Free vibration analysis of composite laminated cylindrical shells using the Haar wavelet method

In this paper, a simple yet accurate solution procedure based on the Haar wavelet discretization method (HWDM) is applied to the free vibration analysis of composite laminated cylindrical shells subjected to various boundary conditions. The Reissner–Naghdi’s shell theory is adopted to formulate the theoretical model. The initial partial differential equations (PDE) are first converted into system of ordinal differential equations by the separation of variables. Then the discretizations of governing equations and corresponding boundary conditions are implemented by means of the HWDM, which leads to a standard linear eigenvalue problem. Accuracy and reliability of the current solutions are validated by comparing the results with those available in the literature. The effects of several significant aspects including boundary conditions, length to radius ratios, lamination schemes and elastic modulus ratios on natural frequencies are discussed. The advantages of the current solutions consist in its simplicity, fast convergence, low computational cost and high accuracy.