Design of a tuned vibration absorber for a slender hollow cylindrical structure

Abstract

In this paper, details of the design work for a tuned vibration absorber to be used on a hollow cylindrical structure is presented. The vibration problem is of resonant type and the tuned vibration absorber is designed to suppress the displacement vibration response of the free end of the slender hollow structure dominated by the contribution of its lowest transverse vibration modes. The structure is modeled using a commercial finite element software. Finite element model of the structure is verified using experimentally obtained frequency response functions and modal parameters. Effective parameters of the tuned vibration absorber design are then determined based on finite element analysis simulations of the vibration suppression performance of the tuned vibration absorber as it is used on the structure. Details of the tuned vibration absorber design are determined and a prototype is fabricated. Prototype tuned vibration absorber is then characterized experimentally both as a standalone system and also as it is used on the main structure. Vibration reduction performance of the physical prototype of the tuned vibration absorber is also compared with its vibration reduction performance estimated from finite element analysis simulations so that the analysis based design process can be validated.

Communicated by Dumitru Caruntu.     

Dynamic interaction of a liquid with the elastic structure of a circular cylindrical container

Summary The present paper investigates the general case of hydroelastic coupled oscillations of a partially filled liquid container with a flexible bottom and an elastic side wall. The bottom behavior is described by the motion of a membrane or a thin, elastic, flat plate, while the sidewall is treated as a thin, elastic shell with its motion described by Donnell's shell equations. The liquid is assumed to be inviscid, homogeneous, and incompressible, the fluid motion is considered to be irrotational.

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Übersicht In der vorliegenden Arbeit wird der allgemeine Fall der gekoppelten hydroelastischen Flüssigkeitsschwingungen im teilweise gefüllten Behälter untersucht. Der flexible Tankboden wird als Membran oder als dünne ebene Platte, die Behälterwand als elastische dünne Schale angenommen. Für die Beschreibung der Auslenkung der Behälterwand werden die Donnell-Schalengleichungen verwandt. Die Flüssigkeit wird als reibungsfrei, homogen und dichtebeständig, die Strömung als wirbelfrei vorausgesetzt.

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Dedicated to Professor Dr.-Ing. K. Klotter on the occasion of his seventieth birthday.

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(formerly School of Engineering Science and Mechanics, Georgia Institute of Technology, Atlanta, Georgia 30332, U.S.A.)     

Two-scale analysis of a filament-wound cylindrical structure and application of periodic boundary conditions

A two-scale numerical approach to predict the effective in-plane properties of helical filament-wound thin-walled cylindrical tubes is provided. A meso-scale repeated unit cell (RUC) model for a filament-wound tube is established according to the manufacturing process, in which cross-overs, undulations and overlaps of fibre bundles are described using a bottom-up solid modelling technique. An approach to implement the general periodic boundary conditions in a finite element analysis scheme is also presented. As an application example, the effective in-plane elastic constants of glass fibre/epoxy filament-wound tubes are predicted and the influences of the number of the winding circuits and the shape of the fibre bundles are analyzed and discussed. In addition, the stress/strain distribution in the RUC is obtained which provides the essential information on the stress/strain concentration due to fibre cross-over/undulation/overlap. This then indicates the location where damage will initiate.     

Vortex shedding and evolution induced by a solitary wave propagating over a submerged cylindrical structure

The shedding and evolution of the vortical structures generated by a solitary wave propagating over a submerged cylindrical structure are investigated experimentally and numerically. The cylindrical structure consists of two concentric cylinders and represents a simplified model for an offshore submerged intake structure typically used in coastal power plants. Flow visualization by dye injection is used to identify the dominant vortical structures near the structure. The flow visualization results show an unexpected flow reversal that causes shedding of secondary vortical structures. The experimental results are used to check a three-dimensional volume of fluid-large eddy simulation (VOF-LES) numerical model. The VOF-LES model is then used to further study the flow structure. A total of six dominant vortical structures generated by the wave motion are identified, followed by two more generated by the flow reversal. In summary, this paper provides the vorticity evolution for a complex fluid–structure interaction problem and a three-dimensional numerical simulation tool has also been validated, which can be extended to study more complex geometries and wave conditions.     

