初应力对压电压磁板中水平剪切振动的影响

针对含有初始应力的压电压磁板中的水平剪切振动问题，从基本的线弹性理论出发，经过适当的变量代换，推导出了精确的解析解，得到了电磁学开路、电学开路磁学短路、电学短路磁学开路、电磁学短路四种情况下的频率控制方程；进一步应用二分法对方程进行求解，并数值模拟了初始应力以及不同的电磁学边界条件对振动频率、位移模态的影响．研究结果表明：初始应力和电磁学边界条件对压电压磁板的水平剪切振动频率都具有显著的影响，且当初始应力变化范围较小时（初始应力与有效刚度系数之比在5%以内），振动频率与初始应力之间呈线性关系；电磁学边界条件能显著改变压电压磁板内振动位移的分布，但初始应力对其影响不大．

Effect of Initial Stress on the Shear Horizontal Vibration of a Magneto-Electroelastic Plate

Based on the linear elasticity theory and the variable substitution approach, an analytical solution about the shear horizontal vibration in a magneto-electroelastic plate with initial stress has been obtained. The control equations of frequency are derived and solved by the method of bisection for four different boundary conditions, i.e., electrically and magnetically open (EOMO), electrically open and magnetically shorted (EOMS), electrically shorted and magnetically open (ESMO), and electrically and magnetically shorted (ESMS). It is shown numerically that the initial stress and electromagnetical boundary conditions have a great influence on the frequencies of shear horizontal vibration. The relationship between the frequency and the initial stress is linear when the ratio of initial stress to effective stiffness is smaller than 5%. The displacement distribution is shown to be sensitive to the electromagnetical boundary conditions, and insensitive to the initial stress.