Random vibration of viscoelastic system under broad-band excitations |
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Authors: | WQ Zhu |
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Institution: | a Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China b Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431, USA |
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Abstract: | An analytical method is proposed to study the response of a viscoelastic system with strongly non-linear stiffness force and under broad-band random excitations. The random excitations can be additive, or multiplicative, or both, and they can be stationary or non-stationary with evolutionary spectra. With the proposed method, contributions of the viscoelastic force to both damping and stiffness are taken into account separately, and then the extended version of the stochastic averaging, called the quasi-conservative averaging, is applied to the system to derive the averaged equation of energy envelope. Probability density functions of system responses, such as the total energy, the amplitude, and the state variables, can then be obtained analytically. The accuracy of the method is substantiated by comparing the analytical results with those from Monte Carlo simulations. Effects of parameters in the viscoelastic force and in the non-linear stiffness force on the system responses are also investigated. |
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Keywords: | Random vibration Viscoelastic force Strongly non-linear system Stochastic averaging method Broad-band excitations |
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