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

Abstract

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.

Nonlinear vibration characteristics and bifurcation control of a class of piecewise constrained systems with dynamic clearances

“…Literature [17] also studied the dynamic characteristics of the nonlinear system, and the system received piecewise elastic forces, as shown in Fig. 3.…”

“…Fig. 3 The piece length elastic force of the system in reference [17] To study the vibration of the system at the piecewise critical point under the influence of different constraint, the velocity curve of the simulation system is shown in Figs. 4 and 5.…”

“…6 Amplitude frequency curve under two constraint cases Fig. 7 shows the amplitude-frequency characteristic curve of the system in literature [17]. At the critical point of the system piecewise, only slight bending occurs in the amplitude-frequency characteristic curve of the system, and no abrupt amplitude change occurs.…”

“…At the critical point of the system piecewise, only slight bending occurs in the amplitude-frequency characteristic curve of the system, and no abrupt amplitude change occurs. Literature [17] did not take into account the law of the influence of the abrupt change of piecewise-elastic force on the system. Therefore, it is meaningful to consider the effect of sudden change of Fig.…”