轴向拉力对变速运动黏弹性梁参激振动稳定性的影响

STABILITY OF PARAMETRIC VIBRATION EXCITED OF AN AXIALLYACCELERATING VISCOELASTIC BEAM SUBJECTED TO AXIAL DISTURBING TENSION

研究了变速轴向运动黏弹性梁参激振动受拉力扰动时在主参数共振和组合参数共振范围内的稳定性.轴向运动梁的黏弹性本构关系引入了物质时间导数.当参激频率接近某一阶固有频率2倍时将发生主参数共振;当参激频率接近某两阶固有频率之和时将发生组合参数共振.运用多尺度法,直接求解轴向运动梁的控制方程,导出了稳定性边界方程.最后,通过数值算例给出了变速轴向运动梁的黏阻尼和干扰拉力对失稳区域的影响结果.

The stability of axially accelerating viscoelastic beam was investigated when the principal parametric resonanceor combination parametric resonance was excited. The material time derivative was used in the viscoe- lastic constitutive relation. When the axial speed variation frequency approaches the sum of two arbitrary natural frequencies or the twice of arbitrary natural frequency, the summation or principal parametric resonance may oc- cur. The method of multiple scales was employed to directly solve the governing equation of axially accelerating viscoelastic beam. Analytical expressions of the instability boundary were obtained for summation and principal parametric resonance. Finally, numerical examples show the effects of viscosity and axial disturbing tension for instability region.