圆弧曲梁振动微分方程推导及振动特性分析  

Derivation of Vibration Differential Equation and Analysis of Vibration Properties about ARC-Curved Beam

作　　者：宋郁民[1] 吴定俊[1] 李奇[1] 

机构地区：[1]同济大学桥梁工程系,上海200092

出　　处：《沈阳建筑大学学报（自然科学版）》2012年第3期400-404,共5页Journal of Shenyang Jianzhu University：Natural Science

基　　金：国家自然科学基金项目(50908178)

摘　　要：目的为研究圆弧曲线梁的振动特性.方法以振动状态下的圆弧曲线梁微段为研究对象,考虑了截面的约束扭转,建立了动内力平衡方程.在引入Timoshenko几何方程和物理方程后,推导得出了圆弧曲线梁的振动微分方程,并对得出的振动方程加以分析.结果当圆弧曲线梁半径趋于无穷大时,且截面退化为轴对称截面时,曲线梁的振动微分方程可退化为直线梁的轴向振动方程、横向振动方程和扭转振动方程.通过对振动微分方程的分析,得出了圆弧曲线梁面内振动和面外振动的特性.结论曲线梁的面内振动与面外振动互不耦合;曲梁面内的纵向振动和横向振动相互耦合;曲梁面外的竖向弯曲振动和扭转振动相互耦合.初步论证了圆弧曲线梁振动微分方程的正确性.This paper is to study the dynamic characteristics of arc-curved. The vibration differential equations of arc-curved beam are derived; some characteristics are obtained by analyzing the derived vibration differential equation. Considering of the constrained torsion of cross-section, the internal force balance equations of arc-curved beam are obtained by analyzing a segment in the vibration state, and the vibration differential equations of arc-curved beam are derived by combining with the Timoshenko＇s geometric equations and physics equations. By analyzing the derived vibration differential equation, the vibration differential e- quation of arc-curved beam can turn into longitudinal vibration equation, lateral vibration equation and torsional vibration equation of straight beam when radius tends to infinity and cross-section turns into circle, which illustrates preliminarily that the vibration differential equation of arc-curved beam is correct. Some conclusions, for example that the in-plane-vibration and the out-of-plane-vibration are not coupled;longitudinal vibration and lateral vibration in plane is mutually coupling;vertical bending vibration and torsional vi- bration out of plane is mutually coupling too, are gotten through discussing its vibration differential equation.

关 键 词：圆弧曲线梁 振动 微分方程 振动特性 求解方法 

分 类 号：U441.2[建筑科学—桥梁与隧道工程]