碰撞过程凭借瞬时冲击模型得以简化,但采用经典的Newton恢复系数模型为计算带来了误差.本研究引入修正的恢复系数模型取代经典的Newton恢复系数模型,预测了一类宽带噪声激励下双边碰撞振动系统的随机动力学响应.位移的碰撞条件借助自由振动系统被转化为能量的碰撞条件.根据系统的能量水平,系统的运动可被分为双边碰撞和无碰撞振动两类.进一步地,两类运动的平均漂移系数和扩散系数可借助能量包线随机平均法求解获得.在此基础上,建立并求解对应的Fokker-Plank-Kolmogorov(FPK)方程,进而得到系统的稳态响应.最后,将所提方法应用于Duffing振子,讨论了屈服速度、挡板间距和噪声激励对响应的影响,并用蒙特卡罗模拟验证了所述方法的有效性.
The vibro-impact process is simplified by the instantaneous impact model,but the classical Newton's restitution coefficient model adopted brings errors in the calculation.In this paper,a modified restitution coefficient model is introduced to replace the classical Newton's model of restitution coefficient,and the stochastic response of a class of vibro-impact systems with bilateral barriers under broad-band noise excitation is investigated.Based on the energy levels of the system,its motion can be categorized into two types:non-colliding vibration and bilateral collision vibration.Subsequently,the average drift and diffusion coefficients for these two types of motion are determined using the energy envelope random averaging method.On this basis,the corresponding Fokker-Planck-Kolmogorov(FPK)equation is established and solved,leading to the steady-state response of the system.For illustration,the proposed method is applied to the Duffing oscillator.The effects of the yield velocity,interval and the noise excitations on the PDFs of stationary responses are examined,and the validation of analytical results is verified by the Monte Carlo simulation data.