Maogang He

By Muzamal Hussain, Aamir Shahzad, Muhammad Nawaz Naeem and Maogang He

Vibration analysis of fluid-filled functionally graded material (FGM) cylindrical shells (CSs) is investigated with ring supports. The shell problem is formulated by deriving strain and kinetic energies of a vibrating cylindrical shell (CS). The method of variations of Hamiltonian principle is utilized to change the shell integral problem into the differential equation (DE) expression. Three differential equations (DE) in three unknown for displacement functions form a system of partial differential equations (PDEs). The shells are restricted along the thickness direction by ring supports. The polynomial functions describe the influence of the ring supports and have the degree equal to the number of ring supports. Fluid loaded terms (FLT) are affixed with the shell motion equations. The acoustic wave equation states the fluid pressure designated by the Bessel functions of first kind. Axial modal deformation functions are specified by characteristic beam functions which meet end conditions imposed on two ends of the shell. The Galerkin method is employed to get the shell frequency equation. Natural frequency of FGM cylindrical shell is investigated by placing the ring support at different position with fluid for a number of physical parameters. For validity and accuracy, results are obtained and compared with the data in open literature. A good agreement is achieved between two sets of numerical results.

Part of the book: Computational Fluid Dynamics