用复模态分析方法研究了在两端简支和固支边界下,轴向受载粘弹性Timoshenko梁自由振动的固有频率、衰减系数和模态函数的特性,给出了模态函数的正交性条件.通过数值算例,讨论了长宽比、轴力和粘弹性系数对梁的固有频率、衰减系数和模态函数的影响.数值结果表明增加轴力使梁的固有频率变大、模态函数幅值变小,但衰减系数 变化不明显；粘弹性系数的增大对梁的固有频率与模态函数幅值影响较小,而衰减系数明显增大.%The natural frequencies,modes and decrement coefficients of a Kelvin viscoelastic Timoshenko beam with two typical boundary conditions including clamped-clamped and pinned-pinned suffering axial tension were investigated by using the complex modal analysis approach. The orthogonality conditions of mode functions were derived from the equations of motion. The effects of some parameters,such as,length-to-depth ratio,axial load and coefficients of viscoelasticity on the frequencies,decrement coefficients and modes were examined,respectively,while other parameters were fixed in several numerical examples. It was shown that the natural frequencies of the beam grow with increase in axial tension,meanwhile the amplitudes of the mode functions drop,the changes of the decrement coefficients are not obvious. The effect of increase in viscoelasticity coefficient on the natural frequencies and the amplitudes of the mode functions is smaller,but the decrement coefficients grow apparently.
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