压电固体中弹性波传播的数学模型  

Mathematical Modeling of Wave Propagation in a Piezoelectric Solid

作　　者：王红[1] 李月秋[1] WANG Hong, LI Yue-qiu(Faculty of Science, Qiqihar University, Qiqihar 161006, Chin)

机构地区：[1]齐齐哈尔大学理学院

出　　处：《数学的实践与认识》2018年第14期232-236,共5页Mathematics in Practice and Theory

基　　金：黑龙江省省属高等学校基本科研业务费科研项目(135209253)

摘　　要：依据动量定理、电荷守恒定律建立了弹性波在压电固体中传播的数学模型．不仅考虑了压电效应，也同时考虑了电流效应．在压电固体中同时存在机械位移场、极化电势场和电流场．求解波动方程，发现不考虑电流效应时，弹性波是非色散的；考虑电流效应后，弹性波是色散的．不仅如此，电流效应还导致弹性波的衰减．通过数值模拟，揭示了平衡载流子浓度对色散和衰减的影响规律．The mathematical model of the elastic wave propagation in the piezoelectric solid is established based on the momentum theorem and the charge conservation law in this paper. Not only the piezoelectric effects but also the electric current effects are taken into consideration. The mechanical displacement field, polarized electric potential field and the electric field coexist and coupled together in the present problem. It is found by solving the coupled equations that the elastic waves are non-dispersive when the electric current effects are not considered while dispersive when the electric current effects are taken into considered. The numerical results also reveal that the elastic wave attenuates as it propagates due to the existence of electric current. The influences of the steady carrier density on the dispersive and attenuation are discussed numerically.

关 键 词：压电效应 电流效应 色散 衰减 弹性波 载流子浓度 

分 类 号：TB34[一般工业技术—材料科学与工程]