单向变厚度Levy型薄板的自由振动分析

摘要

Based on vibration theory, a new solution method for natural frequency of free vibration of Levy-plate with uni-directionally varying thickness was established by substituting an unknown function into the four-order partial differential equation of vibration with variable coefficients, and then the second Volterra integral equation was solved with quadratic spline function.The results show that the new method has the lowest natural frequency of three Levy-plates with different boundary conditions, verifying that this new solution method is reliable and simple with sufficient accuracy and can be applied for analyzing free vibration of Levy-plate with uni-directionally varying rigidity.%针对单向变厚度Levy型薄板的自由振动问题,基于薄板振动理论,将设定的挠度函数代入关于挠度的变系数四阶偏微分的振动控制方程,把变系数四阶偏微分方程求解挠度的问题转化为第二类Volterra积分方程的求解,并采用二次样条函数近似求解积分方程,建立单向变厚度Levy型薄板自由振动固有频率的求解方法.对3种不同边界条件的Levy型薄板最低固有频率的算例进行验证.研究结果表明:该方法合理可靠、计算简便,满足精度要求;该方法还可进一步推广到求解任意单向变刚度Levy型薄板自由振动的最低固有频率.