The stationary probability density function (PDF) solution of a variable-mass system is calculated under Gaussian white noises and Poisson white noises, respectively. For small mass disturbance, the corresponding Fokker–Planck–Kolmogorov equation and Kolmogorov–Feller equation of the system are derived. The solution procedure based on the exponential–polynomial closure (EPC) method is formulated to obtain and study the probabilistic solutions of the strongly nonlinear variable-mass system subjected to Gaussian white noises and Poisson white noises. Both odd and even nonlinear variable-mass systems are considered. Compared with Monte Carlo simulation results, good agreement is achieved with the EPC method in the case of sixth-order polynomial. For large mass disturbance, the PDFs and logarithmic PDFs of displacement and velocity are numerically calculated via the fourth-order Runge–Kutta algorithm.

中文翻译：

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随机激励下变质量系统的概率解

分别在高斯白噪声和泊松白噪声下计算变质量系统的平稳概率密度函数 (PDF) 解。对于小质量扰动，推导出系统相应的 Fokker-Planck-Kolmogorov 方程和 Kolmogorov-Feller 方程。制定了基于指数多项式闭包 (EPC) 方法的求解程序，以获取和研究受高斯白噪声和泊松白噪声影响的强非线性可变质量系统的概率解。奇数和偶数非线性可变质量系统都被考虑。与蒙特卡罗模拟结果相比，EPC 方法在六阶多项式的情况下具有较好的一致性。对于大质量扰动，