【作者】 冯志强；

【导师】 胡宇达；

【作者基本信息】 燕山大学 ， 工程力学， 2010， 硕士

【摘要】 在自然界和工程实际中,轴向运动体系的振动现象是十分普遍的。它广泛存在于军事、航空航天、机械、电子、土木工程中。如动力传送带、磁带、纺织纤维、带锯、纸张、航空航天工程中应用的复合材料层合板等。因此研究此类系统的振动特性具有重要的理论和实际意义。本文致力于研究轴向运动矩形板在外界激励作用下的非线性强迫振动问题。重点研究在不同边界条件下的轴向运动矩形板的超、亚谐波共振等问题。首先,根据薄板理论和轴向运动系统的运动参数,应用伽辽金原理导出了轴向运动矩形板在横向简谐激励作用下的非线性振动方程。其次,针对四边简支轴向运动矩形板的超谐波共振和亚谐波共振问题,应用多尺度法进行求解,分别导出了系统相应的幅频响应方程,并基于李雅普诺夫稳定性理论,得到了解的稳定性判定条件;针对一对边简支一对边自由轴向运动矩形板的超谐波共振和亚谐波共振问题,基于参数变换的思想,进行了数值的分析计算。最后,通过编程计算,对几种不同边界条件下的轴向运动矩形板进行了分析。分别给出了在不同参数情况下,四边简支轴向运动矩形板超谐波共振和亚谐波共振问题的幅频曲线及其时间历程图、相图、庞加莱映射图和频谱图;对于一对边简支一对边自由的轴向运动矩形板的超、亚谐波共振的分析,进行了数值分析计算,并给出其时间历程图、相图、庞加莱映射图和频谱图。讨论了载荷大小、阻尼系数、速度变化以及板厚等参数对系统非线性振动特性的影响。更多还原

【Abstract】 In nature and engineering practice, the vibration of axially moving systems is a very common phenomenon. It is widespread in the military, aerospace, machinery, electronics, civil engineering, such as power transmission belts, tapes, textile fibers, band saw, paper, and the composite laminated panels of aerospace engineering. Therefore, the study on the vibration characteristics of axially moving systems has important theoretical and practical significance.In this paper, the axially moving rectangular plate subjected to external excitation is studied. Super harmonic resonance and subharmonic resonance of the axially moving rectangular plates in the different boundary conditions are focused discussed. Firstly, according to the classical plate theory and the parameters of axially moving systems, the nonlinear forced vibration equations of axially moving rectangular plates respectively under the harmonic excitation in the different boundary conditions were deduced by using Galerkin method.Secondly, for super harmonic resonance and subharmonic resonance of axially moving plate with four simply supported edges, the amplitude-frequency response equations were respectively derived using multi-scale method. Based on Lyapunov stability theory, the critical conditions of steady-state solutions’stability were gotten; for super harmonic resonance and subharmonic resonance of axially moving plate with two opposite ends simply supported and two opposite ends free, based on the parameters transformation, the analysis of numerical calculation was carried on.Finally, the axially moving rectangular plates in different boundary conditions were analyzed by programming calculation. In the super harmonic resonance and subharmoic resonance, the amplitude-frequency curves, the time history plot, the phase chart, the Poincarémap and the spectrum plot of the axially moving rectangular plate with four simply supported edges were derived under different parameters. In the boundary condition of two opposite ends simply supported and two opposite ends free, the time history plot, the phase chart, the Poincarémap and the spectrum plot for the super harmonic resonance and subharmoic resonance the of the axially moving rectangular plate were also derived under different parameters. The influences of different parameters on nonlinear resonance properties of system,such as load, damping, speed and the width of plate , were discussed.更多还原