内共振作用下轴向运动黏弹性梁横向受迫振动

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (17) : 69-73.

论文

黄玲璐1, 毛晓晔1, 丁虎1, 陈立群1,2

作者信息 +

Transverse non-linear forced vibration of axially moving viscoelastic beam with an internal resonance

Huang Ling-lu1, Mao Xiao-ye1, DING Hu1, Chen Li-qun1,2

Author information +

文章历史 +

摘要

研究内共振与外部激励共同作用下，轴向运动粘弹性梁横向非线性振动的稳态响应。在运动梁动力学建模中采用Kelvin本构关系，并取物质时间导数。首次将直接多尺度法应用到轴向运动连续体的内共振研究。通过直接对连续体的偏微分-积分控制方程运用多尺度法，建立内共振条件下的横向非线性受迫共振的可解性条件。并通过稳定性分析，得到稳态响应解的稳定边界。另外，还考察了参数对响应的影响。最后，运用数值仿真验证了近似解析方法的正确性及有效性。

Abstract

The transverse nonlinear forced vibration of axially moving viscoelastic beams with a three-to-one internal resonance is analytically and numerically studied in this paper. The material obeys the kelvin model in which the material derivative is taken part in the viscoelastic constitution relation instead of the simple partial time derivative. For the first time, the method of multiple scales is developed to present the governing partial differential equations of motion for the continuous system. The solvability condition of nonlinear forced vibration in the transverse motion is derived under the internal resonance. The steady-state response and stable boundary are determined. The effects of the system parameters on the steady-state response are examined. The approximate analytical outcomes are qualitatively and quantitatively supported by the numerical simulations.

导出引用

黄玲璐1, 毛晓晔1, 丁虎1, 陈立群1,2. 内共振作用下轴向运动黏弹性梁横向受迫振动[J]. 振动与冲击, 2017, 36(17): 69-73

Huang Ling-lu1, Mao Xiao-ye1, DING Hu1, Chen Li-qun1,2. Transverse non-linear forced vibration of axially moving viscoelastic beam with an internal resonance[J]. Journal of Vibration and Shock, 2017, 36(17): 69-73

参考文献

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