Non-linear interaction of bending deformations of free-oscillating cylindrical shells

Kubenko, V. D.; Koval’chuk, P. S.; Kruk, L. A.

doi:10.1016/s0022-460x(02)01524-9

Cited by 20 publications

(21 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, the parametric vibrations of the shell are described by the system of equations (5) with R i defined by (9). In what follows, the parametric load is given by N t N t x ( ) cos = 1 2n .…”

Section: Problem Formulation and Vibration Equationmentioning

confidence: 99%

“…where N Eh R cr = -2 2 3 1 / ( ) n is the static critical load [9], which has the following value for a shell with parameters (28): …”

Section: Analysis Of Nonlinear Vibrationsmentioning

confidence: 99%

“…The models discussed in [3,4] describe free, forced, and parametric nonlinear vibrations of cylindrical shells with three and four degrees of freedom. The interaction of two pairs of conjugate vibration modes of cylindrical shells was examined in [9]. A detailed review of studies on the dynamics of shells can be found in [8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Parametric vibrations of cylindrical shells subject to geometrically nonlinear deformation: multimode models

Kochurov

Аврамов

2011

Int Appl Mech

View full text Add to dashboard Cite

The nonlinear parametric vibrations of cylindrical shell are described by the Donnell-Mushtari-Vlasov equations. The motions are represented as a mode expansion. Discretization is performed using the Bubnov-Galerkin method. The describing-function method is used to study traveling waves and nonlinear normal modes in systems with and without dissipation Keywords: parametric vibrations, multimode model, Donnell-Mushtari-Vlasov equations, describing function methodIntroduction. The nonlinear vibrations of thin-walled cylindrical shells are studied in a great many publications. The models discussed in [3, 4] describe free, forced, and parametric nonlinear vibrations of cylindrical shells with three and four degrees of freedom. The interaction of two pairs of conjugate vibration modes of cylindrical shells was examined in [9]. A detailed review of studies on the dynamics of shells can be found in [8].An analysis of the linear vibrations of cylindrical shells shows that the natural frequency spectrum can be very crowded. In such cases, only multimode models that describe the interaction between modes with crowded spectrum can be used to describe the nonlinear dynamics of cylindrical shells.To analyze the parametric vibrations of cylindrical shells during geometrically nonlinear deformation, we will consider three pairs of conjugate modes with close frequencies of linear vibrations. We will thoroughly study two types of motion: nonlinear modes and traveling waves. Problem Formulation and Vibration Equation.Consider a hinged cylindrical shell without initial imperfections axially compressed by a distributed periodic load N t N N t x ( ) cos = +

show abstract

Section: Problem Formulation and Vibration Equationmentioning

confidence: 99%

“…where N Eh R cr = -2 2 3 1 / ( ) n is the static critical load [9], which has the following value for a shell with parameters (28): …”

Section: Analysis Of Nonlinear Vibrationsmentioning

confidence: 99%

See 1 more Smart Citation

Parametric vibrations of cylindrical shells subject to geometrically nonlinear deformation: multimode models

Kochurov

Аврамов

2011

Int Appl Mech

View full text Add to dashboard Cite

show abstract

“…where F p is a partial solution of the equation, 1 1 2 2 3 1 4 2 2 2 cos sin cos sin cos cos sy x sy x x x l l l l + F 5 2 cos sy + + + + + F F F F 6 1 7 2 8 1 2 9 3 3 cos sin cos sin cos( ) cos sy x sy x x l l l l ( ) l l ) sy x l l , (1.9) and the function F 0 is the solution of a homogeneous equation for membrane stresses [2,3,15]:…”

mentioning

confidence: 99%

“…where F k (k = 1, …, 23) in (1.9) are functions expressed in some manner in terms of the displacements f f 1 4 ,... , , wave numbers, physical and geometrical parameters of the shell [15]: Applying the Bubnov-Galerkin method to the first equation in (1.1) and using (1.3), (1.4), (1.8)-(1.10), we arrive at the following system of differential equations for the unknown functions f k : …”

mentioning

confidence: 99%

Analysis of nonstationary processes in cylindrical shells interacting with a fluid flow