Experimental investigation flow structure and hydraulic resistance of a cylindrical duct with injection a fan slot jet

The paper describes results of an experimental study of pressure and velocity fields arising during normal injection of a radial slot jet into ducted flow. The experiments were carried out for slots of two different widths and for injection parameters varying in a broad range. The pressure profile along the duct length plotted in generalized coordinates was found to be quite a universal distribution. Experimental correlations for the minimum rarefaction in the separation region behind the injected jet were obtained, and comparison was made with the results of simplest numerical analysis. Results of measurements of local hydraulic losses are presented for the duct section where the normal injection of the slot jet was organized. The experimental data are shown to be underestimated compared with the results predicted by the theory of perfect mixing for a ducted flow with mass supply. The possible reasons of hydraulic losses coefficient behavior are discussed.     

Fluid–structure interaction during the impact of a cylindrical shell on a thin layer of water

A two-dimensional unsteady analysis of an elastic circular cylindrical shell that enters a thin layer of an ideal incompressible liquid is considered. The cylinder initially touches the liquid free surface at a single point and then penetrates the liquid layer at a constant vertical velocity. The problem is coupled because the liquid flow, the shape of the elastic shell and the geometry of the contact region between the body and the liquid must be determined simultaneously. The flow region is subdivided into four complementary regions that exhibit different properties: the region beneath the entering body surface, the jet root, the spray jet, and the outer region. A complete solution is obtained by matching the solutions within these four subdomains. The structural analysis is based on the normal-mode method. Strain-time histories of the inner surface of the cylinder are of particular interest. In the case of a very flexible shell three distinct regimes of the impact process were found. For a high impact velocity the lower part of the shell flattens and the shell does not enter the water. For a moderate impact velocity the shell reaches the bottom and an effect of “fluid capture” may occur. For a low impact velocity the shell penetrates the liquid, but the size of the contact region decreases before the shell reaches the bottom. This behaviour corresponds to exit or “reflection” of the shell from the water layer.     

Submerged fluid-filled cylindrical shell subjected to a shock wave: Fluid–structure interaction effects

A submerged fluid-filled circular cylindrical shell subjected to a shock wave propagating in the external fluid is considered. The study focuses on a number of acoustic and structural effects taking place during the interaction. Specifically, the influence of the acoustic phenomena in the fluid on the stress–strain state of the shell is analysed using two different visualization techniques. The effect that the parameters of the shell have on the internal acoustic field is addressed as well, and the ‘shock transparency’ of various shells is discussed. Special attention is paid to the analysis of the contribution of the terms in the shell equations representing bending stiffness, and the limits of applicability of the membrane theory of thin shells are discussed in the fluid–structure interaction context. The possibility of cavitation in the internal fluid is investigated, and the effect that cavitation could have on the structural dynamics of the shell is discussed. The present paper is a follow-up of the author's earlier study of the interaction between fluid-filled cylindrical shells and external shock waves.     

Coupled vibration of a partially fluid-filled cylindrical container with a cylindrical internal body

In the present paper a method is proposed to investigate the effects of a rigid internal body on the coupled vibration of a partially fluid-filled cylindrical container. The internal body is a thin-walled and open-ended cylindrical shell. The internal body is concentrically and partially submerged inside a container. The radial and axial distances between the internal body and the container are filled with fluid. Along the contact surface between the container and the fluid, the compatibility requirement for the fluid–structure interactions is applied and the Rayleigh–Ritz method is used to calculate the natural frequencies and modes of a partially fluid-filled cylindrical container. The fluid domain is continuous, simply connected, and non-convex. The fluid is assumed to be incompressible and inviscid. The velocity potential for fluid motion is formulated in terms of eigenfunction expansions for two distinct fluid regions. The resulting equations are solved by using the Galerkin method. The results from the proposed method are in good agreement with experimental and numerical solutions available in the literature for the partially water-filled cylindrical container without internal body. A finite element analysis is also used to check the validity of the present method for the partially water-filled cylindrical container with internal body. The effects of the fluid level, internal body radius, and internal body length on the natural frequencies of the coupled system are also investigated.     

