Geometrically Nonlinear Forced Vibrations of Circular Cylindrical Shells Containing Flowing Fluid

2000 ◽  
Author(s):  
F. Pellicano ◽  
M. Amabili ◽  
M. P. Païdoussis
Keyword(s):  
Stochastic Dynamics ◽  
Cylindrical Shells ◽  
Harmonic Excitation ◽  
Linear Potential ◽  
Stochastic Motion ◽  
Flowing Fluid ◽  
Periodic Response ◽  
Shell Motion ◽  
Circular Cylindrical Shells ◽  
Flow Velocities

Abstract The response of a shell conveying fluid to harmonic excitation, in the spectral neighbourhood of one of the lowest natural frequencies, is investigated for different flow velocities. Nonlinearities due to moderately large amplitude shell motion are considered by using the nonlinear Donnell shallow shell theory. Linear potential flow theory is applied to describe the fluid-structure interaction by using the model proposed by Païdoussis and Denise. For different amplitude and frequency of the excitation and for different flow velocities, the following are investigated numerically: (i) periodic response of the system; (ii) unsteady and stochastic motion; (iii) loss of stability by jumps to bifurcated branches. The effect of the flow velocity on the nonlinear periodic response of the system has also been investigated. Poincaré maps and bifurcation diagrams are used to study the unsteady and stochastic dynamics of the system. Amplitude-modulated motions, multi-periodic solutions, chaotic responses and the so-called “blue sky catastrophe” phenomenon have been observed for different values of the system parameters; the latter two have been predicted here probably for the first time for the dynamics of circular cylindrical shells.

Chaotic Vibrations of Circular Shells Conveying Flowing Fluid

2009 ◽  
Author(s):  
Marco Amabili ◽  
Kostas Karagiozis ◽  
Michael P. Pai¨doussis
Keyword(s):  
Natural Frequencies ◽  
Stochastic Dynamics ◽  
Harmonic Excitation ◽  
Linear Potential ◽  
Viscous Effects ◽  
Stochastic Motion ◽  
Flowing Fluid ◽  
Periodic Response ◽  
Chaotic Vibrations ◽  
Flow Velocities

Shells containing flowing fluids are widely used in engineering applications, and they are subject to manifold excitations of different kinds, including flow excitations. Usually these shells are made as thin as possible for weight and cost economy; therefore, they are quite fragile, and their response to such excitations is of great interest. The response of a shell conveying fluid to harmonic excitation, in the spectral neighbourhood of one of the lowest natural frequencies, is investigated for different flow velocities. The theoretical model has been developed using the Donnell theory retaining in-plane inertia. Linear potential flow theory is applied to describe the fluid-structure interaction, and the steady viscous effects are added to take into account flow viscosity. For different amplitudes and frequencies of the excitation and for different flow velocities, the following are investigated numerically: (i) periodic response of the system; (ii) unsteady and stochastic motion; (iii) loss of stability by jumps to bifurcated branches. The effect of the flow velocity on the nonlinear periodic response of the system has also been investigated. Poincare´ maps, bifurcation diagrams and Lyapunov exponents have been used to study the unsteady and stochastic dynamics of the system.

Nonlinear Vibrations and Stability of Shells Conveying Water Flow

2009 ◽  
Author(s):  
Marco Amabili ◽  
Kostas Karagiozis ◽  
Michael P. Pai¨doussis
Keyword(s):  
Nonlinear Vibrations ◽  
Natural Frequencies ◽  
Stochastic Dynamics ◽  
Harmonic Excitation ◽  
Linear Potential ◽  
Viscous Effects ◽  
Stochastic Motion ◽  
Periodic Response ◽  
Structure Interaction ◽  
Flow Velocities

Shells containing flowing fluids are widely used in engineering applications, and they are subject to manifold excitations of different kinds, including flow excitations. The response of a shell conveying fluid to harmonic excitation, in the spectral neighbourhood of one of the lowest natural frequencies, is investigated for different flow velocities. The theoretical model has been developed using the Donnell theory retaining in-plane inertia. Linear potential flow theory is applied to describe the fluid-structure interaction, and the steady viscous effects are added to take into account flow viscosity. For different amplitudes and frequencies of the excitation and for different flow velocities, the following are investigated numerically: (i) periodic response of the system; (ii) unsteady and stochastic motion; (iii) loss of stability by jumps to bifurcated branches. The effect of the flow velocity on the nonlinear periodic response of the system has also been investigated. Bifurcation diagrams and Lyapunov exponents have been used to study the unsteady and stochastic dynamics of the system.

Nonlinear Stability of Circular Cylindrical Shells in Axially Flowing Fluid

2000 ◽  
Author(s):  
M. Amabili ◽  
M. P. Païdoussis ◽  
F. Pellicano
Keyword(s):  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Cylindrical Shells ◽  
Axial Flow ◽  
Longitudinal Direction ◽  
Travelling Wave ◽  
External Flow ◽  
Linear Potential ◽  
Flowing Fluid ◽  
Circular Cylindrical Shells

Abstract The stability of supported, circular cylindrical shells in compressible, inviscid axial flow is investigated. Nonlinearities due to large amplitude shell motion are considered by using the nonlinear Donnell shallow shell theory and the effect of viscous structural damping is taken into account. Two different in-plane constraints are applied to the shell edges: zero axial force and zero axial displacement; the other boundary conditions are those for simply supported shells. Linear potential flow theory is applied to describe the fluid-structure interaction. Both annular and unbounded external flow are considered by using two different sets of boundary conditions for the flow beyond the shell length: (i) a flexible wall of infinite extent in the longitudinal direction, and (ii) rigid extensions of the shell (baffles). The system is discretised by Galerkin projections and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Results for both annular and unbounded external flow show that the system loses stability by divergence through strongly subcritical bifurcations. Jumps to bifurcated positions can happen much before the onset of instability predicted by linear theories, showing the necessity of a nonlinear study.

Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction

2003 ◽  
Vol 56 (4) ◽  
pp. 349-381 ◽  
Author(s):  
Marco Amabili ◽  
Michael P. Paı¨doussis
Keyword(s):  
Cylindrical Shells ◽  
Fluid Structure Interaction ◽  
Harmonic Excitation ◽  
Forced Vibrations ◽  
Geometrically Nonlinear ◽  
Flowing Fluid ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Free And Forced Vibrations ◽  
Circular Cylindrical Shells

This literature review focuses mainly on geometrically nonlinear (finite amplitude) free and forced vibrations of circular cylindrical shells and panels, with and without fluid-structure interaction. Work on shells and curved panels of different geometries is but briefly discussed. In addition, studies dealing with particular dynamical problems involving finite deformations, eg, dynamic buckling, stability, and flutter of shells coupled to flowing fluids, are also discussed. This review is structured as follows: after a short introduction on some of the fundamentals of geometrically nonlinear theory of shells, vibrations of shells and panels in vacuo are discussed. Free and forced vibrations under radial harmonic excitation (Section 2.2), parametric excitation (axial tension or compression and pressure-induced excitations) (Section 2.3), and response to radial transient loads (Section 2.4) are reviewed separately. Studies on shells and panels in contact with dense fluids (liquids) follow; some of these studies present very interesting results using methods also suitable for shells and panels in vacuo. Then, in Section 4, shells and panels in contact with light fluids (gases) are treated, including the problem of stability (divergence and flutter) of circular cylindrical panels and shells coupled to flowing fluid. For shells coupled to flowing fluid, only the case of axial flow is reviewed in this paper. Finally, papers dealing with experiments are reviewed in Section 5. There are 356 references cited in this article.

Stability of Empty and Fluid-Filled Circular Cylindrical Shells Subjected to Dynamic Axial Loads

2002 ◽  
Author(s):  
F. Pellicano ◽  
M. Amabili ◽  
M. P. Pai¨doussis
Keyword(s):  
Dynamic Stability ◽  
Cylindrical Shells ◽  
Travelling Wave ◽  
Finite Amplitude ◽  
Axial Loads ◽  
Simply Supported ◽  
Mean Oscillation ◽  
Shell Motion ◽  
Circular Cylindrical Shells ◽  
The Mean

In the present study the dynamic stability of simply supported, circular cylindrical shells subjected to dynamic axial loads is analyzed. Geometric nonlinearities due to finite-amplitude shell motion are considered by using the Donnell’s nonlinear shallow-shell theory. The effect of structural damping is taken into account. A discretization method based on a series expansion involving a large number of linear modes, including axisymmetric and asymmetric modes, and on the Galerkin procedure is developed. Both driven and companion modes are included allowing for travelling-wave response of the shell. Axisymmetric modes are included because they are essential in simulating the inward deflection of the mean oscillation with respect to the equilibrium position. The shell is simply supported and presents a finite length. Boundary conditions are considered in the model, which includes also the contribution of the external axial loads acting at the shell edges. The effect of a contained liquid is also considered. The linear dynamic stability and nonlinear response are analysed by using continuation techniques.

Comparison of Different Shell Theories for Large-Amplitude Vibrations of Circular Cylindrical Shells

2002 ◽  
Author(s):  
M. Amabili
Keyword(s):  
Large Amplitude ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Continuation Method ◽  
Elastic Strain Energy ◽  
Harmonic Excitation ◽  
Lagrange Equations ◽  
Simply Supported ◽  
Nonlinear Shell ◽  
Circular Cylindrical Shells

Large-amplitude (geometrically nonlinear) vibrations of circular cylindrical shells subjected to radial harmonic excitation in the spectral neighbourhood of the lowest resonances are investigated. The Lagrange equations of motion are obtained by an energy approach, retaining damping through Rayleigh’s dissipation function. Four different nonlinear shell theories, namely Donnell’s, Sanders-Koiter, Flu¨gge-Lur’e-Byrne and Novozhilov’s theories, are used to calculate the elastic strain energy. The formulation is also valid for orthotropic and symmetric cross-ply laminated composite shells. The large-amplitude response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of the lowest natural frequency is computed for all these shell theories. Numerical responses obtained by using these four nonlinear shell theories are also compared to results obtained by Galerkin approach, used to discretise Donnell’s nonlinear shallow-shell equation of motion. A validation of calculations by comparison to experimental results is also performed. Boundary conditions for simply supported shells are exactly satisfied. Different expansions involving from 14 to 48 generalized coordinates, associated to natural modes of simply supported shells, are used. The nonlinear equations of motion are studied by using a code based on arclength continuation method that allows bifurcation analysis.

Sign in / Sign up

Export Citation Format

Share Document