Free Vibration Analysis of Cross-Ply Laminated Conical Shell, Cylindrical Shell, and Annular Plate with Variable Thickness Using the Haar Wavelet Discretization Method

This paper presents a unified solution method to investigate the free vibration behaviors of a laminated composite conical shell, a cylindrical shell, and an annular plate with variable thickness and arbitrary boundary conditions using the Haar wavelet discretization method (HWDM). Theoretical formulation is established based on the first-order shear deformation theory (FSDT), and displacement components are extended to the Haar wavelet series in the axis direction and trigonometric series in the circumferential direction. The constants generated by the integration process are disposed by boundary conditions, and thus the equations of the motion of the total system, including the boundary condition, are transformed into algebraic equations. Then, the natural frequencies of the laminated composite structures are directly obtained by solving these algebraic equations. The stability and accuracy of the present method are verified through convergence and validation studies. The effects of some material properties and geometric parameters on the free vibration of laminated composite shells are discussed and some related mode shapes are given. Some new results for laminated composite conical shell, cylindrical shell, and annular plate with variable thickness and arbitrary boundary conditions are presented, which may serve as benchmark solutions.