弹性地基上铁摩辛柯梁的压弯问题  

Compressing and Bending Problem of Timoshenko Beam on Elastic Foundation

作　　者：胡昌颖[1] 

机构地区：[1]河北工程大学土木工程学院,河北邯郸056038

出　　处：《四川建材》2012年第4期51-52,共2页Sichuan Building Materials

摘　　要：从哈密顿力学出发,由勒让德变换引入对偶变量,导出了弹性地基上铁摩辛柯梁压弯问题的哈密顿对偶求解体系,将梁的控制微分方程转化为哈密顿对偶方程,给出了问题的矩阵指数函数解,可用本征向量展开法求问题的解析解,也可用精细积分法求问题的高精度数值解,由于导出的系统矩阵具有辛矩阵的特性,数值计算具有良好的稳定性。Based on Hamiltonian mechanics,Hamiltonian dual system of compressing and bending problem of Timoshenko beam on elastic foundation can be obtained by introducing dual variables through Legendre transform.The differential equation of the beam is converted into Hamiltonian canonical equation.The solution to the equation then obtained in Matrix exponential function form.Afterwards,analytical solution can be found through eigenvector expansion method.Alternatively,the high-precision numerical solution can be worked out through precise integration methods.Since the obtained systematic matrix holds the properties of the sympletic matrix,the numerical calculation is of a good stability.

关 键 词：弹性地基 铁摩辛柯梁 压弯问题 哈密顿对偶体系 正则方程 

分 类 号：TU3[建筑科学—结构工程]