Application of Haar wavelet method for free vibration of laminated composite conical–cylindrical coupled shells with elastic boundary condition

Abstract In this paper, the Haar wavelet discretization method (HWDM) is proposed for the calculation of natural frequency of the laminated composite conical-cylindrical coupled shells. The displacement components of the system are set by the first order shear deformation shell theory (FSDST), and all the displacement functions of conical and cylindrical shells including boundary conditions are obtained by the Haar wavelet and its integrals. The Hamilton’s principle is applied to the constitution equation and the artificial spring technique is introduced to generalize the boundary and continuity conditions of the coupled structure. The convergence and accuracy of the proposed method are validated by comparing with the results obtained from the previous works and finite element analysis, and the proposed method shows high accuracy, reliability and good convergence in both individual structure and coupled structure. Using the proposed method, in the laminated composite conical–cylindrical coupled shell with any boundary condition, new numerical results on the natural frequency are obtained along with the parameter studies, and these results can provide the referential data for the following research in this field.