不同理论下圆板特征值之间的解析关系

基于经典板理论（CPT）、一阶剪切变形板理论（FPT）以及Reddy三阶剪切变形板理论（RPT）之间，圆板轴对称特征值问题在数学上的相似性，研究了不同理论之间圆板特征值间的解析关系．将特征值问题的求解转化为代数方程的求解，并导出了不同理论之间圆板特征值的显式精确解析关系．从而。只要已知圆板特征值（临界屈曲载荷和固有频率）的经典结果，便很容易从这些解析关系中得到一阶和三阶理论下圆板特征值的相应结果。这便于工程应用，同时也可检验一阶和三阶理论下板特征值的数值结果的有效性、收敛性以及精确性等问题．

Analytical Relations Between the Eigenvalues of Circular Plate Based on Various Plate Theories

Based on the mathematical similarity of the axisymmetric eigenvalue problems of a circular plate between the classical plate theory(CPT),the first-order shear deformation plate theory(FPT) and the Reddy's third-order shear deformation plate theory(RPT),analytical relations between the eigenvalues of circular plate based on various plate theories are investigated.The eigenvalue problem was transformed to solve an algebra equation.Analytical relationships that were expressed explicitly between various theories were presented.Therefore,from these relationships obtained one can easily obtain the exact RPT and FPT solutions of critical buckling load and natural frequency for a circular plate with CPT solutions.The relationships are useful for engineering application,and can be used to check the validity,convergence and accuracy of numerical results for the eigenvalue problem of plates.