2011

View full text Add to dashboard Cite

The paper outlines a technique to analyze the nonstationary vibrations of cylindrical shells interacting with a fluid flow and subjected to external periodic pressure with slowly varying frequency. The dynamic processes occurring in the shell-fluid system as the resonance region is passed forth and back are analyzed Keywords: cylindrical shell, perfect incompressible fluid, critical speed, static and dynamic instability, nonstationary process, resonanceIntroduction. The issue of strength and operational reliability of various pipeline systems necessitates solving some new nonlinear problems related to the dynamic interaction of elastic cylindrical shells with a fluid flow. Of them, important and little-studied are problems of the nonstationary deformation of such shells caused by external or internal quasiperiodic loads with slowly varying parameters. Such dynamic loads can be generated by various pressure facilities (piston compressors, pumps, etc.) designed to convey liquid products in acceleration or deceleration modes [3][4][5]11]. For the conveying shell, these loads are mostly transverse (radial) and may be either concentrated or uniformly distributed over a part of or the whole lateral surface. Such loads can also be due to the pulsations in the pressure of the conveyed fluid. In this case, the load on the shell is parametric and the equations of motion include terms with time-dependent coefficients [4,7,8,12].The present paper outlines a procedure for analysis of the nonstationary vibrations of cylindrical shells interacting with a fluid flow. The nonstationarity of the processes is due to external quasiperiodic forces with slowly varying frequencies. We will use this technique for numerical analysis of how the shell-fluid system passes, forth and back, the resonance regions when the rate of passage is varied. Preliminarily, we will determine the critical speeds of the fluid at which the shell loses stability and the associated nonstationary deformation modes.1. We will use the following mixed equations of motion of a shell with a flowing fluid [1-3]:

show abstract

The Problem of Forced Nonlinear Vibrations of Cylindrical Shells Completely Filled with Liquid

Koval’chuk

Kruk

2005

Int Appl Mech

View full text Add to dashboard Cite

The forced nonlinear vibrations of a thin cylindrical shell completely filled with a liquid are studied. A refined mathematical model is used. The model takes into account the nonlinear terms up to the fifth power of the generalized displacement of the shell. The Bogolyubov-Mitropolsky averaging method is used to plot amplitude-frequency response curves for steady-state vibrations. The steady-state vibrations at the frequency of principal harmonic resonance are analyzed for stability Keywords: cylindrical shell, perfect incompressible liquid, amplitude-frequency response, stability, single-mode deformationThe nonlinear dynamic deformation of cylindrical shells partially or completely filled with a liquid is of considerable interest for the strength and stability analyses of elements of aviation and space systems, main pipeline systems, etc. [11]. The publications [4-10, 12, etc.] report on some results obtained on the assumption that the shell-fluid system either freely vibrates or experiences the action of an external periodic load. In both cases, the vibration analysis was based on simplified models that include nonlinear terms of the third order in generalized displacements. Such models are known to allow a reliable analysis of the amplitude-frequency responses (AFRs) of a shell-fluid system, no matter whether the type of nonlinearity is soft or hard. When the skeletal curves of shells posses a combined nonlinearity (soft-hard), it is necessary to use more accurate models that would account for quartic terms.Note that such compound AFRs are very frequently observed in experiments on "dry" (without liquid) shells [2]. Naturally, a similar pattern is likely for liquid-filled shells.In the present paper, we will use refined models to analyze the forced nonlinear vibrations of a liquid-filled cylindrical shell under the action of external harmonic pressure nonuniformly distributed over the lateral surface. Our main tasks are to plot and analyze the AFRs of the shell in the vicinity of the principal resonance using analytical methods (averaging method) and to study the influence of the liquid on the AFRs and the stability regions of steady-state single-mode vibrations (standing waves).1. Problem Formulation. Original Equations. Consider a liquid-filled circular cylindrical shell of length l, thickness h, and radius R. Its external lateral surface is subjected to transverse pressure described by the formula q(x, y, t) = q 0 (x, y)cosΩt, where q 0 (x, y) is a given function of spatial coordinates x and y (x is the longitudinal coordinate originating at one of the shell's ends and running along its axis, and y is the circumferential coordinate). The shell ends are assumed to be simply supported, i.e.,where w is the radial deflection of the shell (positive in the direction of the center of curvature); v is the circumferential displacement of the median surface of the shell; and M x is the bending moment.To describe the deformation of the shell, we will use mixed equations [2, 3]:

show abstract

Non-linear interaction of bending deformations of free-oscillating cylindrical shells

Cited by 20 publications

References 10 publications

Parametric vibrations of cylindrical shells subject to geometrically nonlinear deformation: multimode models

Parametric vibrations of cylindrical shells subject to geometrically nonlinear deformation: multimode models

Analysis of nonstationary processes in cylindrical shells interacting with a fluid flow

The Problem of Forced Nonlinear Vibrations of Cylindrical Shells Completely Filled with Liquid

Contact Info

Product

Resources

About