中文摘要：

采用改进傅里叶级数法（IFSM）对矩形板在任意边界下的面内自由振动特性进行了研究．将结构的位移容许函数表示为包含正弦三角级数的改进傅里叶级数，正弦三角级数的引入能够有效地解决在边界处存在的不连续或者跳跃现象；将位移容许函数的未知傅里叶展开系数看作广义变量，采用能量原理建立结构的能量泛函，结合Rayleigh—Ritz法对未知傅里叶展开系数求极值，将矩形板的面内问题转换为一个标准特征值求解问题．通过大量的数值算例，并与现有文献中解及有限元方法计算结果进行对比，验证了文中方法的正确性，结果还显示文中方法具有良好的收敛速度与计算精度．

英文摘要：

This paper deals with the in-plane free vibration of rectangular plates in arbitrary boundary conditions via the improved Fourier series method （IFSM）. In the investigation, first, the admissible functions of the plate dis- placement are expressed as an improved Fourier sine series to overcome the relevant discontinuities or jumps of elas- tic boundary conditions. Then, the unknown expansion coefficients of the admissible functions are considered as generalized variables and are determined by using the Rayleigh-Ritz technique combining with the energy functional based on the energy theory. Thus, the common in-plane vibration problem is converted into a standard eigenvalue problem. Finally, the results of rectangular plates in various boundary conditions are presented and are compared with those in the literature and with those obtained by the finite element method. It is found that the proposed method is of strong reliability, good convergence and high accuracy.