Analysis of Nonlinear Bulging of Liquid-Filled Cylindrical Shells Under Local Dynamic Loading

Koval’chuk, P. S.; Podchasov, N. P.; Kholopova, V. V.

doi:10.1023/a:1024470520708

“…For example, in a toroidal shell [16] with outside diameter D sh = 300 mm, inside diameter d = 105 mm, and wall thickness δ sh = 1 mm this process occurs when the first circumferential mode n = 1 is excited within the following ranges of frequencies and vibroacceleration amplitudes: f ex = (190-260) Hz and g ex = (15-30)g 0 . In an elastic cylindrical shell with D sh = 100 mm and δ sh = 1 mm, the disruption of the liquid surface occurs for a wider spectrum of modes: n = 1, 3, 4, 6 [11,16], especially when complex (running) deformation modes are excited [13][14][15][16]. Moreover, the amplitude g sh of wall vibration in an elastic cylindrical shell reaches the level causing surface disruption and bubble formation at rather low levels of vibroacceleration g ex .…”

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Features of the Motion of a Gas-Liquid Medium in a Compound Shell (Sphere and Truncated Cone) Subject to Vibration

Lakiza

¹

2005

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The results from an experimental study into the dynamic behavior of a gas-liquid medium and solid particles in a compound shell (sphere-truncated cone) are reported on. The following processes are studied: formation of gas bubbles and their clusters, strong macroflows, and intensive chaotic motion of the medium in the truncated cone as a nonlinear vibrating liquid-gas system Keywords: gas-liquid medium, compound shell, sphere, truncated cone, local accumulations, vibrationsModern vibration technology has put forward a number of challenges associated with studying the dynamic behavior of gas-liquid systems under periodic actions. Of practical interest is to study the vibrations and dynamic stability of gas bubbles and their clusters in an oscillating liquid contained in tanks of various geometries.The main patterns of motion of gas bubbles in liquids contained in rigid and elastic bodies were studied in [1-4, 10, 12, etc.]. The theoretical and experimental investigations conducted made it possible to gain an insight into the possible modes of motion of gas bubbles in an oscillating liquid and into clustering phenomena resulting in the accumulation of gas somewhere inside the liquid volume. The experiments described in [2][3][4] demonstrated that at certain frequencies and levels of vibration gas bubbles migrate toward the walls and bottom of the vessel, forming there stable gas accumulations. Such bubble clusters change drastically the structure of the gas-liquid medium. In this case, the liquid-gas system as a whole can be regarded as a nonlinear vibrating system in which the gas accumulation plays the role of an elastic element and the liquid column over it, of an inertia element. Note that the geometry of the carrier body (shell) has a significant effect on the behavior of the gas-liquid medium. The studies conducted earlier dealt mainly with simple geometries: cylinder, sphere, ellipsoid, and torus [3-5, 7, 8, 11, 16, 17]. Vibrating bodies of more complex geometry, namely compound cone-shaped shells such as the de Laval nozzle, were addressed in [6,9]. It was revealed that the convergent element between compound cone-shaped shells is responsible for two additional modes of motion: intensive cavitation and chaotic motion.The present paper reports on the results of an experimental study into the possible modes of motion of gas accumulations in a liquid medium contained in a compound shell (sphere and truncated cone). Our main concern will be the chaotic motion of these accumulations, liquid, and solid particles that occurs at certain frequencies and levels of external vibratory actions.1. Model, Equipment, and Technique. The subject of the experiment is a compound shell consisting of a sphere and a truncated cone (Fig. 1) and made of acrylic plastic. The total height of the shell H sh = 270 mm; the height and major and minor diameters of the truncated cone h tc = 140 mm, D tc = 110 mm, and d tc = 50 mm; the inside diameter of the sphere D s = 100 mm; the height and inside diameter of the cylinder connecting the ...

