This paper investigates the dynamic behavior of functionally graded sandwich plates under multiple moving loads. The first-order shear deformation theory of plates is adopted with the effects of shear deformation and rotary inertia included. By using Lagrange’s equations, the equations of motion for the dynamic behavior of the plate are derived. Then they are solved by the Ritz and Newmark time integration methods for the free and forced vibrations of the plates with different boundary conditions. To guarantee that all terms in the admissible functions can cope with the essential boundary conditions, the Gram–Schmidt procedure is used to generate the shape functions for the Ritz method. The influences of several factors on the dynamic response of the plates, such as layer thickness ratio, boundary condition, velocity, excitation frequency, phase angle, etc., are examined and discussed in detail. The numerical study indicates that the dynamic deflection has initial fluctuated growth in the low range of moving load velocity before reaching the peak at the critical velocity, which is followed by the considerable decrease in magnitude. Besides, the gaps or distances between the moving loads also play an important role in predicting the dynamic deflections of the plate when subjected to more than one moving loads.

中文翻译：

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多重移动载荷下功能梯度夹层板的动态分析用Ritz方法和Gram-Schmidt多项式

本文研究了功能梯度夹层板在多个移动载荷下的动态行为。采用板的一阶剪切变形理论，包括剪切变形和转动惯量的影响。通过使用拉格朗日方程，导出了板块动态行为的运动方程。然后通过 Ritz 和 Newmark 时间积分方法求解不同边界条件下板的自由和受迫振动。为了保证容许函数中的所有项都可以处理基本边界条件，使用 Gram-Schmidt 程序来生成 Ritz 方法的形函数。层厚比、边界条件、速度、激励频率、相位角等进行了详细检查和讨论。数值研究表明，动态挠度在运动载荷速度的低范围内有初始波动增长，然后在临界速度达到峰值，随后幅度显着下降。此外，移动载荷之间的间隙或距离对于预测板在多个移动载荷下的动态挠度也起着重要作用。