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Dynamic modeling and analysis of an elastic mechanism with a nonlinear damping model

Dynamic modeling and simulation of a mechanical system with nonlinear strain-frequency-dependent damping are carried out in this paper. First, methods of nonlinear strain-frequency-dependent damping are described, which extracts nonlinear damping information of a damping alloy specimen from the free decay signal by means of the moving autoregressive model method. Second, the viscoelastic theory is introduced to describe the strain-frequency-dependent characteristics of damping more accurately, a viscoelastic three parameter structural damping constitution model is developed whose parameters are identified from the test data by means of an optimization algorithm. The finite element dynamic equations for strain-frequency-dependent damping are derived through the established three parameters constitution. Thirdly, the established element dynamic equations are assembled into the system dynamic equations of an elastic linkage mechanism by means of the kineto-elastodynamic theory, and a closed-form numerical algorithm is constructed in order to solve the high-order differential equations with time-varying coefficients. Lastly, a dynamic simulation example of a four-bar elastic linkage mechanism with damping alloy components is given. It is shown that the elastic vibration can be significantly reduced with the components replaced by damping alloy parts.