功能梯度压电压磁圆柱壳中纵向波的截止频率  

CUT-OFF FREQUENCIES OF LONGITUDINAL WAVES IN FUNCTIONALLY GRADED PIEZOELECTRIC-PIEZOMAGNETIC MATERIALS(FGPPM)CYLINDER SHELLS

作　　者：邓良玉 曹小杉[1] 马星荃 汝艳[1] Deng Liangyu;Cao Xiaoshan;Ma Xingquan;Ru Yan(School of Civil Engineering,Xi’an University of Technology,Xi’an 710048,China)

机构地区：[1]西安理工大学土木建筑工程学院,西安710048

出　　处：《力学学报》2023年第9期1950-1959,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(11572244);陕西省自然科学基金(2021JQ-467);陕西省科技创新团队(2022TD-61);陕西高校青年教师创新团队资助项目.

摘　　要：采用解析方法研究材料参数沿径向变化的功能梯度压电压磁圆柱壳体中纵向导波的截止频率.建立了利用位移函数、电势函数和磁势函数表示的柱坐标系下功能梯度压电压磁圆柱壳中纵向波的力、电和磁耦合波动方程并表征齐次边界条件.在波数趋于0的条件下,采用Wentzel-Kramers-Brillouin(WKB)方法求解方程并推导得到梯度壳体中纵向导波截止频率的显式近似解析解.分别对比均质压电压磁圆柱壳体中纵向导波的截止频率的贝塞尔函数解和由功能梯度压电压磁圆柱壳体中纵向导波频散曲线所得的截止频率,验证了WKB解的高精确性.通过进一步解析推导简化可得:纵向波的截止频率是两个近似等差数列的集合;其公差分别与材料两种等效波速的倒数沿径向的积分成反比.数值算例表明,直接利用两个数列的公差表示截止频率具有足够的精度.研究对比分析了弹性参数、密度、电学参数、磁学参数和壳体厚度单独变化对截止频率的影响规律.其中弹性参数和密度梯度变化对截止频率影响较为明显;电学参数与磁学参数梯度变化对其截止频率影响较小;壳体厚度增加会导致截止频率降低.文中给出的分析方法与结论可适用于功能梯度弹性材料与功能梯度压电材料圆柱壳中纵向导波的截止频率,这些结论可为基于截止频率的非均质材料圆柱壳的超声无损检测提供理论依据.In this paper,the cut-off frequencies of longitudinal wave propagating in functionally graded piezoelectricpiezomagnetic material(FGPPM)cylinder shells is investigated analytically.The mechanical,the electrical and the magnetical coupling waves equations of the longitudinal wave propagating in FGPPM cylinder shells in the cylindrical coordinate system expressed by the displacement function,the electric potential function and the magnetic potential function are established and the homogeneous boundary conditions are characterized.Considering that the wave number approaches zero,the Wentzel-Kramers-Brillouin(WKB)method is employed for solving these equations and derive an explicit approximate analytical solution for the cutoff frequency of longitudinal guided waves in an FGPPM shell.By comparing WKB solution with the Bessel function solution for the cut-off frequency of longitudinal guided waves in homogeneous piezoelectric and piezomagnetic cylinder shells and with the cut-off frequencies obtained from the dispersion curves of functionally graded piezoelectric and piezomagnetic cylinder shells,respectively,the high precision of the WKB solution has been verified.Further analysis and simplification shows that the cut-off frequency of longitudinal waves is a combination of two approximate arithmetic progressions with a common difference inversely proportional to the integral of reciprocal wave velocity along the radial direction.Numerical examples demonstrate that representing the cut-off frequency using the common differences of these two progressions yields sufficient accuracy.The effects of varying elastic parameters,density,electrical parameters,magnetic parameters,and shell thickness on the cut-off frequencies are investigated and compared.It is found that variations in elastic parameters and density have a significant impact on the cut-off frequency,while variations in electrical and magnetic parameters have a relatively smaller effect.Increasing the shell thickness leads to a decrease in the cut-off frequency

关 键 词：截止频率 功能梯度压电压磁材料 WKB 法 圆柱壳中的纵向波 

分 类 号：O347.41[理学—固体力学]