Free Vibration Analysis of Laminated Composite Spherical Shell with Variable Thickness and Different Boundary Conditions

In this paper, the free vibration characteristics of laminated composite spherical shells with variable thickness are investigated using the Haar wavelet discretization method (HWDM), as numerical solution technique. The first-order shear deformation theory (FSDT) is adopted to establish theoretical formulation. The displacements and rotations at any point of spherical shell are extended Haar wavelet series in the meridional direction and Fourier series in the circumferential direction. The constants generating from the integrating process are disposed by adding the boundary conditions equations, and thus the equations of motion of total system including the boundary condition are transformed into an algebraic equations. Then, natural frequencies and corresponding mode shapes of the laminated composite spherical shell are directly obtained by solving these algebraic equations. Stability and accuracy of the present method are confirmed by performing of convergence and verification studies. The influences of some material parameters and geometric dimensions on the vibration behavior of laminated composite spherical shells with variable thickness are discussed. Some new results for laminated composite spherical shell with variable thickness and general boundary conditions are reported, which may serve as benchmark solutions.