功能梯度压电、压磁柱壳问题的振动分析

Vibration Analysis of a Cylindrical Shell of Functionally Graded Piezoelectirc-magnetic Material

本文在不考虑体力、体电流和体电荷的情况下,假定压电、压磁柱壳的材料参数沿圆柱厚度方向呈幂函数分布,研究了径向载荷作用下功能梯度压电、压磁空心柱壳的空间柱对称径向振动问题.首先在柱坐标系下,由功能梯度压电、压磁空心柱壳的参数、本构、梯度和运动方程推导得出外激励作用下以Bessel函数表示圆柱壳的应力、电势、磁势等物理量的稳态解,进而对空间柱对称的功能梯度压电、压磁柱壳的动力控制问题进行了理论分析.进一步可以看出,当梯度参数β=0时,即完全退化为横观各向同性压电、压磁柱对称的振动问题,与文献[20]的基本方程为柱坐标下得出的结果完全一致.最后给出数值算例,数值结果表明,材料不均匀性对沿径向振动各物理量有显著影响,且用一个特定不均匀性参数β值可以优化力电磁耦合的性能,这在现代工程设计中尤为重要.

In this paper,the symmetric radial vibration of a cylindrical shell of functionally graded piezoelectirc-magnetic material under radial loading is studied on the assumption that the material parameters of a piezoelectric and piezomagnetic cylindrical shell are distributed as a power function along the thickness of the shell without considering volume force,volume current or volume charge.Firstly,in the cylindrical coordinate system,assuming that the material properties are power functions of the radial position,and employing the constitutive,gradient and equilibrium equations of the functionally graded piezoelectirc-magnetic materials and boundary conditions,a non-homogeneous second-order differential equation is obtained.The Bessel function is used to express solutions of the second-order differential equation,and the steady-state solutions of the stress,electric potential and magnetic potential of a cylindrical shell are obtained under the action of external excitation.Furthermore,the theoretical analysis of the dynamic control of functionally graded piezoelectric-magnetic materials is carried out.It can be seen that when the gradient parameterβ=0,the results are completely reduced to the symmetric vibration of a transversely isotropic piezoelectric-magnetic cylinder,which are consistent with the results of the literature[20]when the basic equation is under cylindrical coordinate.Finally,numerical examples are given with BaTiO3-CoFeO4 composite materials.The results show that the inhomogeneity index of the material has a significant effect on the physical variables in the radial vibration,and the mechanical-electromagnetic-field coupling performance can be optimized with a specific value of the inhomogeneity parameterβ,which is of particular importance in modern engineering design.