基于含广义节点自由度单元的板面内振动分析OA

To improve the accuracy and numerical stability of in-plane vibration analysis for thin plates,this paper proposes a four-node rectangular finite element(NQ4-24D)including the generalized nodal degrees of freedom.The proposed element aims to overcome the poor convergence and limited accuracy associated with conventional ele-ments in in-plane vibration problems.Each node of the element incorporates displacements and their first-order par-tial derivatives as degrees of freedom.A two-dimensional Hermite interpolation function is employed to construct the displacement field,from which the corresponding stiffness and mass matrices are derived.Free vibration analyses of rectangular thin plates under fully free and fully simply supported boundary conditions are conducted.The computed natural frequencies are compared with reference solutions from the literature and results obtained using the conven-tional Q4 element.The results demonstrate that the proposed element achieves higher accuracy and faster conver-gence,especially under complex boundary conditions.The NQ4-24D element exhibits significant advantages in in-plane vibration analysis and provides an efficient and reliable finite element approach for high-precision dynamic analysis of thin plate structures.