Interaction of a transient cylindrical acoustic wave with a multimode cylindrical piezoelectric transducer

The interaction between a transient cylindrical acoustic wave and a cylindrical piezoelectric transducer with sectioned electrodes is considered. The solution is obtained using the integral Laplace transform with respect to time (in the form of natural-mode series). In going to the space of originals, the problem is reduced to integral Volterra equations. The results of calculation are presented for various angular dimensions of the electrode sections and various distances from the wave source to the piezoelectric transducer. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 37–45, October, 1999.     

Small twist of a circular cylindrical tube exhibiting cylindrical aeolotropy of a nonorthogonal type

Summary At each point of an elastic cylindrical tube the aeolotropy is defined with respect to a triad of nonorthogonal curves. When the tube undergoes a small twist the effect of the nonorthogonality appears in the form of extra terms in the expression for the couple on the tube. Restrictions on the elastic properties of the material are obtained for zero warping of the cylinder sections, and a solution is given when warping is present.     

Dynamics of a cylindrical body in a liquid-filled sector of a cylindrical layer under rotational vibration

The dynamics of a rigid cylindrical body subjected to high-frequency rotational vibration about its own axis in a liquid-filled sector of a horizontal cylindrical layer are investigated experimentally and theoretically. It is found that the vibrations generate an average force on the body which in the case of a body denser than the fluid is directed toward the axis of rotation. Under certain conditions this force exceeds the gravity force, causing the body to float. This effect is analyzed theoretically in the high-frequency low-amplitude vibration approximation. It is shown that the force detected acts on the body over the entire fluid volume. Perm’. Paris. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 29–39, July–August, 1998. The work partially supported by the Russian Foundation for Basic Research (project No. 96-01-00932) and Grant No. 920-5208/95 of the US National Aviation and Space Administration (US NASA).     

Stress intensity factors for a moving cylindrical crack in a nonhomogeneous cylindrical layer in composite materials

Stresses are determined for a finite cylindrical crack that is propagating with a constant velocity in a nonhomogeneous cylindrical elastic layer, sandwiched between an infinite elastic medium and a circular elastic cylinder made from another material. The Galilean transformation is employed to express the wave equations in terms of coordinates that are attached to the moving crack. An internal gas pressure is then applied to the crack surfaces. The solution is derived by dividing the nonhomogeneous interfacial layer into several homogeneous cylindrical layers with different material properties. The boundary conditions are reduced to two pairs of dual integral equations. These equations are solved by expanding the differences in the crack surface displacements into a series of functions that are equal to zero outside the crack. The Schmidt method is then used to solve for the unknown coefficients in the series. Numerical calculations for the stress intensity factors were performed for speeds and composite material combinations.     

双层环肋圆柱壳受多个物体撞击下的结构动响应

针对双层环肋圆柱壳受到多个物体的撞击问题,采用MSC.Dytran软件对受撞过程中的结构损伤变形、撞击力变化和能量转换进行数值模拟,并与模型试验相对比后发现:双层环肋圆柱壳结构同时受多物体撞击是一个瞬态动响应过程,在巨大瞬时冲击载荷作用下,受撞区壳板会迅速超越弹性变形而产生塑性变形;多物体撞击会造成外壳板一定区域的损伤变形,撞击力会相互干扰,导致其非线性特征更明显。结果表明,双层圆柱壳的外壳能对内壳起到较好的防护作用,在外壳没被撞穿的情况下,其结构变形会吸收绝大部分的撞击动能,可以通过优化外壳的吸能效率来达到双层壳体结构物内壳防撞的目的。