Free vibrations of non-uniform composite cylindrical shells

A semi-analytical investigation of dynamic analysis of laminated multi-layered anisotropic, open and closed cylindrical shells has been developed by taking into account the shear deformation and rotary inertia effects. The structure may be uniform or non-uniform in the circumferential direction. The method used is a combination of hybrid finite element analysis and the shearable shell theory. The shell is subdivided into cylindrical panels having 5° of freedoms at each nodal line. The set of matrices describing their relative contributions to equilibrium is determined by exact analytical integration of the equilibrium equations instead of the usually used and more arbitrarily interpolating polynomials. This theory gives zero strains for rigid-body motions in such a way that the developed displacement functions satisfy the convergence criteria of the finite element method. This theory can be used for vibration analysis of axisymmetric (n = 0), beam-like (n = 1) and shell mode (n ≥ 2) behavior of cylindrical shells. It yields the high as well as the low eigenvalues and eigenmodes with comparable high accuracy. Reasonable agreement is found with other theories and experiments.