The SDOF vibro-impact under stochastic excitation belongs to very typical non-smooth system which is taken as the main object of study. This paper analyzes the steady-state responses of the system and studies the influence of noise on its response, then obtains the stationary probability densities of amplitude, total energy and displacement and the joint probability density of the velocity of the system and uses the numerical simulation to verify its correctness.%以随机激励下单自由度碰撞振动系统这种非常具有代表性的非光滑系统作为主要研究对象,分析了此类系统的稳态响应并研究了噪声对系统响应的影响,分别得到了该系统的位移、能量、幅值的稳态概率密度以及位移与速度的联合概率密度,并利用数值模拟验算了该方法的准确性.
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