矩形薄板热电磁弹耦合作用下的主共振

Primary Resonance Analysis of Rectangular Thin Plate With Thermo-Electric-Magnetic-Elastic Coupling

本文研究了考虑热、电、磁、力多物理场作用下的矩形薄板主共振。根据冯卡门大挠度理论和哈密顿原理得到模型的非线性控制方程,使用谐波平衡法分析得到了系统的一阶近似响应及幅频函数,分析表明模型表现出硬非线性、跳跃等现象。对不同温差、阻尼、板厚、磁场、模态、长宽比对主共振的影响进行了分析,得到了幅频响应曲线,并使用MATLAB的龙格库塔方法对其进行了数值验证。结果表明,温差是影响矩形薄板主共振的最大因素,磁场是影响矩形薄板主共振最小因素,这是由于材料的压磁系数和热弹耦合系数的差异所致。

The primary resonance of a rectangular thin plate under the action of multiple physical fields such as thermal,electric,magnetic and elastic fields was studied in this paper.The nonlinear governing equations of the model were obtained according to von Karman’s principle of large deflection and Hamilton’s principle.The first order approximate response and amplitude-frequency function of the system were obtained by harmonic balance method.The results show that the model exhibits hard nonlinearity and jumping.The influence of different temperature differences,damping,plate thickness,magnetic field,mode,length-width ratio on the primary resonance was analyzed,and the amplitude-frequency response curve was obtained.The Runge-Kutta method of MATLAB was used to verify the curve numerically.The analysis shows that temperature difference is the largest factor affecting the primary resonance of rectangular thin plate,and magnetic field is the smallest factor affecting the primary resonance of rectangular thin plate,which is caused by the difference between the compression-magnetic coefficient and the thermoelastic coupling coefficient of the material.