旋转运动导电圆板的磁弹性参数振动分析

针对磁场中旋转运动圆板,在动能、应变能表达式基础上,根据哈密顿原理导出圆板的磁弹性振动方程．应用伽辽金积分法,得到横向磁场中旋转变速运动圆板的轴对称参数振动微分方程．通过坐标变换得到包含两个变系数项的马蒂厄振动方程．应用弗洛凯理论和平均法对系统的参数振动问题进行求解．通过数值计算得到周期稳定图、对应的振动响应特性图和相轨迹图．结果表明：在稳定区域内,系统的幅频曲线呈现为周期或概周期变化形式;在不稳定区内,系统的幅频响应曲线呈现为发散变化形式．     

Magneto-elastic combination resonances analysis of current-conducting thin plate

Based on the Maxwell equations, the nonlinear magneto-elastic vibration equations of a thin plate and the electrodynamic equations and expressions of electro- magnetic forces are derived. In addition, the magneto-elastic combination resonances and stabilities of the thin beam-plate subjected to mechanical loadings in a constant transverse magnetic filed are studied. Using the Galerkin method, the corresponding nonlinear vibration differential equations are derived. The amplitude frequency response equation of the system in steady motion is obtained with the multiple scales method. The excitation condition of combination resonances is analyzed. Based on the Lyapunov stability theory, stabilities of steady solutions are analyzed, and critical conditions of stability are also obtained. By numerical calculation, curves of resonance-amplitudes changes with detuning parameters, excitation amplitudes and magnetic intensity in the first and the second order modality are obtained. Time history response plots, phase charts, the Poincare mapping charts and spectrum plots of vibrations are obtained. The effect of electro-magnetic and mechanical parameters for the stabilities of solutions and the bifurcation are further analyzed. Some complex dynamic performances such as period- doubling motion and quasi-period motion are discussed.     

超磁致伸缩换能器耦合磁弹性模型与振动特性分析

针对应用于非圆车削加工的超磁致伸缩换能器,建立了其耦合磁弹性动力学模型与复系数动力学微分方程,基于实验建立的激励电流磁致伸缩材料轴向位移-磁场强度三者之间的关系式,得到了换能器磁力-位移关系的磁动方程的解析解,分析了系统的频响特性及不同频率下,激励电流与换能器输出位移之间的滞回关系,对现有磁场-电流公式进行了修正,讨论...     

磁场中旋转运动圆环板主共振分岔及混沌研究

研究了磁场中旋转运动圆环板的磁弹性主共振及分岔、混沌问题.通过Hamilton(哈密顿)原理推得磁场中旋转运动圆环板的横向振动方程,并采用Bessel(贝塞尔)函数作为振型函数进行Galerkin(伽辽金)积分,得到磁场中旋转运动圆环板的无量纲非线性振动常微分方程.利用多尺度法展开,得到静态分岔方程、对应的转迁集与分岔图,以及物理参数作为分岔控制参数时的分岔图.利用Mel’nikov(梅利尼科夫)方法,对系统混沌特性进行研究,得到外边夹支内边自由边界条件下异宿轨破裂的条件;通过数值计算,得到外激振力幅值作为分岔控制参数时系统的分岔图与指定参数条件下系统响应图.结果表明,磁场扼制多值现象的产生;激振频率、转速、磁感应强度越小,激振力幅值越大,系统的异宿轨越容易发生破裂,从而引发混沌或概周期运动.