Nonlinear energy sinks (NESs) are critically important for structural vibration suppression. They can absorb vibrational energy across a broad frequency spectrum, possess strong robustness, and have a relatively small mass. This study addresses the vibration suppression in a piecewise linear stiffness NES system under random excitation. Initially, a theoretical model of the piecewise linear stiffness NES system is developed. The piecewise linear stiffness function is approximated using Legendre polynomial approximation. Following this, the steady-state Fokker–Planck–Kolmogorov (FPK) equation of the system is formulated via the Generalized Harmonic Function Method. The FPK equation is solved using the fourth-order central difference method, and the effectiveness of this approach is validated by comparing the FDM results with numerical simulations. Lastly, the influence of varying system parameters on the stability of the piecewise linear stiffness NES system is analyzed.

非线性能量汇 (NES) 对于结构振动抑制至关重要。它们可以吸收宽频谱的振动能量，具有很强的鲁棒性，并且质量相对较小。本研究解决了随机激励下分段线性刚度 NES 系统的振动抑制问题。首先，开发了分段线性刚度 NES 系统的理论模型。使用勒让德多项式近似来近似分段线性刚度函数。随后，系统的稳态 Fokker-Planck-Kolmogorov (FPK) 方程通过广义调和函数法建立。采用四阶中心差分法求解FPK方程，并通过FDM结果与数值模拟的比较验证了该方法的有效性。最后，分析了不同系统参数对分段线性刚度NES系统稳定性的影响。