中文摘要：

研究了轴向加速黏弹性Timoshenko梁的非线性参数振动．参数激励是由径向变化张力和轴向速度波动引起的．引入了取决于轴向加速度的径向变化张力，同时还考虑了有限支撑刚度对张力的影响．应用广义哈密尔顿原理建立了Timoshenko梁耦合平面运动的控制方程和相关的边界条件．黏弹性本构关系采用Kelvin模型并引入物质时间导数．耦合方程简化为具有随时间和空间变化系数的积分一偏微分型非线性方程．采用直接多尺度法分析了Timoshenko梁的组合参数共振．根据可解性条件得到了Timoshenko梁的稳态响应，并应用Routh—Hurvitz判据确定了稳态响应的稳定性．最后通过一系列数值例子描述了黏弹性系数、平均轴向速度、剪切变形系数、转动惯量系数、速度脉动幅值、有限支撑刚度参数以及非线性系数对稳态响应的影响．

英文摘要：

Nonlinear parametric vibrations are investigated for axially accelerating viscoelastic Timoshenko beams sub- ject to parametric excitations resulting from longitudinally varying tensions and axial accelerations. The dependence of the tension on the finite axial support rigidity is also considered. The goveming equations of coupled planar vibration of the Timoshenko beam and the associated boundary conditions are established from the generalized Hamilton principle and the Kelvin viscoelastic constitutive relation. The governing equation of transverse vibration is simplified into a nonlinear integro-partial-differential equation with time-dependent and space-dependent coefficients. The method of multiple scales is employed to investigate parametric resonances with the focus on steady-state responses. Some numerical examples are presented to demonstrate the effects of the viscosity coefficient, the mean axial speed, the axial speed fluctuation ampli- tude, the large rotary inertia, the rotary inertia, and the small nonlinear coefficient on the amplitudes of the steady-state oscillating response.