Free vibration analysis of functionally graded conical shells and annular plates using the Haar wavelet method

• A Haar wavelet method is applied to free vibration analysis of FGM conical shells.
• The first-order shear deformation shell theory is adopted to formulate the model.
• The Haar wavelet discretization is applied with respect to the axial direction.
• Accurate solution can be obtained by using a small number of collocation points.
• The advantages of the method consist in its simplicity and fast convergence.

The main aim of this paper is to provide a simple yet efficient solution for the free vibration analysis of functionally graded (FG) conical shells and annular plates. A solution approach based on Haar wavelet is introduced and the first-order shear deformation shell theory is adopted to formulate the theoretical model. The material properties of the shells are assumed to vary continuously in the thickness direction according to general four-parameter power-law distributions in terms of volume fractions of the constituents. The separation of variables is first performed; 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. Then natural frequencies of the FG shells are obtained by solving algebraic equations. Accuracy and reliability of the current method are validated by comparing the present results with the existing solutions. Effects of some geometrical and material parameters on the natural frequencies of shells are discussed and some selected mode shapes are given for illustrative purposes. It’s found that accurate frequencies can be obtained by using a small number of collocation points and boundary conditions can be easily achieved. The advantages of this current solution method consist in its simplicity, fast convergence and excellent accuracy.