Data from: A generalized solution procedure for in-plane free vibration of rectangular plates and annular sectorial plates

A generalized solution procedure is developed for in-plane free vibration of rectangular and annular sectorial plates with general boundary conditions. For the annular sectorial plate, the introduction of a logarithmic radial variable simplifies the basic theory and the expression of the total energy. The coordinates, geometric parameters and potential energy for the two different shapes are organized in a unified framework such that a generalized solving procedure becomes feasible. By using the improved Fourier-Ritz approach, the admissible functions are formulated in trigonometric form, which allows the explicit assembly of global mass and stiffness matrices for both rectangular and annular sectorial plates, thereby making the method computationally effective, especially when analyzing annular sectorial plates. Moreover, the improved Fourier expansion eliminates the potential discontinuity of the original normal and tangential displacement functions and their derivatives in the entire domain, and accelerates the convergence. The generalized Fourier-Ritz approach for both shapes has the characteristics of generality, accuracy and efficiency. These features are demonstrated via a few numerical examples.

针对具有一般边界条件的矩形板与环形扇形板的面内自由振动问题，本文构建了一套广义求解流程。对于环形扇形板，引入对数径向变量可简化基础理论与总能量表达式。将两种板形的坐标、几何参数及势能统一纳入同一分析框架，使得广义求解流程具备可行性。通过改进的傅里叶-里兹（Fourier-Ritz）法，以三角形式构建容许函数，可显式组装矩形板与环形扇形板的整体质量矩阵与刚度矩阵，进而提升该方法的计算效率，尤其在分析环形扇形板时效果突出。此外，改进的傅里叶展开可消除全域内原始法向、切向位移函数及其导数的潜在间断性，并加快收敛速度。针对这两种板形的广义傅里叶-里兹法兼具通用性、准确性与高效性。通过若干数值算例验证了该方法的上述特性。