Large-Amplitude Vibrations of Empty and Fluid-Filled Circular Cylindrical Shells With Imperfections: Theory and Experiments

2002 ◽  
Author(s):  
M. Amabili ◽  
M. Pellegrini ◽  
F. Pellicano
Keyword(s):  
Large Amplitude ◽  
Cylindrical Shells ◽  
Continuation Method ◽  
Harmonic Excitation ◽  
Steel Shell ◽  
Nonlinear Phenomena ◽  
Inviscid Fluid ◽  
Simply Supported ◽  
Circular Cylindrical Shells ◽  
Actual Geometry

The large-amplitude response of perfect and imperfect, simply supported circular cylindrical shells to harmonic excitation in the spectral neighbourhood of some of the lowest natural frequencies is investigated. Donnell’s nonlinear shallow-shell theory is used and the solution is obtained by Galerkin method. Several expansions involving 16 or more natural modes of the shell are used. The boundary conditions on the radial displacement (simply supported shell at both ends) and the continuity of circumferential displacement are exactly satisfied. The effect of internal quiescent, incompressible and inviscid fluid is investigated. The nonlinear equations of motion are studied by using a code based on arclength continuation method. A series of accurate experiments on forced vibrations of an empty and water-filled stainless-steel shell have been performed. Several modes have been intensively investigated for different vibration amplitudes. A closed loop control of the force excitation has been used. The actual geometry of the test shell has been measured and the geometric imperfections have been introduced in the theoretical model. Several interesting nonlinear phenomena have been experimentally observed and numerically reproduced, as: softening-type nonlinearity, different types of travelling wave response in the proximity of resonances and amplitude-modulated response. For all the modes investigated, the theoretical and experimental results are in strong agreement.

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.

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.

Nonlinear Vibrations of Circular Cylindrical Shells With Different Boundary Conditions

2009 ◽  
Author(s):  
M. Amabili ◽  
Ye. Kurylov
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Vibrations ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Continuation Method ◽  
Elastic Strain Energy ◽  
Variable Boundary ◽  
Different Boundary Conditions ◽  
Simply Supported ◽  
Circular Cylindrical Shells

Large-amplitude nonlinear vibrations of circular cylindrical shells with different boundary conditions are investigated. The Sanders-Koiter nonlinear shell theory, which includes shear deformation, is used to calculate the elastic strain energy. Shell’s displacement fields (longitudinal, circumferential and radial) are expanded by means of a double mixed series: harmonic functions for the circumferential variable; Chebyshev polynomials for the longitudinal variable. Boundary conditions for both simply supported and clamped-clamped shells are exactly satisfied. The Lagrangian approach is applied to obtain a system of nonlinear ordinary differential equations. Different expansions involving from 14 to 34 generalized co-ordinates, associated with natural modes of both simply supported and clamped-clamped shells are used to study the convergence of the solution. The nonlinear equations of motion are studied by using arclength continuation method and bifurcation analysis. Numerical responses obtained in the spectral neighborhood of the lowest natural frequency are compared with the results available in literature.

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.

Free vibration analysis of porous laminated rotating circular cylindrical shells

2019 ◽  
Vol 25 (18) ◽  
pp. 2494-2508 ◽  
Author(s):  
Ahmad Reza Ghasemi ◽  
Mohammad Meskini
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Equilibrium Equations ◽  
Rotating Speed ◽  
Simply Supported ◽  
Numerical Result ◽  
Love’S Shell Theory ◽  
Circular Cylindrical Shells

In this research, investigations are presented of the free vibration of porous laminated rotating circular cylindrical shells based on Love’s shell theory with simply supported boundary conditions. The equilibrium equations for circular cylindrical shells are obtained using Hamilton’s principle. Also, Navier’s solution is used to solve the equations of the cylindrical shell due to the simply supported boundary conditions. The results are compared with previous results of other researchers. The numerical result of this study indicates that with increase of the porosity coefficient the nondimensional backward and forward frequency decreased. Then the results of the free vibration of rotating cylindrical shells are presented in terms of the effects of porous coefficients, porous type, length to radius ratio, rotating speed, and axial and circumferential wave numbers.

ON THE FUNDAMENTAL FREQUENCIES AND MODES OF FREE VIBRATION OF CYLINDRICAL SHELLS

1991 ◽  
Vol 15 (2) ◽  
pp. 147-159
Author(s):  
J.L. Urrutia-Galicia ◽  
L.J. Arango
Keyword(s):  
Free Vibration ◽  
Elastic Material ◽  
Cylindrical Shells ◽  
Simply Supported ◽  
Fundamental Frequencies ◽  
Circular Cylindrical Shells

The fundamental frequencies and modes of free vibration of simply supported circular cylindrical shells are explored. The results include the fundamental frequencies ωmn and the modes (m,n) of steel cylindrical shells which are presented in the form of a nomogram, see Figure 6. Besides, single more general formulas are given for cylindrical shells made out of any elastic material which turn out to be very suitable for design and analysis purposes.

Nonlinear Vibrations of Rectangular Plates With Different Boundary Conditions: Theory and Experiments

2005 ◽  
Author(s):  
M. Amabili ◽  
C. Augenti
Keyword(s):  
Boundary Condition ◽  
Good Accuracy ◽  
Continuation Method ◽  
Laser System ◽  
Normal Displacement ◽  
Vibration Modes ◽  
Rectangular Plates ◽  
Geometric Imperfections ◽  
Simply Supported ◽  
Actual Geometry

Large-amplitude vibrations of rectangular plates subjected to harmonic excitation are investigated. The von Ka´rma´n nonlinear strain-displacement relationships are used to describe the geometric nonlinearity. A specific boundary condition, with restrained normal displacement at the plate edges and fully free in-plane displacements, not previously considered, has been introduced as a consequence that it is very close to the experimental boundary condition. Results for this boundary condition are compared to nonlinear results previously obtained for: (i) simply supported plates with immovable edges; (ii) simply supported plates with movable edges, and (iii) fully clamped plates. The nonlinear equations of motion are studied by using a code based on arclength continuation method. A thin rectangular stainless-steel plate has been inserted in a metal frame; this constraint is approximated with good accuracy by the newly introduced boundary condition. The plate inserted into the frame has been measured with a 3D laser system in order to reconstruct the actual geometry and identify geometric imperfections (out-of-planarity). The plate has been experimentally tested in laboratory for both the first and second vibration modes for several excitation magnitudes in order to characterize the nonlinearity of the plate with imperfections. Numerical results are able to follow experimental results with good accuracy for both vibration modes and for different excitation levels once the geometric imperfection is introduced in the model. Effects of geometric imperfections on the trend of nonlinearity and on natural frequencies are shown; convergence of the solution with the number of generalized coordinates is numerically verified.

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