Nonlinear parametric vibrations of orthotropic cylindrical shells interacting with a pulsating fluid flow

Koval’chuk, P. S.; Kruk, L. A.

doi:10.1007/s10778-010-0241-4

Cited by 13 publications

(1 citation statement)

References 10 publications

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“…Earlier publications demonstrated that the divergence speed is practically independent of the damping parameters [10][11][12][13]. As for the effect of these parameters on the flutter speed, some destabilization is possible because of the "nonconservative" nature of the hydrodynamic load exerted by the fluid flow on the shell [2].…”

Section: Discussionmentioning

confidence: 99%

Stability of cylindrical shells with added mass in fluid flow

Koval’chuk

Puchka

2010

Int Appl Mech

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The paper proposes a technique for the stability analysis of an elastic cylindrical shell with added mass interacting with a flowing fluid. Three cases of mass-shell contact are considered: the added mass (i) is attached to the shell at one point, (ii) has the form of a circular ring, and (iii) is distributed uniformly over the length. For each case, equations to determine the critical speeds of the fluid corresponding to the quasistatic (divergent) and dynamic (flutter) buckling of the shell are derived Keywords: cylindrical shell, ideal incompressible fluid, added mass, critical speed, stability, divergence, flutterIntroduction. Some sections of pipelines quite often have local "inclusions" such as rigidly attached concentrated masses. A mass may be attached to a structure at a point or linearly distributed over a shell surface. Such "inclusions" may significantly affect both quasistatic (divergence) and dynamic (flutter) buckling modes of pipelines interacting with the fluid flowing inside them [4,5].The present paper outlines a technique for the stability analysis of a finite pipeline section modeled by an elastic cylindrical shell loaded by a small added mass and filled with a moving fluid. Three cases of mass-shell contact are considered: (a) the mass is concentrated at one point of the free surface; (b) the mass is uniformly distributed over a circular ring contacting with the shell; (c) the mass is distributed along the length. Problem Formulation. Starting Equations of Motion of a Shell with a Concentrated Mass.Consider an elastic closed cylindrical shell containing a fluid moving with a constant speedU. The geometry of the shell is shown in Fig. 1. A point mass M is rigidly attached to the shell at a point with coordinates x 0 and y 0 . We will introduce the following assumptions and restrictions, which are usually used to solve most dynamic problems for shells with concentrated masses [1, 5-8, etc.]. Since the tangential rigidity of the shell is much higher than its radial rigidity (especially at lower vibration frequencies), the tangential inertial forces can be neglected. Assume that the added concentrated mass transmits only the radial force to the shell. The rotational inertia of the mass showing up during the vibrations of the shell is also neglected. The fluid filling the shell is ideal and incompressible, and its motion is potential.If there is no fluid, the problem of the concurrent vibrations of the shell and added mass is usually solved by determining the natural frequencies and modes by the well-known method of separation of motions [1, 6-8, etc.]. This method "separates" the mass from the shell and models its effect by some concentrated reaction force. The displacements of the shell caused by this force are determined from the equations of its motion. Finally, the frequency equation is derived from the displacement compatibility conditions to find the frequency spectrum of the discrete-continuous system under consideration. The frequencies can be used to identify the natural modes of the sh...

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Section: Discussionmentioning

confidence: 99%

Stability of cylindrical shells with added mass in fluid flow

Koval’chuk

Puchka

2010

Int Appl Mech

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Nonlinear vibrations of cylindrical shells filled with a fluid and subjected to longitudinal and transverse periodic excitation

