功能梯度压电空心圆柱中分数阶热弹导波的频散和衰减特性  

Dispersion and Attenuation Characteristics of Fractional⁃Order Thermoelastic Guided Waves in Functionally Graded Piezoelectric Hollow Cylinders

作　　者：禹建功[1] 王开 任小强 王现辉[1] 张博 YU Jiangong;WANG Kai;REN Xiaoqiang;WANG Xianhui;ZHANG Bo(School of Mechanical and Power Engineering,Henan Polytechnic University,Jiaozuo,Henan 454000,P.R.China)

机构地区：[1]河南理工大学机械与动力工程学院,河南焦作454000

出　　处：《应用数学和力学》2023年第11期1325-1340,共16页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(12102131);河南省高校科技创新团队基金项目(23IRTSTHN016);中国博士后科学基金(2021M701102)。

摘　　要：基于分数阶热电弹性理论和Legendre多项式方法,构建了功能梯度空心圆柱中导波传播的数学模型.讨论了分数阶次、压电效应、径厚比等对导波传播,特别是对其衰减的影响规律.数值结果表明,压电效应对衰减的影响主要集中在截止频率和突变频率附近,并使得突变频率发生前移;分数阶对热波模态相速度和衰减的影响较大,且热波相速度存在模态交叉,在交叉频率点附近分数阶对相速度的影响相反;热波衰减随着分数阶增大而逐渐减小;第一阶纵向模态衰减受到了压电效应的抑制,其余模态衰减都显著增大,并且电开路受到的影响要比电短路状态大.Based on the fractional-order thermo-electric-elastic theory and the Legendre polynomial series method,a mathematical model for guided wave propagation in functionally graded hollow cylinders was estab-lished.The effects of the fractional order,the piezoelectric effect,and the radius-thickness ratio on the wave propagation,especially on its attenuation,were discussed.The numerical analysis results indicate that,the pie-zoelectric effect on attenuation mainly concentrates near the cutoff frequency and the mutation frequency,and causes the mutation frequency to shift forward.The fractional order has a great impact on the phase velocity and attenuation of the thermal wave mode,and has an opposite impact on the phase velocity around the cross-over frequency point where the crossover mode occurs with the thermal wave velocity.But the thermal wave at-tenuation gradually decreases with the fractional order.Meanwhile,the 1st longitudinal mode attenuation is suppressed by the piezoelectric effect.However,the attenuation of other modes significantly increases,and the impact of the electrical open circuit is greater than that of the electrical short circuit.

关 键 词：导波 分数阶热电弹 功能梯度空心圆柱 频散 衰减 

分 类 号：O348[理学—固体力学]