轴向运动黏弹性Timoshenko梁横向非线性强受迫振动

研究轴向运动黏弹性Timoshenko梁横向非线性强受迫振动的稳态响应。由广义Hamilton变分原理推导出轴向运动黏弹性Timoshenko梁横向振动的控制方程及相应的边界条件。模型中考虑剪切模量、转动惯量对梁的影响。黏弹性本构关系中运用Kelvin模型并引入物质时间导数。对控制方程施用直接多尺度法,建立强受迫共振的可解性条件,得到稳态响应振幅与激励频率关系曲线。应用Routh-Hurwitz判据判断稳态响应振幅的稳定性。利用数值结果给出不同参数下,如非线性系数、激励振幅与黏弹性阻尼等对稳态幅频响应及稳定性影响。

Nonlinear vibrations of axially moving viscoelastic Timoshenko beams under strong external excitation

Nonlinear vibrations of axially moving viscoelastic Timoshenko beams under strong external excitations were investigated.The governing partial-differential equations were derived according to the extended Hamilton’s principle.The effects of shear deformation and rotary inertia were taken into account.The beam material obeys the Kelvin model in which the material derivative was taken part in the viscoelastic constitution relation instead of the simple partial time derivative.The method of multiple scales was applied to obtain the steady state response and establish the solvability conditions.The stability boundaries were formulated analytically via Routh-Hurwitz criterion.Some numerical examples were presented to demonstrate the effects of related parameters on the response.