A Multi-Mode Approach for the Nonlinear Vibrations of Circular Cylindrical Shells

2001 ◽  
Author(s):  
Francesco Pellicano ◽  
Marco Amabili ◽  
Michael P. Païdoussis
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Vibrations ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Symbolic Manipulation ◽  
Comparison Functions ◽  
Circular Cylindrical Shells ◽  
Multi Mode

Abstract The nonlinear vibrations of simply supported, circular cylindrical shells, having geometric nonlinearities is analyzed. Donnell’s nonlinear shallow-shell theory is used, and the partial differential equations are spatially discretized by means of the Galerkin procedure, using a large number of degrees of freedom. A symbolic manipulation code is developed for the discretization, allowing an unlimited number of modes. In the displacement expansion particular care is given to the comparison functions in order to reduce as much as possible the dimension of the dynamical system, without losing accuracy. Both driven and companion modes are included, allowing for traveling-wave response of the shell. The fundamental role of the axisymmetric modes, which are included in the expansion, is confirmed and a convergence analysis is performed. The effect of the geometric shell characteristics, radius, length and thickness, on the nonlinear behavior is analyzed.

The Influence of Initial Stresses and Boundary Restraints on the Nonlinear Vibrations of Cylindrical Shells

2000 ◽  
Author(s):  
David A. Evensen
Keyword(s):  
Nonlinear Vibrations ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Initial Stresses ◽  
Plane Boundary ◽  
Vibration Modes ◽  
Simple Support ◽  
Ritz Procedure ◽  
The Moment

Abstract A Rayleigh-Ritz procedure is used in conjunction with nonlinear shallow shell theory to study the influence of axisymmetric initial stresses on the nonlinear flexural vibrations of thin-walled cylindrical shells. A similar formulation is used to determine the effect of in-plane boundary conditions on the nonlinear vibrations. Both analyses make use of an assumed vibration mode which possesses a moment restraint at the edges of the shell. The results show that compressive initial stresses cause the vibrations to become increasingly nonlinear as buckling is approached. Initial tensile stresses generally cause the vibrations to become more nearly linear. In-plane restraints on the axial displacement at the ends of the shell have a hardening influence on the nonlinear behavior. This influence is most pronounced for vibration modes with high axial wave numbers. A study of the moment restraint at the boundary shows that for thin shells, the conditions of simple-support are closely approximated by the present analysis.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment

2004 ◽  
Author(s):  
U. Yuceoglu ◽  
V. O¨zerciyes
Keyword(s):  
Cylindrical Shell ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Adhesive Layer ◽  
Shear Stresses ◽  
First Order ◽  
Stress Resultant ◽  
Circular Cylindrical Shells

This study is concerned with the “Free Asymmetric Vibrations of Composite Full Circular Cylindrical Shells Stiffened by a Bonded Central Shell Segment.” The base shell is made of an orthotropic “full” circular cylindrical shell reinforced and/or stiffened by an adhesively bonded dissimilar, orthotropic “full” circular cylindrical shell segment. The stiffening shell segment is located at the mid-center of the composite system. The theoretical analysis is based on the “Timoshenko-Mindlin-(and Reissner) Shell Theory” which is a “First Order Shear Deformation Shell Theory (FSDST).” Thus, in both “base (or lower) shell” and in the “upper shell” segment, the transverse shear deformations and the extensional, translational and the rotary moments of inertia are taken into account in the formulation. In the very thin and linearly elastic adhesive layer, the transverse normal and shear stresses are accounted for. The sets of the dynamic equations, stress-resultant-displacement equations for both shells and the in-between adhesive layer are combined and manipulated and are finally reduced into a ”Governing System of the First Order Ordinary Differential Equations” in the “state-vector” form. This system is integrated by the “Modified Transfer Matrix Method (with Chebyshev Polynomials).” Some asymmetric mode shapes and the corresponding natural frequencies showing the effect of the “hard” and the “soft” adhesive cases are presented. Also, the parametric study of the “overlap length” (or the bonded joint length) on the natural frequencies in several modes is considered and plotted.

