铁木辛柯梁固有振动频率的边界元解法

根据傅里叶变换推导具有两个广义位移的铁木辛柯梁固有振动的基本解.利用加权残量方法,从控制微分方程出发建立边界积分方程,进而根据边界条件得到频率方程,采用代数特征值方法和影响系数方法求解频率,并分析了两种方法的特点.以杆为例证明了对于一维均匀结构,对不同的边界条件利用边界元方法(BEM,Boundary Element Method)都可以得到精确频率.将铁木辛柯梁的BEM结果与有限元结果和精确解进行了比较.

Boundary element solution method of free vibration of Timoshenko beam

The fundamental solution for free vibration of Timoshenko beam was derived using the Fourier transform.Weighted residual method was adapted to deduce the boundary integral formulation from the control differential equations,from which and using boundary conditions one could find the frequency equation which could be solved through algebraic eigenvalue method and influence coefficient method.For any boundary condition,natural frequencies via boundary element method(BEM) for uniform 1D structure are exact,which is validated via the case of rod.The frequencies by BEM of Timoshenko beam were compared with those of finite element method(FEM) and the exact ones.