气动载荷下旋转运动圆板磁弹性主共振分析

基于Kirchhoff薄板理论与哈密顿原理，建立旋转运动导电圆板的磁-气动弹性非线性动力学方程．根据电磁场基本原理得到旋转运动圆板所受电磁力表达式，同时采用一种简化的气动模型以描述作用于板上的气动载荷．基于贝塞尔函数形式振型函数的选取，应用伽辽金法得到旋转圆板的磁气动弹性轴对称非线性振动微分方程．应用多尺度法推导出主共振下系统的幅频响应方程，并依据Lyapunov方法得到系统稳态运动稳定性判据．通过算例，得到周边夹之约束下圆板主共振的幅频特性曲线图，以及振幅随磁感应强度和激励力幅值的变化曲线图；阐述了不同参数对系统共振幅值的影响规律，并对解的稳定性进行了分析．

Magneto-Elastic Primary Resonance of a Rotating Conductive Circular Plate under Aerodynamic Load

Based on the Kirchoff plate theory and Hamiltonian principle, the magneto-aeroelastic nonlinear dynamic equation for the forced vibration of the rotating conductive circular plate is deduced. According to principles of electromagnetic field, the expressions of electromagnetic force of rotating circular plate are presented. In addition, the aerodynamic load acting on the rotating plate is expressed from a simplified aerodynamic model. Bessel and modified Bessel functions of order zero, combined with the Galerkin method, are utilized to obtain the nonlinear axisymmetric differential equation for the forced vibration of the rotating circular plate. The amplitude-frequency response equations in steady state are obtained by means of the multi-scale method. The stability criterion for the steady-state solutions of the system is obtained by employing Lyapunov method. Through the numerical examples, the amplitude-frequency curves of primary resonance of the system with clamped edge are plotted. The curves of the amplitude are plotted for different varying parameters, respectively. The effects of the magnetic flux density and the rotational speed on the amplitude of primary resonance are analyzed. The stability of steady-state motions of the system is evaluated.