Abstract：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 parameter , 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 parameter , which is of particular importance in modern engineering design.
2020, Vol. 41 
