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.
Highlights
Piecewise linear systems are systems where the stiffness or damping coefficients remain constant over a range of amplitude and dramatically change to another set of constant values once a threshold is reached [1]
In this paper, the amplitude-frequency response of a piecewise linear system subjected to the base harmonic excitation is investigated
(1) The analytical results given by the averaging method is consistent with the numerical and experimental results
Summary
Piecewise linear systems are systems where the stiffness or damping coefficients remain constant over a range of amplitude and dramatically change to another set of constant values once a threshold is reached [1]. Piecewise linear systems can be classified into two categories. The vector field of the first category is discontinuous due to the rigid constraint or dry friction. The vector field of the second category is nonsmooth but continuous, and the nonsmoothness may be caused by a clearance or elastic constraint. Piecewise linear systems have been used to represent switching circuit and resistors [2], [3], mechanical system with Coulomb friction [4], [5], gene regulatory networks [6], [7], and so on. Owing to the practical significance and wide application, a great deal of effort has been devoted to the study of piecewise linear systems over the years
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