In this paper, the nonlinear vibrations of functionally graded (FGM) circular cylindrical shells are analyzed. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The displacement fields are expanded by means of a double mixed series based on Chebyshev orthogonal polynomials for the longitudinal variable and harmonic functions for the circumferential variable. Both driven and companion modes are considered, allowing for the travelling-wave response of the shell. Numerical analyses are carried out in order to characterize the nonlinear response when the shell is subjected to an harmonic external load. A convergence analysis is carried out to obtain the correct number of axisymmetric and asymmetric modes describing the actual nonlinear behavior of the shells. The effect of the geometry on the nonlinear vibrations of the shells is analyzed, and a comparison of nonlinear amplitude-frequency curves of cylindrical shells with different geometries is carried out. The influence of the companion mode participation on the nonlinear response of the shells is analyzed; frequency-response curves with companion mode participation (i.e. the actual response of the shell) are obtained. The present model is validated in the linear field (natural frequencies) by means of data present in the literature.

Nonlinear vibrations of functionally graded cylindrical shells: Effect of companion mode participation / Strozzi, Matteo; Pellicano, Francesco. - (2012). (Intervento presentato al convegno 19th International Congress on Sound and Vibration ICSV 2012 tenutosi a Vilnius, Lithuania nel July 8-12, 2012).

Nonlinear vibrations of functionally graded cylindrical shells: Effect of companion mode participation

STROZZI, MATTEO;PELLICANO, Francesco
2012

Abstract

In this paper, the nonlinear vibrations of functionally graded (FGM) circular cylindrical shells are analyzed. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The shell deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The displacement fields are expanded by means of a double mixed series based on Chebyshev orthogonal polynomials for the longitudinal variable and harmonic functions for the circumferential variable. Both driven and companion modes are considered, allowing for the travelling-wave response of the shell. Numerical analyses are carried out in order to characterize the nonlinear response when the shell is subjected to an harmonic external load. A convergence analysis is carried out to obtain the correct number of axisymmetric and asymmetric modes describing the actual nonlinear behavior of the shells. The effect of the geometry on the nonlinear vibrations of the shells is analyzed, and a comparison of nonlinear amplitude-frequency curves of cylindrical shells with different geometries is carried out. The influence of the companion mode participation on the nonlinear response of the shells is analyzed; frequency-response curves with companion mode participation (i.e. the actual response of the shell) are obtained. The present model is validated in the linear field (natural frequencies) by means of data present in the literature.
2012
19th International Congress on Sound and Vibration ICSV 2012
Vilnius, Lithuania
July 8-12, 2012
Strozzi, Matteo; Pellicano, Francesco
Nonlinear vibrations of functionally graded cylindrical shells: Effect of companion mode participation / Strozzi, Matteo; Pellicano, Francesco. - (2012). (Intervento presentato al convegno 19th International Congress on Sound and Vibration ICSV 2012 tenutosi a Vilnius, Lithuania nel July 8-12, 2012).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1083491
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