Influence of initial stress on the vibrations of simply supported circular cylindrical shells

AIAA Journal ◽  
1964 ◽  
Vol 2 (9) ◽  
pp. 1607-1612 ◽  
Author(s):  
ANTHONY E. ARMENAKAS
Keyword(s):  
Initial Stress ◽  
Cylindrical Shells ◽  
Simply Supported ◽  
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.

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.

Remarks on Donnell’s Equations

1955 ◽  
Vol 22 (1) ◽  
pp. 117-118
Author(s):  
Joseph Kempner
Keyword(s):  
Differential Equations ◽  
Cylindrical Shells ◽  
Radial Line ◽  
Line Load ◽  
Simply Supported ◽  
Circular Cylindrical Shells ◽  
Line Loads ◽  
Good Agreement

Abstract Flügge’s set of differential equations of equilibrium for circular cylindrical shells is expressed in a form analogous to the Donnell equations. The results of solutions of the two sets of equations for a simply supported cylinder under a centrally applied, uniformly distributed radial line load over a generator segment, as well as under sinusoidally applied line loads, are in very good agreement for the particular geometry investigated.

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.

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.

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