The Haar wavelet method for free vibration analysis of functionally graded cylindrical shells based on the shear deformation theory

A simple yet efficient solution approach based on the Haar wavelet is presented for the free vibration analysis of functionally graded (FG) cylindrical shell. The first-order shear deformation shell theory is adopted to formulate the theoretical model. The separation of variables is first performed according to Levi approach; then Haar wavelet discretization is applied with respect to the axial direction and Fourier series is assumed with respect to the circumferential direction. The constants appearing from the integrating process are determined by boundary conditions, and thus the partial differential equations are transformed into algebraic equations. The natural frequencies of the FG cylindrical shells are obtained by solving algebraic equations. The accuracy and reliability of the current solutions are validated by numerical examples and comparison with the results available in the literature. It is shown that accurate frequencies can be obtained by using a small number of collocation points and boundary conditions can be easily achieved. Detailed parametric analysis is carried out to show the effects of some geometrical and material parameters on the natural frequencies of FG cylindrical shells. The advantages of this current solution method consist in its simplicity, fast convergence, low computational cost and high precision.