Vibration impact is often used in the piezoelectric energy harvesting (PEH) system to increase the effective bandwidth of the harvester. Viscoelastic materials have been used successfully to mitigate vibration problems in various types of mechanical systems such as buildings, cars, aircraft and industrial equipment. However, less research has been done on the energy harvesting system with impact and viscoelastic force driven by random excitation. Stochastic response of an impact PEH system with viscoelastic force under Gaussian white noise excitation is investigated in this paper. Firstly, by transforming the variables, viscoelastic force can be substituted with the stiffness and damping terms to get an approximately equivalent system without viscoelastic term. Secondly, the approximate analytical solutions are acquired by the stochastic averaging method and nonsmooth coordinate transformation. The validity of this theoretical approach is confirmed by comparing the analytical solutions with the numerical solutions derived from the Monte Carlo method. Then, the effect of noise intensity and nonlinear damping coefficient on the stochastic response of the system is discussed. It is concluded that the restitution coefficient, viscoelastic component, relaxation time and linear damping coefficient can induce the occurrence of stochastic P-bifurcation. Finally, the roles of system parameters on the mean square voltage and average output power of the energy harvester are investigated respectively.

振动冲击常用于压电能量收集 (PEH) 系统，以增加收集器的有效带宽。粘弹性材料已成功用于减轻各种类型的机械系统（例如建筑物、汽车、飞机和工业设备）中的振动问题。然而，关于随机激励驱动的冲击和粘弹力能量收集系统的研究较少。本文研究了在高斯白噪声激励下具有粘弹性力的冲击 PEH 系统的随机响应。首先，通过变量变换，可以用刚度和阻尼项代替粘弹性力，得到近似等效的不含粘弹性项的系统。第二，通过随机平均法和非光滑坐标变换得到近似解析解。通过将解析解与从蒙特卡洛方法导出的数值解进行比较，证实了该理论方法的有效性。然后，讨论了噪声强度和非线性阻尼系数对系统随机响应的影响。得出的结论是，恢复系数、粘弹性分量、弛豫时间和线性阻尼系数可以诱发随机 P 分岔的发生。最后，分别研究了系统参数对能量采集器均方电压和平均输出功率的影响。通过将解析解与从蒙特卡洛方法导出的数值解进行比较，证实了该理论方法的有效性。然后，讨论了噪声强度和非线性阻尼系数对系统随机响应的影响。得出的结论是，恢复系数、粘弹性分量、弛豫时间和线性阻尼系数可以诱发随机 P 分岔的发生。最后，分别研究了系统参数对能量采集器均方电压和平均输出功率的影响。通过将解析解与从蒙特卡洛方法导出的数值解进行比较，证实了该理论方法的有效性。然后，讨论了噪声强度和非线性阻尼系数对系统随机响应的影响。得出的结论是，恢复系数、粘弹性分量、弛豫时间和线性阻尼系数可以诱发随机 P 分岔的发生。最后，分别研究了系统参数对能量采集器均方电压和平均输出功率的影响。得出的结论是，恢复系数、粘弹性分量、弛豫时间和线性阻尼系数可以诱发随机 P 分岔的发生。最后，分别研究了系统参数对能量采集器均方电压和平均输出功率的影响。得出的结论是，恢复系数、粘弹性分量、弛豫时间和线性阻尼系数可以诱发随机 P 分岔的发生。最后，分别研究了系统参数对能量采集器均方电压和平均输出功率的影响。