Fundamental frequency of the laminated composite cylindrical shell with clamped edges

• Free vibrations problem for the laminated composite cylindrical shell with clamped edges is solved.
• The laminated shell theory accounting for the transverse shear strains is employed.
• An analytical formula is obtained using the Galerkin method.
• Effectiveness of the approach is demonstrated using particular examples.
• The results are verified using a finite-element analysis.

Free vibrations of the laminated composite cylindrical shell with clamped edges are considered in this paper. Equations of the theory of laminated shells taking into account the average transverse shear strains are employed for the vibration analysis. A solution of the equations of motion of the shell is based on the Fourier decomposition and the Galerkin method and yields an analytical formula for the calculation of a fundamental frequency. Applications of this formula to the determination of the fundamental frequencies for the filament-wound composite cylindrical shells are demonstrated using numerical examples. The calculations have been verified by comparison with a finite-element solution. It has been shown that the analytical formula presented in this paper provides an efficient means for rapid and reliable calculation of the fundamental frequency which can be used for the assessment of the structural stiffness of the shells in the design analysis.