Experimental Modelling and Amplitude-Frequency Response Analysis of a Piecewise Linear Vibration System

The amplitude-frequency response of a nonlinear vibration system with the coexistence of stiffness and viscous damping piecewise linearities are analysed by means of analytical, numerical and experimental investigations. First, a mechanical model of the piecewise linear system under simple harmonic base excitation is established, and the amplitude-frequency response equation is obtained by the averaging method. Second, an experimental device is built to realize the piecewise linear system. The stiffness and damping coefficients are identified by the least square method. Third, case studies are conducted to illustrate the effect of the clearance and base excitation amplitude on the amplitude-frequency response. The experimental results show that the introduction of the piecewise linear stiffness and damping significantly decreases the response amplitude at the primary resonance. The piecewise linear stiffness, damping coefficients, primary resonance frequency and frequency range of the bi-stable state depend on the clearance and excitation amplitude. The experimental results are consistent with the theoretical predictions and numerical simulation results of the method of backward differentiation formulas. This research provides instructive ideas to the design of the nonlinear isolator in practical engineering.