【作者】 张翼颖；

【导师】 胡宇达；

【作者基本信息】 燕山大学 ， 工程力学， 2012， 硕士

【摘要】 在工程实际中，多种工程系统如动力传送带、磁带、带锯、纸张、航空航天工程中应用的复合材料层合板等都可以模型化为轴向运动板。因此，研究轴向运动板的振动问题具有重要的理论和实际意义。本文研究了在横向磁场环境中轴向运动条形薄板的非线性磁弹性振动问题。首先，利用电磁场理论推导出了薄板的电动力学方程和电磁力表达式，再应用哈密顿变分原理导出了机械场和磁场共同作用下的轴向运动条形薄板的非线性磁弹性振动方程。将满足对边简支对边自由边界条件下的位移解代入到振动方程，运用伽辽金积分并进行无量纲化处理，推导出其达芬型振动微分方程。其次，采用多尺度法分别对条形板的非线性自由振动、主共振、组合共振问题进行求解，得到了一次近似解析解。针对主共振和组合共振的情况，得到了幅频响应方程。基于李雅普诺夫稳定性理论，得到了解的稳定性判定条件，并对系统稳态运动下解的稳定性进行了分析。最后，通过数值算例，分别给出了在不同参数情况下非线性自由振动、主共振、组合共振的时间历程响应图和相图。针对主共振和组合共振的情况，通过幅频响应方程，得到了幅频曲线图。针对组合共振情况，得到了频谱图。分析了磁感应强度、频率调谐参数、轴向速度、激励幅值、板厚等电磁参数和机械参数对系统振动特性的影响，并对系统存在的单周期运动、概周期运动和混沌等复杂动力学行为进行了探讨。更多还原

【Abstract】 A variety of engineering systems with axially moving such as power transmissionbelts, tapes, band saw, paper and the composite material laminate of aerospace engineer-ing etc.can be simplified as axially moving plates in engineering practice application.Therefore, the investigation on vibration of the axially moving plates is significant notonly in thoeretical but also in engineering practice.In this paper, research works ofnonlinear magnetoelastic vibration of the axially moving strip thin plates subjected to antransverse magnetic field have done.First, based on the electromagnetic theory,electrodynamics equation electromagne-tic forces are deduced. A sets of nonlinear magnetoelastic vibration equation of theaxially moving strip thin plates which in the mechanic filed and magnetic filed are givenby using Hamiltonian variational principle. Substitute the displacement solution into thevibration equation which meet the boundary condition of two opposite ends simplysupported and two opposite ends free, using the method of Galerkin to integrate it andmake it dimensionles, then the Duffing type vibration differential equation is deduced.Second, solve the problems of nonlinear free vibration, main resonances and com-bination resonances by using the method of Multiple Scales, and the first approximateanalytic solutions is deduced, and amplitude-frequency fuctions of main resonances andcombination resonances are also obtained. based on the lyapunov stability theory, thediscriminant of stable solutions is obtained, and the stability of stable solution isanalyzed.At last, by means of calculated example, the time history response plots and phasecharts of three vibration conditions: nonlinear free vibration, main resonances and com-bination resonances are obtained. In cases of mian resonances and combination resonan-ces, spectrum charts is obtained, and obtained the amplitude frequency curve by theamplitude frequency response equation. The influences of system’s vibration characteris-tics under the condition of magnetic induction intensity, speed, frequency tuning parame-ters, incentive amplitude, thickness of the electromagnetic parameters and mechanical parameters are analyzed, and the complex dynamic behaviors of axially moving systems:such as as single-frequency periodic motion, quasi-period motion and dou-bling-periodmotion are discussed.更多还原