Timoshenko简支梁的振动模态特性精确解

应用模态摄动法求解Timoshenko梁的振动模态特性，应用这一方法可将Timoshenko染无阻尼自由振动方程的求解过程加以简化，转化成一非线性代数方程组的求解，对两端简支的Timoshenko梁，得到了精确理论解，在此基础上，对比了两端简支的Timoshenko梁、Euler梁及纯剪切梁的模态特性及其影响因素，讨论了Timo-shenko简支梁自振频率随着长细比及模态数的变化情况。

Precise Solution to Modal Characteristics of Timoshenko Pin - ended Beams

A method of modal perturbation,based on Ritz vector,is developed for solving the modal characteristics of Timoshenko beam including the second effects of shear deformation and rotational inertia.In this method,the free-vibration equation of motion for Timoshenko beam,that is a partial differential equation,is transferred as a set of nonlinear algebraic equations.Therefore,the solution of the modal characteristics of the Timoshenko beam can be easily obtained by solving the algebraic equations.Appling the method to Timoshenko beam with both two pin-ended boundaries,the exact solution of its modal characteristics can be achieved.By the numerical results,the modal characteristics of Timoshenko,Euler and pure shear beams are compared.The effect of the shear deformation and rotational inertia on natural frequencies of Timoshenko pin-ended beam with the slenderness and modal numbers is investigated.