应用数学和力学2025，Vol.46Issue(12)：1540-1549,10.DOI:10.21656/1000-0887.450292
修正Timoshenko梁系统的归一化与对偶关系
Normalization and Duality Relations of Modified Timoshenko Beams
摘要
Abstract
The duality conditions and classification of the modified Timoshenko beam systems were investiga-ted,with its theoretical significance highlighted.First,the modified dynamic equations for the Timoshenko beam were normalized through time and space scaling transformations.Based on the normalized equations,the existence of parametric duality relations was established under arbitrary identical boundary conditions.Next,the parametric dual characteristics corresponding to different cross-sectional geometries were analyzed.Finally,under clamped-hinged,clamped-clamped,and clamped-free boundary conditions,the normalized equations were solved,to develop a novel method for building dual beams.Through examples from the literatures,the parametric dual characteristics of modified Timoshenko beams were further elucidated.The results demonstrate that,the frequencies of the modified Timoshenko dual beams derived via the normalization algorithm are identi-cal,which confirms the parametric dual conditions of the modified beams.This study reveals that the paramet-ric duality of dynamic properties is an intrinsic feature of modified Timoshenko beams,and the time and space scaling transformations provide a robust framework for uncovering these properties.关键词
修正Timoshenko梁/对偶关系/归一化算法/动力学方程Key words
modified Timoshenko beam/duality relation/normalization algorithm/dynamic equation分类
生物科学引用本文复制引用
蔡汶秀,郑罡,唐宇,孙测世,叶念雨,薛文琪..修正Timoshenko梁系统的归一化与对偶关系[J].应用数学和力学,2025,46(12):1540-1549,10.基金项目
国家自然科学基金(52378284) （52378284）
