The main aim of this paper is to examine the efficiency and the effect of various single-term weighted residual methods, including Bubnov–Galerkin, least squares, and point collocation methods on the free vibration behavior of viscoelastic plates. The refined classical plate theory and Kelvin–Voigt/standard solid viscoelastic models are adopted for kinematic and constitutive relations of foam plates, respectively. The spatial domain is discretized using weighted residual methods with shape functions of bending component of transverse deflections. The resulted algebraic eigenvalue problems with frequency-dependent coefficients are solved via an iterative numerical algorithm. For elastic plates, the present results based on four different methods are compared with their counterparts which are obtained based on 3-dimensional, classical, first- and higher-order shear deformation theories under Navier, Levy, and fully clamped boundary conditions. For simply supported viscoelastic plates, frequencies are compared with exact solutions, and acceptable accuracy is observed. Then, parametric studies are undertaken to assess the vibration mode, bulk/shear ratio, thickness ratio, material model, and boundary condition. From these results, it is revealed that bulk–shear ratio is a key factor while material model makes no significant difference on the real part of the vibration frequencies of fully free plates.

本文的主要目的是研究各种单项加权残差方法（包括Bubnov-Galerkin，最小二乘和点配置方法）对粘弹性板自由振动行为的效率和效果。泡沫板的运动学和本构关系分别采用改进的经典板理论和开尔文-沃伊格/标准固体粘弹性模型。使用权重残差法将空间域离散化，权重残差法具有横向偏转的弯曲分量的形状函数。通过迭代数值算法解决由此产生的具有频率相关系数的代数特征值问题。对于弹性板，将基于四种不同方法的当前结果与基于3维，经典，Navier，Levy和完全夹紧的边界条件下的一阶和高阶剪切变形理论。对于简单支撑的粘弹性板，将频率与精确解进行比较，并观察到可接受的精度。然后，进行参数研究以评估振动模式，体积/剪切比，厚度比，材料模型和边界条件。从这些结果可以看出，体积-剪切比是一个关键因素，而材料模型对完全自由板的振动频率的实部没有显着影响。进行了参数研究，以评估振动模式，体积/剪切比，厚度比，材料模型和边界条件。从这些结果可以看出，体积-剪切比是一个关键因素，而材料模型对完全自由板的振动频率的实部没有显着影响。进行了参数研究，以评估振动模式，体积/剪切比，厚度比，材料模型和边界条件。从这些结果可以看出，体积-剪切比是一个关键因素，而材料模型对完全自由板的振动频率的实部没有显着影响。