Multimode Approach to Nonlinear Supersonic Flutter of Imperfect Circular Cylindrical Shells

2001 ◽  
Vol 69 (2) ◽  
pp. 117-129 ◽  
Author(s):  
M. Amabili ◽  
F. Pellicano
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Dynamic Pressure ◽  
Cylindrical Shells ◽  
Travelling Wave ◽  
Finite Amplitude ◽  
Research Center ◽  
Piston Theory ◽  
Nasa Ames Research ◽  
Circular Cylindrical Shells

The aeroelastic stability of simply supported, circular cylindrical shells in supersonic flow is investigated by using both linear aerodynamics (first-order piston theory) and nonlinear aerodynamics (third-order piston theory). Geometric nonlinearities, due to finite amplitude shell deformations, are considered by using the Donnell’s nonlinear shallow-shell theory, and the effect of viscous structural damping is taken into account. The system is discretized by Galerkin method and is investigated by using a model involving up to 22 degrees-of-freedom, allowing for travelling-wave flutter around the shell and axisymmetric contraction of the shell. Asymmetric and axisymmetric geometric imperfections of circular cylindrical shells are taken into account. Numerical calculations are carried out for a very thin circular shell at fixed Mach number 3 tested at the NASA Ames Research Center. Results show that the system loses stability by travelling-wave flutter around the shell through supercritical bifurcation. Nonsimple harmonic motion is observed for sufficiently high post-critical dynamic pressure. A very good agreement between theoretical and existing experimental data has been found for the onset of flutter, flutter amplitude, and frequency. Results show that onset of flutter is very sensible to small initial imperfections of the shells. The influence of pressure differential across the shell skin has also been deeply investigated. The present study gives, for the first time, results in agreement with experimental data obtained at the NASA Ames Research Center more than three decades ago.

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.

Nonlinear Stability of Circular Cylindrical Shells in Annular and Unbounded Axial Flow

2001 ◽  
Vol 68 (6) ◽  
pp. 827-834 ◽  
Author(s):  
M. Amabili ◽  
F. Pellicano ◽  
M. A. Pai¨doussis
Keyword(s):  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Cylindrical Shells ◽  
Axial Flow ◽  
Longitudinal Direction ◽  
Finite Amplitude ◽  
External Flow ◽  
Linear Potential ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

The stability of circular cylindrical shells with supported ends in compressible, inviscid axial flow is investigated. Nonlinearities due to finite-amplitude shell motion are considered by using Donnell’s nonlinear shallow-shell theory; the effect of viscous structural damping is taken into account. Two different in-plane constraints are applied at 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 discretized by the Galerkin method and is investigated by using a model involving seven degrees-of-freedom, allowing for traveling-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 states can occur well before the onset of instability predicted by linear theory, showing that a linear study of shell stability is not sufficient for engineering applications.

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.

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.

Imperfection Sensitivity of Compressed Circular Cylindrical Shells Under Periodic Axial Loads

2009 ◽  
Author(s):  
Francesco Pellicano
Keyword(s):  
Differential Equations ◽  
Dynamic Stability ◽  
Cylindrical Shells ◽  
Nonlinear Partial Differential Equations ◽  
Excitation Frequency ◽  
Finite Amplitude ◽  
Axial Loads ◽  
Imperfection Sensitivity ◽  
Lagrange Equations ◽  
Circular Cylindrical Shells

In the present paper the dynamic stability of circular cylindrical shells is investigated; the combined effect of compressive static and periodic axial loads is considered. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration; Lagrange equations are used to reduce the nonlinear partial differential equations to a set of ordinary differential equations. The dynamic stability is investigated using direct numerical simulation and a dichotomic algorithm to find the instability boundaries as the excitation frequency is varied; the effect of geometric imperfections is investigated in detail. The accuracy of the approach is checked by means of comparisons with the literature.

