As an effective means to overcome the shortcomings of linear systems only performing well near the resonance frequency, monostable piezoelectric energy harvesters (MPEHs) have been investigated widely in the area of energy harvesting. However, it is difficult to achieve a perfectly symmetric potential energy function due to the asymmetries in magnets and materials. Therefore, the response characteristics of the asymmetric MPEHs with quartic potential function under Gaussian white noise excitation are explored in this paper. The method of moment differential equation is applied to approximately determine the output performance of the asymmetric potential MPEHs under the excitation of Gaussian white noise. For the symmetric MPEH, the influence of external excitation intensity and internal system parameters on the outputs is firstly analyzed theoretically and numerically. When a quadratic nonlinear coefficient is introduced and only using its variation to characterize the variation of the asymmetry, the output performance of the MPEH is enhanced and the power increases with an increase in the asymmetry. Particularly, the existence of asymmetry leads the system to have a nonzero mean value for the displacement response, which then influences the shape of the probability density function. In the condition that more coefficients are employed to represent the asymmetry, the influence of asymmetry on the output depends on the potential energy function’s shape.

作为克服线性系统仅在谐振频率附近表现良好的缺点的有效手段，单稳态压电能量收集器（MPEH）在能量收集领域已得到广泛研究。但是，由于磁体和材料的不对称性，很难实现完全对称的势能函数。因此，本文研究了具有高斯白噪声激励的具有四次势函数的非对称MPEHs的响应特性。应用矩微分方程方法近似确定高斯白噪声激发下非对称电位MPEHs的输出性能。对于对称MPEH，首先从理论和数值上分析了外部激励强度和内部系统参数对输出的影响。当引入二次非线性系数并且仅使用其非线性变化来表征不对称性变化时，MPEH的输出性能会增强，功率会随着不对称性的增加而增加。特别是，不对称的存在导致系统对位移响应的平均值不为零，从而影响了概率密度函数的形状。在使用更多系数表示不对称的情况下，不对称对输出的影响取决于势能函数的形状。当引入二次非线性系数并且仅使用其非线性变化来表征不对称性变化时，MPEH的输出性能会提高，功率会随着不对称性的增加而增加。特别是，不对称性的存在导致系统对位移响应的平均值不为零，从而影响了概率密度函数的形状。在使用更多系数表示不对称的情况下，不对称对输出的影响取决于势能函数的形状。当引入二次非线性系数并且仅使用其非线性变化来表征不对称性变化时，MPEH的输出性能会提高，功率会随着不对称性的增加而增加。特别是，不对称的存在导致系统对位移响应的平均值不为零，从而影响了概率密度函数的形状。在采用更多系数表示不对称的情况下，不对称对输出的影响取决于势能函数的形状。然后影响概率密度函数的形状。在使用更多系数表示不对称的情况下，不对称对输出的影响取决于势能函数的形状。然后影响概率密度函数的形状。在使用更多系数表示不对称的情况下，不对称对输出的影响取决于势能函数的形状。