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.

A New Nonlinear Higher-Order Shear Deformation Theory for Nonlinear Vibrations of Laminated Shells

2010 ◽  
Author(s):  
M. Amabili ◽  
J. N. Reddy
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Curvilinear Coordinates ◽  
Geometrically Nonlinear ◽  
Geometric Imperfections ◽  
Laminated Shells

A consistent higher-order shear deformation nonlinear theory is developed for shells of generic shape; taking geometric imperfections into account. The geometrically nonlinear strain-displacement relationships are derived retaining full nonlinear terms in the in-plane displacements; they are presented in curvilinear coordinates in a formulation ready to be implemented. Then, large-amplitude forced vibrations of a simply supported, laminated circular cylindrical shell are studied (i) by using the developed theory, and (ii) keeping only nonlinear terms of the von Ka´rma´n type. Results show that inaccurate results are obtained by keeping only nonlinear terms of the von Ka´rma´n type for vibration amplitudes of about two times the shell thickness for the studied case.

scholarly journals EXPERIMENTAL AND NUMERICAL INVESTIGATIONS ON THE STABILITY OF CYLINDRICAL SHELLS

2021 ◽  
Vol 26 (4) ◽  
pp. 34-39
Author(s):  
ATTILA BAKSA ◽  
DAVID GONCZI ◽  
LASZLA PETER KISS ◽  
PETER ZOLTAN KOVACS ◽  
ZSOLT LUKACS
Keyword(s):  
Cylindrical Shells ◽  
Element Model ◽  
Tolerance Range ◽  
Axial Pressure ◽  
Geometric Imperfections ◽  
Numerical Investigations ◽  
Negative Effect ◽  
Geometrical Imperfections ◽  
Post Buckling ◽  
The Stability

The stability of thin-walled cylindrical shells under axial pressure is investigated. The results of both experiments and numerical simulations are presented. An appropriate finite element model is introduced that accounts not only for geometric imperfections but also for non-linearities. It is found that small geometrical imperfections within a given tolerance range have considerable negative effect on the buckling load compared to perfect geometry. Various post buckling shell shapes are possible, which depend on these imperfections. The experiments and simulations show a very good correlation.

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.

Effects of Initial Geometric Imperfections on Parametric Instability of Rectangular Plates

2001 ◽  
Author(s):  
Lyne St-Georges ◽  
G. L. Ostiguy
Keyword(s):  
Lateral Displacement ◽  
Plate Thickness ◽  
Parametric Instability ◽  
Experimental Tests ◽  
Rectangular Plates ◽  
Rational Analysis ◽  
Geometric Imperfections ◽  
Simply Supported ◽  
Geometrical Imperfections ◽  
Initial Geometric Imperfections

Abstract The authors present a rational analysis of the effect of initial geometric imperfections on the dynamic behaviour of rectangular plates activated by a parametric excitation. This subject has been extensively investigated theoretically in the past, but no experimental data seems to be complete enough to validate the theory. The main objective of this investigation is to fill this void by performing experimental tests on geometrically imperfect plates, and to highlight the geometric imperfection’s influence on resonance’s curves. The study is carried out for an isotropic, elastic, homogeneous, and thin rectangular plate. The plate under investigation is subjected to the action of an in-plane force uniformly distributed along two opposite edges, is initially stress free and simply supported. Theoretical calculation and experimental tests are performed. In the theoretical approach, a dynamic version of the Von Kármán non-linear theory is used to evaluate the lateral displacement of the plate. The test rig used in the experimentation simulates simply supported edges and can accept plates with different aspect ratio. The test plates are pre-formed with lateral deflection or geometrical imperfections, in a shape corresponding to various vibration modes. Comparison between experimental and theoretical results reveals good agreement and allows the determination of the theory’s limitations. The theory used correctly describes the behaviour of the plate when imperfection amplitude is inferior to the plate thickness.

Effects of Axial Imperfections on Vibrations of Anti-Symmetric Cross-Ply, Oval Cylindrical Shells

1986 ◽  
Vol 53 (3) ◽  
pp. 675-680 ◽  
Author(s):  
David Hui ◽  
I. H. Y. Du
Keyword(s):  
Vibration Mode ◽  
Cylindrical Shells ◽  
Homogeneous Material ◽  
Fundamental Vibration ◽  
Geometric Imperfections ◽  
Simply Supported ◽  
Fundamental Frequencies ◽  
Young’S Moduli ◽  
Wave Numbers ◽  
Oval Cylindrical Shells

This paper examines the effects of axial geometric imperfections on the fundamental vibration frequencies of cross-ply simply-supported oval cylindrical shells. It is found that the presence of such imperfection with small amplitudes may significantly raise or lower the fundamental frequencies, depending on the wave numbers of the imperfection and vibration mode. The effects of oval eccentricity, bending-stretching coupling of the material, the reduced-Batdorf parameter and Young’s moduli ratio are examined. It appears that the present problem has not been examined, even in the simplified case of oval cylindrical shells made of isotropic-homogeneous material.

Experimental Study on Pre-Stressed Circular Cylindrical Shell

2012 ◽  
Author(s):  
Antonio Zippo ◽  
Marco Barbieri ◽  
Matteo Strozzi ◽  
Vito Errede ◽  
Francesco Pellicano
Keyword(s):  
Experimental Study ◽  
Cylindrical Shell ◽  
Axial Load ◽  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Experimental Studies ◽  
Element Model ◽  
Experimental Setup ◽  
Circular Cylindrical Shells

In this paper an experimental study on circular cylindrical shells subjected to axial compressive and periodic loads is presented. Even though many researchers have extensively studied nonlinear vibrations of cylindrical shells, experimental studies are rather limited in number. The experimental setup is explained and deeply described along with the analysis of preliminary results. The linear and the nonlinear dynamic behavior associated with a combined effect of compressive static and a periodic axial load have been investigated for different combinations of loads; moreover, a non stationary response of the structure has been observed close to one of the resonances. The linear shell behavior is also investigated by means of a finite element model, in order to enhance the comprehension of experimental results.

Influence of Geometric Imperfections and In-Plane Constraints on Nonlinear Vibrations of Simply Supported Cylindrical Panels

1984 ◽  
Vol 51 (2) ◽  
pp. 383-390 ◽  
Author(s):  
David Hui
Keyword(s):  
Shell Thickness ◽  
Nonlinear Vibrations ◽  
Vibration Mode ◽  
Vibration Frequencies ◽  
Linear Vibration ◽  
Geometric Imperfections ◽  
Simply Supported ◽  
Cylindrical Panels ◽  
Initial Geometric Imperfections ◽  
Large Amplitude Vibrations

This papers deals with the effects of initial geometric imperfections on large-amplitude vibrations of cylindrical panels simply supported along all four edges. In-plane movable and in-plane immovable boundary conditions are considered for each pair of parallel edges. Depending on whether the number of axial and circumferential half waves are odd or even, the presence of geometric imperfections (taken to be of the same shape as the vibration mode) of the order of the shell thickness may significantly raise or lower the linear vibration frequencies. In general, an increase (decrease) in the linear vibration frequency corresponds to a more pronounced soft-spring (hard-spring) behavior in nonlinear vibration.

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.

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