2010

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The paper proposes an approach to studying the nonlinear vibrations of thin cylindrical shells filled with a fluid and subjected to a combined transverse-longitudinal load. Methods of nonlinear mechanics are used to find and analyze periodic solutions of the system of equations that describes the dynamic behavior of the shell when the natural frequencies of the shell and the frequencies of both periodic forces are in resonance relations Keywords: elastic cylindrical shell, ideal incompressible fluid, combined load, amplitude-frequency response, stabilityIntroduction. The flexural vibrations of thin cylindrical shells filled with a fluid are studied in a geometrically nonlinear formulation in a great many publications. Such studies are reviewed in, e.g., [6, 9-11, etc.]. Most studies deal with dynamic problems for fluid-filled shells subjected to either radial (transverse) or axial (longitudinal) force. However, in real operation conditions, shell structures conveying a fluid (such as segments of pipelines) are quite often subjected to combined loading, i.e., a combination of longitudinal and transverse periodic forces. Therefore, of practical and scientific interest is to study the dynamic behavior of shells filled with a fluid and subjected to a combined vibratory load. The superposition principle fails here because of the nonlinearity of such a problem formulation: the response of the dynamic shell-fluid system to a combination of longitudinal and transverse periodic loads is not the sum of the responses of this system to the individual loads. Here we may expect qualitatively new nonlinear effects that were not observed in the partial problems of forced [7,[10][11][12][13][14]18] or parametric [2,4,11,16] vibrations of shell-fluid objects.The present paper sets out to develop a method and to apply it to study the nonlinear deformation of elastic cylindrical shells filled with a fluid and subjected to longitudinal-and-transverse periodic excitation. We will primarily analyze the dynamic behavior of filled shells in the worst (with respect to dynamic stress) case where the natural frequencies of the shell-fluid system are in resonance relations with the frequencies of both external periodic forces. The results obtained in the general case will be compared with those obtained in the partial cases where either only longitudinal or only transverse load acts. Nonlinear Equations of Motion of a Fluid-Filled Shell.For the equations of motion of a shell filled with a fluid, we will use the geometrically nonlinear equations of the theory of shallow shells in mixed form [3,4]:

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Nonlinear wave generation on a fluid in a moving parabolic tank

Limarchenko

Semenova

2011

Int Appl Mech

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The cooperative motion of a fluid and a parabolic tank is modeled. Use is made of a discrete model based on the Hamilton-Ostrogradsky principle for an arbitrary body of revolution and a non-Cartesian parametrization of the domain occupied by the fluid. A set of coordinate functions satisfying kinematic boundary conditions and solvability conditions is set up. The discrete model is used to study the transients in the system. It is shown that the model adequately describes the nonlinear dynamic properties of the system Introduction. Dynamic problems for fluids with free surface in moving tanks are of considerable theoretical and practical interest. This kind of structures requires high-accuracy modeling in connection with the development and sophistication of new space-, air-, and sea-craft. The chief results on dynamic modeling of such systems were obtained in [3, 5-10, etc.]. Despite the long path of development of theoretical methods for solving such problems, the overwhelming majority of publications deal with the dynamics of fluids in cylindrical tanks moving in a prescribed manner. Though problems for noncylindrical structures and cooperative motion of bodies and fluids were formulated long ago [6,7], relevant quantitative results are yet to be obtained. It is interesting that the available approaches to studying the dynamics of noncylindrical bodies based on point discretization of the domain occupied by the fluid, as well as analytic methods encounter difficulties of meeting the requirement of conservation of volume and energy in the system [5]. Actually, such a state of the art in the dynamics of fluid with free surface in noncylindrical tanks suggests that the problem formulation for the motion of noncylindrical tanks with fluid is incomplete and incorrect and should be modified.1. Problem Formulation. We will now address the nonlinear vibrations of fluid with free surface in a moving parabolic tank. Assume that the fluid is perfect, homogeneous, incompressible and its motion is irrotational. Then it is possible to use a velocity potential j to describe the motion of the fluid [5][6][7][8].Let us formulate a dynamic problem for a fluid with free surface:

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Nonlinear parametric vibrations of orthotropic cylindrical shells interacting with a pulsating fluid flow

Cited by 13 publications

References 10 publications

Stability of cylindrical shells with added mass in fluid flow

Stability of cylindrical shells with added mass in fluid flow

Nonlinear vibrations of cylindrical shells filled with a fluid and subjected to longitudinal and transverse periodic excitation

Nonlinear wave generation on a fluid in a moving parabolic tank

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