In this paper, the effect of the geometry on the nonlinear vibrations of functionally graded (FGM) cylindrical shells is 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 harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. In the linear analysis, after spatial discretization, mass and stiff matrices are computed, natural frequencies and mode shapes of the shell are obtained. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions obtained by the linear analysis; specific modes are selected. The Lagrange equations reduce nonlinear partial differential equations to a set of ordinary differential equations. Numerical analyses are carried out in order to characterize the nonlinear response of the shell. A convergence analysis is carried out to determine the correct number of the modes to be used. The analysis is focused on determining the nonlinear character of the response as the geometry of the shell varies.

Nonlinear vibrations of functionally graded cylindrical shells: Effect of the geometry / Strozzi, Matteo; Pellicano, Francesco; Zippo, Antonio. - 1:(2012), pp. 973-979. (Intervento presentato al convegno ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012 tenutosi a Chicago, IL, usa nel August 12-15, 2012) [10.1115/DETC2012-70417].

Nonlinear vibrations of functionally graded cylindrical shells: Effect of the geometry

Abstract

In this paper, the effect of the geometry on the nonlinear vibrations of functionally graded (FGM) cylindrical shells is 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 harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. In the linear analysis, after spatial discretization, mass and stiff matrices are computed, natural frequencies and mode shapes of the shell are obtained. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions obtained by the linear analysis; specific modes are selected. The Lagrange equations reduce nonlinear partial differential equations to a set of ordinary differential equations. Numerical analyses are carried out in order to characterize the nonlinear response of the shell. A convergence analysis is carried out to determine the correct number of the modes to be used. The analysis is focused on determining the nonlinear character of the response as the geometry of the shell varies.
Scheda breve Scheda completa Scheda completa (DC)
2012
ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012
Chicago, IL, usa
August 12-15, 2012
1
973
979
Strozzi, Matteo; Pellicano, Francesco; Zippo, Antonio
Nonlinear vibrations of functionally graded cylindrical shells: Effect of the geometry / Strozzi, Matteo; Pellicano, Francesco; Zippo, Antonio. - 1:(2012), pp. 973-979. (Intervento presentato al convegno ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012 tenutosi a Chicago, IL, usa nel August 12-15, 2012) [10.1115/DETC2012-70417].
File in questo prodotto:
File
Strozzi_Pellicano_Zippo_Final_Paper_ASME_2012.pdf

Open access

Tipologia: Abstract
Dimensione 538.19 kB
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/1083499`