A semi-analytical method for in-plane vibration analysis of a composite laminated annular and sector plate with elastic constraints is presented. The theoretical model is on the basis of a variational method and a multi-segment technique. Displacement variables are expanded by the Jacobian orthogonal polynomial. Boundary conditions and continuity conditions between segments are characterized by penalty parameters. On this basis, a series of numerical examples are given. The results show that the method has good convergence speed and accuracy. Finally, the parametric study of geometric and material parameters is carried out to provide important support for solving the in-plane characteristics of this kind of composite structure.

提出了一种具有弹性约束的叠层环形扇形板平面内振动分析的半解析方法。理论模型是基于变分方法和多段技术的。位移变量通过雅可比正交多项式展开。段之间的边界条件和连续性条件由惩罚参数表征。在此基础上，给出了一系列数值示例。结果表明，该方法具有良好的收敛速度和准确性。最后，对几何和材料参数进行了参数研究，为解决这种复合结构的面内特性提供了重要的支持。