非局部薄板动力学特性分析的广义有限积分变换方法

基于应力梯度非局部薄板理论模型,推导了非局部薄板动力学特性求解的广义有限积分变换方法。通过选取适应边界条件的积分核函数并构建广义积分变换对,应用积分变换将非局部薄板的高阶偏微分方程变换成线性方程组,直接求解得到固有频率。将广义有限积分变换方法的计算结果和有限元法及已有文献的结果进行对比,验证了本文方法的正确性。在此基础上,又研究了非局部参数、薄板的尺度对系统固有频率的影响。该方法为非局部薄板模型的求解提供了一个新的途径。

Generalized finite integral transform method for dynamic characteristic analysis of nonlocal thin plate

The generalized finite integral transform method was applied to get the dynamic characteristic of a nonlocal thin plate based on the stress gradient nonlocal theory. The integral transform pairs were established by using the integral kernels which can satisfy the boundary conditions. The higher-order partial differential equation of the nonlocal thin plate was transformed in to a series of linear algebraic equations through the integral transform, and the nature frequencies of the governing equations can be solved exactly. To confirm the validity of the simulated, the results were compared with the finite element method and the existing ones. The effects of the nonlocal parameter and the dimension of the plate on the nature frequency were studied. The proposed method provides a new way to solve the mathematical problem of the nonlocal plate problem.