动力刚度法在修正后铁木辛柯梁上的应用

The application of the dynamic stiffness matrix in the modified Timoshenko beam

为了精确地计算出修正后铁木辛柯梁的固有频率,基于无阻尼修正后铁木辛柯梁的自由振动控制微分方程,推导出该梁理论对应的动力刚度矩阵。使用Wittrick-Williams算法来计算3种不同跨径、3种不同边界条件下结构的固有频率。通过数值分析,证明了该方法的正确性和实用性。该方法比有限元法具有高计算精度和低计算成本的优点。

In order to accurately calculate natural frequency of the modified Timoshenko beam, the dynamic stiffness matrix which comes from undamped free vibration governing equation of the modified Timoshenko beam is deduced. The well-established Wittrick-Williams algorithm can be used to calculate the frequency elegantly in three different spans and three different boundary conditions. Numerical results for the modified Timoshenko beam show that this method is not only reliable and efficient but also exact and economical compared with results from traditional FEM.