The free vibration of a functionally graded material hollow spheresubmerged in a compress- ible fluid medium is exactly analyzed. Thesphere is assumed to be spherically isotropic with material consta-nts being inhomog...The free vibration of a functionally graded material hollow spheresubmerged in a compress- ible fluid medium is exactly analyzed. Thesphere is assumed to be spherically isotropic with material consta-nts being inhomogeneous along the radial direction. By employing aseparation technique as well as the spherical harmonics expansionmethod, the governing equations are simplified to an uncoupledsecond-order ordinary differential equation, and a coupled system oftwo such equations. Solutions to these equations are given when theelastic constants and the mass density are power functions of theradial coordinate. Numerical examples are finally given to show theeffect of the material gradient on the natural frequencies.展开更多
An exact 3D analysis of free vibration of a piezoceramic hollow sphere submerged in a compressible fluid is presented in this paper. A separation method is adopted to simplify the basic equations for spherically isotr...An exact 3D analysis of free vibration of a piezoceramic hollow sphere submerged in a compressible fluid is presented in this paper. A separation method is adopted to simplify the basic equations for spherically isotropic piezoelasticity. It is shown that there are two independent classes of vibration. The first one is independent of the fluid medium as well as the electric field, while the second is associated with both the fluid parameter and the piezoelectric effect. Exact frequency equations are derived and numerical results are obtained.展开更多
基金the National Natural Sciences Foundation of China(No.19872060)
文摘The free vibration of a functionally graded material hollow spheresubmerged in a compress- ible fluid medium is exactly analyzed. Thesphere is assumed to be spherically isotropic with material consta-nts being inhomogeneous along the radial direction. By employing aseparation technique as well as the spherical harmonics expansionmethod, the governing equations are simplified to an uncoupledsecond-order ordinary differential equation, and a coupled system oftwo such equations. Solutions to these equations are given when theelastic constants and the mass density are power functions of theradial coordinate. Numerical examples are finally given to show theeffect of the material gradient on the natural frequencies.
基金The project supported by the National Natural Science Foundation of China(No.19872060)
文摘An exact 3D analysis of free vibration of a piezoceramic hollow sphere submerged in a compressible fluid is presented in this paper. A separation method is adopted to simplify the basic equations for spherically isotropic piezoelasticity. It is shown that there are two independent classes of vibration. The first one is independent of the fluid medium as well as the electric field, while the second is associated with both the fluid parameter and the piezoelectric effect. Exact frequency equations are derived and numerical results are obtained.
