Physics

Geology

Mathematics

Economic growth

Psychotherapist

Boundary (topology)

Structural engineering

Displacement (psychology)

Engineering

Mathematical analysis

Series (stratigraphy)

Paleontology

Boundary value problem

Psychology

Vibration

Economics

Acoustics

Fourier series

Convergence (economics)

Rayleigh–Ritz method

Mechanics of Advanced Materials and Structures

In this paper, the analytical model is established on base of multi-segment partitioning strategy and first-order shear deformation theory. The displacement functions are made up of the Jacobi polynomials along the axial direction and Fourier series along the circumferential direction. In order to obtain continuity conditions and satisfy arbitrary boundary conditions, the penalty method about spring technique is adopted. The solutions about free vibration behaviors of combined composite laminated shell were obtained by approach of Rayleigh–Ritz. The convergence study and numerical verifications are carried out. Results show that the proposed method has a good stable and rapid convergence property.

Free vibration analysis of combined composite laminated cylindrical and spherical shells with arbitrary boundary conditions