Three-dimensional free vibration analysis of thick cylindrical shells with general end conditions and resting on elastic foundations

• A unified 3D vibration analysis method is developed for thick cylindrical shells.
• Each of the shell displacements is expanded as an improved Fourier series.
• The change of end conditions can be easily achieved by varying the boundary restraining parameters.
• The proposed method is appropriate for arbitrary end conditions and elastic foundations.

A unified method based on the three-dimensional theory of elasticity is developed for the free vibration analysis of thick cylindrical shells with general end conditions and resting on elastic foundations. Each shell displacements, regardless of boundary conditions, is expanded as a standard Fourier cosine series supplemented with four auxiliary functions introduced to eliminate any possible discontinuities of the original displacement and its derivatives throughout the entire shell space including the boundaries and then to effectively enhance the convergence of the results. Mathematically, such series expansions are capable of representing any functions (including the exact displacement solutions). Since the displacement field is constructed adequately smooth throughout the whole solution domain, an accurate solution can obtained by using Rayleigh–Ritz procedure based on the energy functions of the shell. The current method can be universally apply to a variety of end conditions including all the classical cases and their combinations and arbitrary elastic foundations. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. Effects of the boundary restraining parameters and foundation coefficients on frequency parameters are investigated as well. New results for thick cylindrical shells with various end conditions and resting on elastic foundations are presented, which may serve as benchmark solutions for validating new computational techniques in future.