中文摘要：

用局部加权残值法建立了非均质中厚板的局部径向点插值离散系统方程，采用无网格局部径向点插值法分析了非均质中厚板的自由振动和强迫振动问题。用径向基函数耦合多项式基函数来近似试函数，用四次样条函数做为加权残值法中的权函数。所构造的形函数具有Kronecker delta性质，可以很方便地施加本质边界条件。该方法不需要任何形式的网格划分，所有的积分都在规则形状的子域及其边界上进行。在计算过程中，取积分中的高斯点的材料参数来模拟问题域材料特性的变化。计算结果表明。利用该方法计算非均质中厚板的自由振动和强迫振动问题可以得到具有较高精度的解。

英文摘要：

The meshless local radial point interpolation method （LRPIM） for solving free vibration and forced vibration problems for a non-homogeneous moderately thick plate is presented in this paper. The discretized system equation of the moderately thick plate is obtained using a locally weighted residual method. It uses a radial basis function （RBF） coupled with a polynomial basis function as a trial function, and uses the quartic spline function as a test function of the weighted residual method. The shape function has the Kronecker delta function properties, and no additional treatment to impose essential boundary conditions. The present method is a true meshless method as it doesn＇t need any grids, and all integrals can he easily evaluated over regularly shaped domains and their boundaries. In computational procedures, variations of material properties in the considered domain are simulated by adopting proper material parameters at Gauss points in integrations. The numerical results indicate that the presented method can give quite accurate results to free vibration and forced vibration problems of the non- homogeneous moderately thick plate.