Random Response Study of Hard Spring Slip System Shi Zhixiao 1. Xing Xuejun Li Dawang, Mi Dexian 21. School of Civil Engineering, Zhengzhou University. Zhengzhou, Henan 450002; 2. Analytical solution of China Chemical Engineering Construction Company, Shanxi Taiyuan 030031. Compared with the Monte Carlo simulation solution, the analytical solution can predict the steady-state Gaussian random response of the slip system.
The sliding friction system is a common base isolation measure. Because it has strong vibration nonlinearity, the corresponding dynamic reliability analysis is difficult. In this paper, the dynamic reliability of the pure plane friction slip system without reset mechanism is studied. The literature discusses the vibration reliability of the slip system with linear resilience mechanism. The literature 3 advances the corresponding optimization design. However, the study of random response gauges for the Gaussian ground effect of a planar slip system with a hard return spring. The author did not report this article as an analytical model. It is proposed to use the equivalent line method to analytically predict the steady-state random response of the system and evaluate the viscosity of the analytical solution by Monte Carlo simulation. The vibrational differential equation and its equivalent linearized analytical solution assume that the frictional force on the sliding interface is satisfied. Coulomb's law, the dynamic balance equation of a rigid slip-isolated system with a gradually hardening spring is a white noise random process is the dynamic friction coefficient of the material on the sliding interface, and the gravity acceleration is the system parameter.
Equation 1 is a nonlinear equation. Consider the following damping linearization equation approximation instead of the Cambodian call 7, error. The mean square of 1 is small. It can be based on the base, the position of the system, the probability density function of the 7 and the velocity 7 response, and the Bessel function of 4, which is obtained by the formula 5 and the 1414 order correction.
Substituting the formulas 6 and 7 into the formula 3, the equivalent linearization coefficient fund project Henan Provincial Education Commission Natural Science Foundation funded project 19995700034 inch 13 value substitution type 4 and 5 can obtain the probability density function of the steady state displacement and velocity response of the system.
2 Monte Carlo simulation now evaluates the accuracy of the above analytical solution with numerical simulation results. The digital simulation is performed according to Equation 1. At this time, the Gaussian white noise ground action is first converted into the following time series and connected in a linear manner. Where 1 is the independent sequence generated by the standard normal distribution random number generator, = 27, which is the sampling interval, and 4 = 0.01 in this paper.
3 Results and conclusions The distribution law of the steady-state displacement and velocity response probability density function of the system is basically the same as the digital simulation result. It is feasible to use the equivalent linearization method to analyze the steady-state random response of the prediction system.
Fi Hongfeng, Wang Qianxin, Jiang Jinren. Random Slip Response and Reliability Analysis of Base Sliding Isolation Rigid Structure 1. Earthquake Engineering and Engineering Vibration, 1991323 Li Dawang, Huo Da, Jin Yan, et al. Optimal Design of Sliding Isolation System Based on Dynamic Reliability Analysis 1. Earthquake Engineering and Engineering Vibration, 1998, 1848 4 Zhu Zhuqiu. Randomly vibrate the elbow. Beijing Science Press, 1992.
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