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Variational methods of solving dynamic problems for fluid-containing bodies

Lukovskii

¹

2004

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A variational approach to solving linear and nonlinear problems for a body with cavities partially filled with a perfect incompressible fluid is enunciated. The approach applies a nonclassical variational principle to describe the spatial motion of a finite fluid with a free surface and the classical variational principle, which is widely used in rigid-body dynamics. These principles are used to formulate variational problems that are the basis of direct methods of solving nonlinear and linear dynamic problems for body-fluid systems. The approach allows us to derive an infinite system of nonlinear ordinary differential equations describing the joint motion of the rigid body and fluid and to develop an algorithm for determining the hydrodynamic coefficients. Linearized differential equations of motion of the mechanical system are presented and approximate methods are given to solve linear boundary-value problems and to determine the hydrodynamic coefficients.Introduction. The theory of motion of bodies fully or partially filled with a fluid, which is an important division of body mechanics, is widely used to solve a large variety of applied problems. Primarily, these are problems arising in designing modern vehicles for transportation of large amounts of fluid. Such problems include the determination of the mechanical interaction of a tank car and the fluid partially filling it, strength analysis of vessels with environmentally dangerous fluids in seismic areas, stability analysis and efficient control of air/space/sea craft, etc.This paper deals only with dynamic systems consisting of a perfectly rigid body and a perfect incompressible fluid. Formulations of problems for a body interacting with an internal or external fluid are detailed in [7, 13, 15, 52, 71, 79, 93-95, etc.].Mathematical models of such mechanical systems are based on the nonlinear dynamic equations of a body and the nonlinear equations of waves on the free surface of a finite fluid. Scientists working in this area of mechanics aimed their efforts at overcoming the chief difficulty of the theory-the necessity to describe the joint motion of two essentially different objects: a body and a fluid.The motion of a body is known to be described by nonlinear ordinary differential equations, whereas the description of the wave motions of the free liquid surface involves the formulation and solution of nonlinear initial-boundary-value problems for partial differential equations. 1 2 l l J J J J t t 12 1 / , (3.32) J J J J J J 1 0. (3.34)The generalized forces will appear on the right-hand sides of Eqs. (3.32) and (3.33), where

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Variational methods of solving dynamic problems for fluid-containing bodies

Lukovskii

¹

2004

View full text Add to dashboard Cite

A variational approach to solving linear and nonlinear problems for a body with cavities partially filled with a perfect incompressible fluid is enunciated. The approach applies a nonclassical variational principle to describe the spatial motion of a finite fluid with a free surface and the classical variational principle, which is widely used in rigid-body dynamics. These principles are used to formulate variational problems that are the basis of direct methods of solving nonlinear and linear dynamic problems for body-fluid systems. The approach allows us to derive an infinite system of nonlinear ordinary differential equations describing the joint motion of the rigid body and fluid and to develop an algorithm for determining the hydrodynamic coefficients. Linearized differential equations of motion of the mechanical system are presented and approximate methods are given to solve linear boundary-value problems and to determine the hydrodynamic coefficients.Introduction. The theory of motion of bodies fully or partially filled with a fluid, which is an important division of body mechanics, is widely used to solve a large variety of applied problems. Primarily, these are problems arising in designing modern vehicles for transportation of large amounts of fluid. Such problems include the determination of the mechanical interaction of a tank car and the fluid partially filling it, strength analysis of vessels with environmentally dangerous fluids in seismic areas, stability analysis and efficient control of air/space/sea craft, etc.This paper deals only with dynamic systems consisting of a perfectly rigid body and a perfect incompressible fluid. Formulations of problems for a body interacting with an internal or external fluid are detailed in [7, 13, 15, 52, 71, 79, 93-95, etc.].Mathematical models of such mechanical systems are based on the nonlinear dynamic equations of a body and the nonlinear equations of waves on the free surface of a finite fluid. Scientists working in this area of mechanics aimed their efforts at overcoming the chief difficulty of the theory-the necessity to describe the joint motion of two essentially different objects: a body and a fluid.The motion of a body is known to be described by nonlinear ordinary differential equations, whereas the description of the wave motions of the free liquid surface involves the formulation and solution of nonlinear initial-boundary-value problems for partial differential equations.

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Analysis of Nonlinear Bulging of Liquid-Filled Cylindrical Shells Under Local Dynamic Loading

Cited by 6 publications

References 6 publications

Features of the Motion of a Gas-Liquid Medium in a Compound Shell (Sphere and Truncated Cone) Subject to Vibration

Features of the Motion of a Gas-Liquid Medium in a Compound Shell (Sphere and Truncated Cone) Subject to Vibration

Variational methods of solving dynamic problems for fluid-containing bodies

Variational methods of solving dynamic problems for fluid-containing bodies

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