Development of beam modal function for free vibration analysis of FML circular cylindrical shells

2017 ◽  
Vol 24 (14) ◽  
pp. 3026-3035 ◽  
Author(s):  
Masood Mohandes ◽  
Ahmad Reza Ghasemi ◽  
Mohsen Irani-Rahagi ◽  
Keivan Torabi ◽  
Fathollah Taheri-Behrooz
Keyword(s):  
Free Vibration ◽  
Shell Theory ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Governing Equations ◽  
Fiber Metal Laminate ◽  
Circular Cylindrical Shells ◽  
Fiber Metal

The free vibration of fiber–metal laminate (FML) thin circular cylindrical shells with different boundary conditions has been studied in this research. Strain–displacement relations have been obtained according to Love’s first approximation shell theory. To satisfy the governing equations of motion, a beam modal function model has been used. The effects of different FML parameters such as material properties lay-up, volume fraction of metal, fiber orientation, and axial and circumferential wavenumbers on the vibration of the shell have been studied. The frequencies of shells have been calculated for carbon/epoxy and glass/epoxy as composites and for aluminum as metal. The results demonstrate that the influences of FML lay-up and volume fraction of composite on the frequencies of the shell are remarkable.

The Influence of Modal Geometrical Imperfections on the Nonlinear Vibrations of a Thin-Walled Circular Cylindrical Shell

2016 ◽  
Author(s):  
Lara Rodrigues ◽  
Paulo B. Gonçalves ◽  
Frederico M. A. Silva
Keyword(s):  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Geometric Imperfections ◽  
Modal Expansion ◽  
Simply Supported ◽  
Transversal Displacement ◽  
Geometrical Imperfections ◽  
Standard Galerkin Method

This work investigates the influence of several modal geometric imperfections on the nonlinear vibration of simply-supported transversally excited cylindrical shells. The Donnell nonlinear shallow shell theory is used to study the nonlinear vibrations of the shell. A general expression for the transversal displacement is obtained by a perturbation procedure which identifies all modes that couple with the linear modes through the quadratic and cubic nonlinearities. The imperfection shape is described by the same modal expansion. So, a particular solution is selected which ensures the convergence of the response up to very large deflections. Substituting the obtained modal expansions into the equations of motions and applying the standard Galerkin method, a discrete system in time domain is obtained. Several numerical strategies are used to study the nonlinear behavior of the imperfect shell. Special attention is given to the influence of the form of the initial geometric imperfections on the natural frequencies, frequency-amplitude relation, resonance curves and bifurcations of simply-supported transversally excited cylindrical shells.

Vibrations of Circular Cylindrical Shells With Complex Boundary Conditions

2006 ◽  
Author(s):  
Francesco Pellicano
Keyword(s):  
Boundary Conditions ◽  
Harmonic Functions ◽  
Nonlinear Vibrations ◽  
Cylindrical Shells ◽  
Rigid Bodies ◽  
Geometrically Nonlinear ◽  
Lagrange Equations ◽  
Displacement Fields ◽  
Complex Boundary ◽  
Circular Cylindrical Shells

In the present paper vibrations of circular cylindrical shells having different boundary conditions are analyzed. Sanders-Koiter theory is considered for shell modeling: both linear and nonlinear vibrations are analyzed. An energy approach based on Lagrange equations is considered; a mixed expansion of displacement fields, based on harmonic functions and Tchebyshev polynomials, is applied. Several boundary conditions are analyzed: simply supported, clamped-clamped, connection with rigid bodies. Comparisons with experiments and finite element analyses show that the technique is capable to model several and complex boundary conditions. Applications to geometrically nonlinear shells show that the technique is effective also in the case of nonlinear vibration: comparisons with the literature confirm the accuracy of the approach.

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