Non-Linear Vibrations of Fluid-Filled, Simply Supported Circular Cylindrical Shells: Theory and Experiments

2000 ◽  
Author(s):  
M. Amabili ◽  
F. Pellicano ◽  
M. P. Païdoussis
Keyword(s):  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Harmonic Excitation ◽  
Travelling Wave ◽  
Galerkin Projection ◽  
Inviscid Fluid ◽  
Simply Supported ◽  
Longitudinal Modes ◽  
Circular Cylindrical Shells

Abstract The large-amplitude response of thin, simply supported circular cylindrical shells to a harmonic excitation in the spectral neighbourhood of one of the lowest natural frequencies is investigated. Donnell’s nonlinear shallow-shell theory is used and the solution is obtained by Galerkin projection. A mode expansion including driven and companion modes, axisymmetric modes and additional asymmetric modes is used. In particular, asymmetric modes with twice the number of circumferential waves of driven and companion modes are included in the analysis. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied. The effect of internal quiescent, incompressible and inviscid fluid is investigated. The equations of motion are studied by using a code based on the Collocation Method. Validation of the present model is obtained by comparison with other authoritative results and new experimental results. The effect of the number of axisymmetric modes used in the expansion on the response of the shell is investigated, clarifying questions open for a long time. The contribution of additional longitudinal modes is absolutely insignificant in both the driven and companion mode responses. The effect of modes with harmonics of the circumferential mode number n under consideration is limited so far as the trend of nonlinearity is concerned, but is significant in the response with companion mode participation for lightly damped shells (empty shells). Results show the occurrence of travelling wave response in the proximity of the resonance frequency, the fundamental role of the first and third axisymmetric modes in the expansion of the radial deflection with one longitudinal half-wave, and limit cycle responses. A liquid (water) contained in the shell generates a much stronger softening behaviour of the system. Experiments with a water-filled circular cylindrical shell made of steel are in very good agreement with the present theory.

Dynamic Stability of Transverse Axisymmetric Waves in Circular Cylindrical Shells

1974 ◽  
Vol 41 (1) ◽  
pp. 77-82 ◽  
Author(s):  
J. H. Ginsberg
Keyword(s):  
Asymptotic Expansion ◽  
Phase Velocity ◽  
Degrees Of Freedom ◽  
Cylindrical Shells ◽  
Transverse Displacement ◽  
First Approximation ◽  
Uniform Asymptotic Expansion ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Stability Limits

Previous experiments [1] have indicated that axisymmetric waves may be unstable and that nonsymmetric waves may result. To show that it is possible for such a phenomenon to occur even in perfectly cylindrical shells, a new mechanism for the coupling of the two types of waves is determined. Relationships for the phase velocity of steady-state waves as a function of the amplitude of transverse displacement are obtained. The stability of the system is shown to be defined by an equivalent nonlinear system with two degrees of freedom. It is found that the stability limits are the bifurcation points in the amplitude-phase velocity diagram for the axisymmetric and nonsymmetric waves. The solution is a uniform asymptotic expansion of the modal series for the displacement components and retains all effects significant to the first approximation of the nonlinearity.

On the Buckling of Rings Subject to Impulsive Pressures

1965 ◽  
Vol 32 (3) ◽  
pp. 511-518 ◽  
Author(s):  
W. Stuiver
Keyword(s):  
Experimental Data ◽  
Plastic Flow ◽  
Analytical Procedure ◽  
Cylindrical Shells ◽  
Elastic Instability ◽  
Circular Cylindrical Shells ◽  
Single Approach

It is shown in this paper that previous, independent analyses of the phenomena of dynamic elastic instability and dynamic plastic-flow buckling of circular cylindrical shells can be combined in a single approach leading to results consistent with those that follow from these analyses. The response of the shell in both cases is governed by the interaction between the fundamental radial, purely extensional mode of deformation and inextensional flexural modes always present in the response. An analytical procedure is given for the determination of dominant modes in the elastic and plastic phases of the response, and the results of this procedure are verified by comparison with numerical and experimental data.

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