苏州科技大学学报（自然科学版）2026，Vol.43Issue(1)：12-19,8.DOI:10.12084/j.issn.2096-3289.2026.01.002
基于含广义节点自由度单元的板面内振动分析
In-plane vibration analysis of plates based on elements with generalized nodal degrees of freedom
摘要
Abstract
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.关键词
矩形板/面内振动/Hermite插值/固有频率Key words
rectangular plate/in-plane vibration/Hermite interpolation/natural frequency分类
数理科学引用本文复制引用
仝建坤,鲍四元..基于含广义节点自由度单元的板面内振动分析[J].苏州科技大学学报（自然科学版）,2026,43(1):12-19,8.基金项目
国家自然科学基金项目(12572003) （12572003）
