轴向运动黏弹性梁:积分—偏微分非线性组合参数共振

Axially Moving Beams:Integro-partial-differntial Nonlinear Summation Parametic Resonance

研究了轴向运动黏弹性梁积分-偏微分非线性组合参数共振。变速轴向运动梁的黏弹性本构关系引入了物质时间导数,考虑了由均匀轴向运动梁变形的影响而导致梁轴向伸长而引起的附加力,并以轴向张力平均值代替梁上各点的精确值,梁的横向运动由积分-偏微分非线性控制方程描述。应用渐近摄动法直接求解梁的控制方程并导出了当扰动速度的频率接近未扰系统任意两个固有频率之和时所发生的组合参数共振的稳态响应和振幅方程。运用微分求积法数值求解简支边界的轴向变速运动黏弹性梁的非线性控制方程,通过修正权系数矩阵处理了简支梁边界条件中的二阶偏导数为零的项。计算结果显示了相关参数对梁的稳态响应影响,数值解验证了解析结果。

Steady-state response of nonlinear axially beams is investigated in summation parametric resonance.The material time derivative is used in the viscoelastic constitutive relation.The transverse motion can be governed a nonlinear integro-partial-differential equation.The summation parametric resonance may occur when the axial speed variation frequency approaches the sum of any two natural frequencies.The asymptotic analysis is performed to determine steady-state responses.The differential quadrature scheme is developed to solve numerically the governing equation and verify results via asymptotic analysis.Numerical examples show the effects of correlative parameter on steady-state response.The numerical results validate the analytical results.