计及非齐次边界条件的面内变速运动黏弹性板的稳态响应

Steady-state responses of a viscoelastic plate with in plane variable speed motion under non-homogeneous boundary conditions

研究非齐次边界条件和1∶3内共振下面内平动黏弹性板的横向非线性1∶2主参数振动的稳态响应。考虑黏弹性对边界条件的影响,建立了面内平动板的偏微分运动方程和相应的非齐次边界条件。采用直接多尺度法建立了次谐波参数共振时的可解性条件,并根据Routh-Hurvitz判据判别了系统幅频响应的稳定性。讨论了速度扰动幅值和黏弹性系数对幅频响应的影响,对比了齐次和非齐次边界条件下稳态响应的差异。最后,引入微分求积法验证直接多尺度法的近似解析结果。

Steady-state responses for lateral nonlinear 1∶2 principal parametric resonance of a viscoelastic plate with in plane 1∶3 internal resonance of translation were investigated under nonhomogeneous boundary conditions.A governing partial differential equation of motion and corresponding nonhomogeneous boundary conditions for the plate with in plane translation were established considering effects of viscoelasticity on boundary conditions.The multi-scale method was applied to establish the solvability conditions during the plate having sub-harmonic parametric resonance.The stability of the system’s frequency-amplitude responses was judged using Routh-Hurvitz criterion.Effects of in-plane translation speed disturbance amplitude and viscoelastic coefficient on the system’s steady-state responses were investigated.The system’s steady-state responses under homogeneous boundary conditions and non-homogeneous ones were compared.Finally,the differential quadrature method was introduced to verify approximate analytical results using the multi-scale method.