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Discontinuity and non-smoothness of system displacement and velocity caused by mechanical impact make the related research on dynamics of vibro-impact systems very difficult and complex. For the sake of bypassing the problems resulting from impact to some extent, Zhuravlev and Ivanov coordinate transformations were proposed, which can effectively convert the vibro-impact system to one without impact terms. In this paper, a more direct and universal transformation for general bilateral rigid vibro-impact systems is proposed. It is inspired by the main technique of Ivanov transformation, which makes the trajectories remain continuous in an auxiliary phase space. It can be directly applied to common vibro-impact systems, whether the positions of barriers are symmetrical or the restitution coefficients of barriers on both sides are consistent. In particular, this method can also be applied to the unilateral vibro-impact system. Validity of the proposed methodology is examined by means of case studies.

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The mechanism of stochastic factors in wind load on iced transmission line galloping has attracted widespread attention. In this paper, the random part of wind load is simulated by Gaussian white noise, and a galloping model of the iced transmission line excited by stochastic wind is established. The path integration method based on the Gauss–Legendre formula and short-time approximation is used to solve the steady-state probability density function of the system and the evolution of the transient probability density. The resonance response of the system is considered when the fluctuating wind acts. Meanwhile, through path integration, the stability of galloping motion is evaluated based on the first passage theory. Comparing with the Monte Carlo simulation, the effectiveness of the proposed method is verified. It turns out that the large external excitation intensity and the small natural frequency are not conducive to the stability of iced transmission line galloping.

This paper proposes a non-convex penalty regression method to identify governing equations of nonlinear dynamical systems from noisy state measurements. The idea to connect the non-convex penalty function instead of the l1 - norm with least squares is due to the fact that the l1 - norm excessively penalizes large coefficients and may incur estimation bias. The purpose of this work is to improve the accuracy and robustness in regression tasks. A threshold non-convex penalty sparse least squares optimization algorithm is developed, wherein the threshold parameter is selected using the L-curve criterion. With two examples of nonlinear dynamical systems, we illustrate the accuracy and robustness of the non-convex penalty least squares on noisy state measurements, indicating the validity of our method in a wide range of potential applications.