic motions for a three-piecewise linear system under a periodic excitation , 2005 .

[28]  F. Badrakhan,et al.  Lagrangian formulation and first integrals of piecewise linear dissipative systems , 1982 .

[29]  M. E. Gurtin,et al.  On the Use of Clearance in Viscous Dampers to Limit High Frequency Force Transmission , 1961 .

[30]  M. F. Golnaraghi,et al.  Optimal design of passive linear suspension using genetic algorithm , 2004 .

[31]  I. A. Mahfouz,et al.  Chaotic behaviour of some piecewise-linear systems, part II: Systems with clearance , 1990 .

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

[33]  R. M. Rosenberg.  Steady-state forced vibrations , 1966 .

[34]  Q. Cao,et al.  Bifurcation and chaos of a harmonically excited oscillator with both stiffness and viscous damping piecewise linearities by incremental harmonic balance method , 2003 .

[35]  S. Natsiavas,et al.  Steady state oscillations and stability of non-linear dynamic vibration absorbers , 1992 .

[36]  D. Jianga,et al.  Large-amplitude non-linear normal modes of piecewise linear systems , 2004 .

[37]  L. Dai,et al.  On Oscillatory Motion of Spring-Mass Systems Subjected to Piecewise Constant Forces , 1991 .

[38]  Jinchen Ji,et al.  Dynamics of a piecewise linear system subjected to a saturation constraint , 2004 .