热过屈曲梁振动的解析解  

ANALYTICAL SOLUTIONS FOR VIBRATION OF THERMAL BUCKLED BEAMS

作　　者：马连生[1] 

机构地区：[1]兰州理工大学理学院,兰州730050

出　　处：《工程力学》2012年第10期1-4,12,共5页Engineering Mechanics

基　　金：国家自然科学基金项目(11072100);甘肃省教育厅项目(0603B-05);兰州理工大学工程力学重点学科团队项目

摘　　要：该文导出了面内热载荷作用下,梁在其过屈曲构形附近微幅振动的解析解。首先基于经典梁理论,推导了控制轴向和横向变形的基本方程。然后,将2个非线性方程化为一个关于横向挠度的四阶非线性积分-微分方程。假设梁的振幅以及由此引起的附加应变为无限小,另设其响应为谐振,则该非线性积分-微分方程将化为两组耦合的微分方程:一组控制非线性静态响应;另一组就是叠加于梁屈曲构形之上的线性振动方程。直接求解这些问题,可以得到梁热过屈曲构形以及固有频率的解析解,这些解是外加热载荷的函数。该文得到的精确解可以用于验证或改进各类近似理论和数值方法。Analytical solution is obtained for the dynamic responses in the vicinity of the buckled configuration of beams subjected to a uniform in-plane thermal loading.The equations governing the axial and transverse deformations of FGM beams are derived based on the classical beam theory.Then,the two equations are reduced to a single nonlinear fourth-order integral-differential equation governing the transverse deformations.By assuming that the amplitude of beam’s vibration and the additional strains induced in it are infinitesimal,and its response harmonic,the non-linear partial differential equations are reduced to two sets of coupled ordinary differential equations;one for the nonlinear static response,and the other for linear vibrations of the beam superimposed upon the buckled configuration.The nonlinear equation is directly solved and analytical solutions for static response and natural frequency are obtained as a function of the applied thermal load.The exact solutions obtained herein can be served as benchmarks to verify and improve various approximate theories and numerical methods.

关 键 词：精确解 固有频率 梁 面内热载荷 过屈曲 

分 类 号：TU323.3[建筑科学—结构工程]