Abstract
Nonlinear vibration systems with adjustable stiffness property have attracted considerable attentions for their prominent broadband performances. In the present manuscript, we consider the stochastic dynamical systems with adjustable stiffness and proposed a numerical method for the random responses analysis of the Gaussian white noise excited systems. A multi-dimensional Fokker-Plank-Kolmogorov equation governing the joint probability density of the mechanical states is derived according to the theory of diffusion processes. We solve the multi-dimensional equation using a splitting method and obtained the stationary probability densities and the mean-square responses directly. Two classical nonlinear vibration systems with adjustable stiffness, including the energy harvesting system and the Duffing system with Dahl friction, are presented as examples. Their comparisons with the results from Monte-Carlo simulations illustrate the effectiveness of the proposed procedure for both monostable and bistable cases, even for cases with strong excitation. In addition, the splitting method is efficient for higher-dimensional problem and has advantages of simple implementation, less storage of intermediate values and so on. Hence, in terms of the application scope, the proposed procedure is superior to the current mainstream methods for the random response evaluation of nonlinear vibration systems with adjustable stiffness.
Highlights
Nonlinear systems with noise have attracted considerable attentions over the last few decades
Jin et al [8] employed the equivalent nonlinearization technique and imported the generalized harmonic transformation to establish a semi-analytical solution of random response for nonlinear vibration energy harvesters subjected to Gaussian white noise excitation
We investigate the random responses of the nonlinear vibration systems with adjustable stiffness property under Gaussian white noise excitation
Summary
Nonlinear systems with noise have attracted considerable attentions over the last few decades. Xu et al [7] used the same approach to investigate the random vibration with inelastic impact subject to Gaussian white noise, so as to analytically obtain the joint probability density of nonlinear system and the statistics of system response. Jin et al [8] employed the equivalent nonlinearization technique and imported the generalized harmonic transformation to establish a semi-analytical solution of random response for nonlinear vibration energy harvesters subjected to Gaussian white noise excitation. From the investigations and results in previous studies, the equivalent nonlinearization technique [6,7,8] and the stochastic averaging method [12,13,14,15,16,17] have been widely applied in the random response evaluation due to their accuracy and simplicity. We compare the results obtained by splitting method with those from Monte-Carlo simulations (MCS) and evaluate the effectiveness and the applicability of the proposed procedure for both mono-stable and bi-stable cases
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