【摘要】 研究了具有双边碰撞约束的形状记忆合金梁非线性随机响应问题。首先，基于双边碰撞约束下的形状记忆合金梁模型，分析了形状记忆合金梁振动系统在碰撞过程的总能量与碰撞位置之间的势能关系，计算出了系统在碰撞过程中的能量损失。其次，利用能量包线随机平均法讨论了当H<G(Δ)和H>G(Δ)时系统的漂移系数和扩散系数，从而获得了Fokker-Planck-Kolmogorov(FPK)方程和系统的稳态概率密度函数。最后，通过蒙特卡罗方法验证了能量包线随机平均法的有效性，探讨了恢复因子、碰撞约束位置、噪声强度等参数对系统总能量稳态概率密度的影响。更多还原

【Abstract】 In this paper, the nonlinear stochastic response of shape memory alloy beams with bilateral collision constraints is studied.Firstly, based on the shape memory alloy beam model with bilateral impact constraints, the relationship between the total energy of the shape memory alloy beam and the potential energy of the collision position is analyzed, and the energy loss of the system in the collision process is calculated.Secondly, the drift coefficient and diffusion H<G(Δ) and H>G(Δ) coefficient of the system are discussed by using the random average method of energy envelope.Thus, the Fokker-Planck Kolmogorov(FPK) equation and the steady-state probability density function of the system are obtained.Finally, Monte Carlo method is used to verify the effectiveness of the energy envelope random average method, and the effects of recovery factor, collision constraint position, noise intensity and other parameters on the steady-state probability density of the total energy of the system are analyzed.更多还原