Design of a piecewise linear vibration isolator for jump avoidance

Abstract

Piecewise linear isolators are smart passive vibration isolators that provide effective isolation for high frequency/low amplitude excitation. This can be done by introducing a soft primary suspension and a relatively damped secondary suspension. Such a piecewise isolator prevents the system from a high relative displacement in low frequency/high amplitude excitation. By employed an averaging method it is possible to obtain an implicit function for frequency response of a symmetric bilinear vibration isolator system under steady-state harmonic excitation. This function is examined for jump avoidance. A condition is derived which when met ensures that the undesirable phenomenon of ‘jump’ does not occur and the system response is functional. The jump avoidance and sensitivity of the condition are examined and investigated as the dynamic parameters vary. The results of this investigation can be directly employed in design of effective piecewise linear vibration isolators. A linear vibration system is defined as one in which the quantities of mass (or inertia), stiffness, and damping are linear in behaviour and do not vary with time [1]. Although mathematical models employing a linear ordinary differential equation with constant coefficients portray a simple and manageable system for analytical study, in most cases they are an incomplete representation simplified for the sake of analysis. Most real physical vibration systems are more accurately depicted by non-linear governing equations, in which the non-linearity may stem from structural constraints causing a change in stiffness and damping characteristics, or from inherent non-linear behaviour of internal springs and dampers. This paper focuses on a general form of such a non-linear system. This study of piecewise-linear systems will allow hazardous system behaviour over operating frequency ranges to be gauged and controlled in order to avoid premature fatigue damage, and prolong the life of the system.

Nonlinear frequency response analysis and dynamics design of a solid and liquid mixture nonlinear vibration isolator

“…For instances, many researchers including Friswell and Penny (1994), Worden (1996) and Brennan et al (2008), estimated jump-up and jumpdown frequencies of a Duffing oscillator with linear viscous damping. For a piecewise linear vibration isolation system, Deshpande et al (2006, 2007 carried on a series of researches on the design and optimization of a isolator from the point of view of jump avoidance.…”

Frequency Energy Plots of Dynamical Systems Attached to Piecewise Nonlinear Energy Sink

“…As a result, plenty of works studied nonsmooth NESs for implementation in TET because they become of particular interest for rapid suppression of shock and seismic excitations. A soft primary suspension and a relatively damped secondary suspension were investigated to produce a piecewise isolator that prevents the system from a high relative displacement in low frequency/high amplitude excitation [19]. A slider with two stop block was added to the piecewise NES to enable tuneable stiffness which resulted in optimum vibration absorption range [20].…”

Dynamic properties of piecewise linear systems with fractional time-delay feedback

“…The selection of proper piecewise stiffness or dampness can improve the performance of the original dynamic system by improving the stability and buffer performance of the system. [14][15][16] Based on the extensive application of fractional calculus and interdisciplinary development, fractional calculus has appeared in models in numerous disciplinary fields and practical problems, [17][18][19] such as the fractal Micro-Electro-Mechanical System (MEMS) and Toda oscillators. Zuo 20 designed a gecko-inspired fractal-like receptor system for the three-dimensional printing process.…”

“…The selection of proper piecewise stiffness or dampness can improve the performance of the original dynamic system by improving the stability and buffer performance of the system. 14–16…”