Orthogonal polynomials

Displacement (psychology)

Physics

Mathematical optimization

Mathematical analysis

Series (stratigraphy)

Paleontology

Psychology

Economics

Boundary value problem

Vibration

Fourier series

Ritz method

Geometry

Convergence (economics)

Mathematics

Jacobi polynomials

Economic growth

Psychotherapist

Penalty method

Boundary (topology)

Quantum mechanics

Rayleigh–Ritz method

Biology

Computers & Mathematics with Applications

A semi analytical approach is employed to analyze free vibration characteristics of uniform and stepped circular cylindrical shells subject to arbitrary boundary conditions. The analytical model is established on the basis of multi-segment partitioning strategy and Flügge thin shell theory. The admissible displacement functions are handled by unified Jacobi polynomials and Fourier series. In order to obtain continuous conditions and satisfy arbitrary boundary conditions, the penalty method about the spring technique is adopted. The solutions about free vibration behavior of circular cylindrical shells were obtained by approach of Rayleigh–Ritz. To confirm the reliability and accuracy of this method, convergence study and numerical verifications for circular cylindrical shells subject to different boundary conditions, Jacobi parameters, spring parameters and maximum degree of permissible displacement function are carried out. Through comparative analyses, it is obvious that the present method has a good stable and rapid convergence property and the results of this paper agree closely with the published literature. In addition, some interesting results about the geometric dimensions are investigated.

Jacobi–Ritz method for free vibration analysis of uniform and stepped circular cylindrical shells with arbitrary boundary conditions: A unified formulation