Large-amplitude nonlinear vibrations of circular cylindrical shells with different boundary conditions are investigated. The Sanders-Koiter nonlinear shell theory, which includes shear deformation, is used to calculate the elastic strain energy. Shell’s displacement fields (longitudinal, circumferential and radial) are expanded by means of a double mixed series: harmonic functions for the circumferential variable; Chebyshev polynomials for the longitudinal variable. Boundary conditions for both simply supported and clamped-clamped shells are exactly satisfied. The Lagrangian approach is applied to obtain a system of nonlinear ordinary differential equations. Different expansions involving from 14 to 34 generalized co-ordinates, associated with natural modes of both simply supported and clamped-clamped shells are used to study the convergence of the solution. The nonlinear equations of motion are studied by using arclength continuation method and bifurcation analysis. Numerical responses obtained in the spectral neighborhood of the lowest natural frequency are compared with the results available in literature.
Only experimental studies are available on large amplitude vibrations of cantilever shells. In the present paper, large-amplitude nonlinear vibrations of cantilever circular cylindrical shell are investigated. Shells with perfect and imperfect shape are studied. The Sanders-Koiter nonlinear shell theory, which includes shear deformation, is used to calculate the elastic strain energy. Shell’s displacement fields (longitudinal, circumferential and radial) are expanded by means of a double mixed series: harmonic functions for the circumferential variable; Chebyshev polynomials for the longitudinal variable. Boundary conditions are exactly satisfied. The Lagrangian approach is applied to obtain a system of nonlinear ordinary differential equations. The nonlinear equations of motion are studied by using arclength continuation method and bifurcation analysis. Numerical responses in the spectral neighborhood of the lowest natural frequency are obtained.
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