Abstract
It is well-known that practical vibro-impact systems are often influenced by random perturbations and external excitation forces, making it challenging to carry out the research of this category of complex systems with non-smooth characteristics. To address this problem, by adequately utilizing the stochastic response analysis approach and performing the stochastic response for the considered non-smooth system with the external excitation force and white noise excitation, a modified conducting process has proposed. Taking the multiple nonlinear parameters, the non-smooth parameters, and the external excitation frequency into consideration, the steady-state stochastic P-bifurcation phenomena of an elastic impact oscillator are discussed. It can be found that the system parameters can make the system stability topology change. The effectiveness of the proposed method is verified and demonstrated by the Monte Carlo (MC) simulation. Consequently, the conclusions show that the process can be applied to stochastic non-autonomous and non-smooth systems.
Highlights
Non-smooth systems are a major area of interest within the field of non-linear dynamics, which can be applied to the modeling of many nonlinear dynamic phenomena in the fields of aerospace, structural engineering, and mechanical engineering[1,2,3,4,5]
It is proven that the method is well coincident with the Monte Carlo (MC) simulation method
This study strengthens the idea that there is no need to change the one-step transition probability matrix once it is obtained, and we just need to calculate the matrix iteration multiplication to obtain the probability density functions (PDFs)
Summary
Non-smooth systems are a major area of interest within the field of non-linear dynamics, which can be applied to the modeling of many nonlinear dynamic phenomena in the fields of aerospace, structural engineering, and mechanical engineering[1,2,3,4,5]. With the development of nonlinear disciplines and the upgrading of computers, there are many effective methods to study the responses of such systems, including analytical methods and numerical algorithms[13,14,15,16]. Unless performing the approximate transformation, there are seldom rigorous analytical methods used to solve non-smooth systems directly. Wang et al.[26] proposed an improved cell mapping algorithm for solving original non-smooth impact systems. A special and fast cell mapping method is used to calculate the PDFs of non-autonomous vibro-impact system for the first time.
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