Amplitude Of Forced Vibration Research Articles

Analysis of fluid-structure interaction by an arbitrary Lagrangian-Eulerian finite element formulation

In this paper, the interaction fluid–rigid body is analysed by a finite element procedure that incorporates the arbitrary Lagrangian–Eulerian (ALE) method into a well-known two-step projection scheme. The flow is assumed to be two-dimensional, incompressible and viscous, with no turbulence models being included. The flow past a circular cylinder at ℛℯ=200 is first analysed, for fixed and oscillating conditions. The dependence of lock-in upon the shift between the mechanical and the Strouhal frequencies, for a given amplitude of forced vibration, is illustrated. The aerodynamic forces and the wake geometry are compared for locked-in conditions with different driving frequencies. The behaviour of a rectangular cylinder (B/D=4) at ℛℯ=500 (based on height D) is also analysed. The flutter derivatives associated with aerodynamic damping (H1* and A2* in Scanlan's notation) are evaluated by the free oscillation method for several values of reduced flow speed above the Strouhal one (namely for 3≤U*≤8). Torsional flutter was attained at U*≥5, with all the other situations showing stable characteristics. Copyright © 1999 John Wiley & Sons, Ltd.

The Maximum Factor by Which Forced Vibration of Blades Can Increase Due to Mistuning

In 1966 it was shown that the maximum factor by which the amplitude of forced vibration of blades can increase due to mistuning is, with certain assumptions, 1/2(1+N), where N is the number of blades in the row. This report gives a further investigation of the circumstances when this factor can be obtained. These are small damping, and a relationship must hold between the mistuning distribution γ(s) and the interblade coupling function c(r), where r is the model number. The mistuning distribution must be symmetric about the blade on which maximum amplitude is to occur, s = 0. The coupling function must be symmetric about r = R, where R is the mode number of the excitation. If the coupling is purely mechanical, additional conditions apply. The coupling function c(r) must consist of a number of identical symmetric substrips. A 1976 result for mechanical coupling is amended.

Dynamic optimization of a turbine foundation

In this paper, the dynamic optimization problem for the frame foundation of a turbine is formulated and solved by sequential linear programming. A new scheme is presented to evaluate the response sensitivity when Solokin's damping is considered. This scheme is applied in the multiple-objective optimization of the turbine foundation, where the structural weight and the forced vibration amplitude are to be minimized. Numerical results show that more satisfactory designs can be obtained by this approach.

P68 An alternative to the customary reporting of common toxicity criteria

The paper presents an active control system that counteracts the development of chatter vibration. The vibration amplitude depends on the dynamic properties of the machine tool, cutting tool and work-piece. In the paper we analyze the case when the loss of machining stability is caused by the work-piece. The proposed active control system employs electromagnet or piezoelectric actuator to suppress vibration during milling. The active control introduces damping into the system, thereby raising the critical depth of cut and reducing forced vibration amplitude. It enables stable cutting under a much wider range of cutting parameters that for the uncontrolled system. Cutting tests are performed on JAFO FYN-50 machine with mill DIN 845 B-25 K-N HSS to demonstrate an effectiveness of the proposed systems.

Optimum distribution of smart stiffeners in sandwich plates subjected to bending or forced vibrations

The problems of optimum distribution of active stiffeners manufactured from piezoelectric or shape memory alloy materials and bonded to or embedded within the facings of a sandwich plate are considered. The sandwich plate consists of thin composite or isotropic facings which are in the state of plane stress and a thick shear deformable core. The amplitude of forced vibrations of the plate is reduced using symmetric couples of piezoelectric stiffeners subjected to out-of-phase dynamic voltages. Shape memory alloy stiffeners are used to reduce bending deformations. In the latter case, a desirable effect is achieved by activating the stiffeners on one side of the middle surface. Optimum design is considered based on the requirement of minimal transverse static or dynamic deflections subject to a constraint on the volume of smart stiffeners. The variables employed in the process of optimization are the ratios of the cross-sectional areas of the stiffeners in each direction to their respective spacings. It is shown, that, dependent on the load, materials, and geometry, optimum design can significantly reduce deflections, i.e. enhance the strength, of sandwich plates.

Chain dampers for control of wind-induced vibration of tower and mast structures

This paper outlines the operation of hanging chain impact dampers and their use in reducing vibration amplitudes of tower and mast structures due to wind excitation. Hanging chain dampers are employed inside towers to increase their structural damping, thus reducing the amplitude of forced vibration and reducing the possibility of structural damage. Four case histories are examined which detail the design of individual chain dampers.

An Analysis of the Vibration of Fabrics Considering the Bending Hysteresis.

The dynamic bending response of a woven fabric was theoretically estimated from its static bending property including hysteresis. The hysteresis loop obtained by pure bending test was simulated by the Rate madel, based on which the equivalent flexural rigidity and damping coefficient were estimated. The response of the model strip of fabric with these parameters to forced oscillation was analyzed by a nonlinear FEM. The results showed that the calculated results agreed well with the experimental ones in value as well as in dependence on the amplitude of forced vibration.

Vortex shedding controlled by the transverse vibration of three in-line elliptic cylinders in a uniform flow

An experimental study has been conducted on the vortex shedding frequency from three in-line elliptic cylinders with one of them undergoing forced transverse vibration in a uniform flow at frequencies up to 4 times the natural vortex shedding frequency. The possibility that the vortex shedding from each elliptic cylinder can be controlled by the vibrating cylider is examined by FFT analyses. It is shown that the locking-on characteristics of each cylinder depend on the arrangement of the elliptic cylinders, the amplitude and frequency of forced vibration, the uniform flow Reynolds number and the location of the vibratinf cylinder.

単結晶フェライトの微細溝形成時におけるバリ生成現象

This paper presents some experimental results of single crystal ferrite in scratch tests with various shapes of diamond chisels and in grooving tests with diamond wheels.On scratch tests with diamond chisels, there is no crack on the surface of a groove but plastic flow is generated at a small scratch load less than 0.02-0.05 N. The height of plastic flow is as large as the depth of a groove. On the other hand, such small plastic flow, called as burr, as about 0.1 μm high and 1, μm wide, is created on both shoulders of grooves in groove grinding of single crystal ferrite using diamond wheels. The burr height has a strong correlation with the uncut chip thickness which is determined by such factors as wheel speed, table speed, depth of cut and the amplitude of forced vibration of a wheel. For restraining the burr height, keeping the small uncut chip thickness on each cutting edge of grains are recommended.

Investigations of the effect of eccentricity on the unsteady fluid forces on the centrebody of an annular diffuser

In recent years several analytical and experimental studies have been carried out into the excitation of coaxial cylindrical bodies by annular flows, and an understanding of the mechanisms which lead to self-excited vibrations has been achieved. It has been observed experimentally, however, that sometimes geometries which are stable when concentric become unstable if eccentricity is introduced. Often in these cases the flow is severely nonaxisymmetric and unsteady and sometimes reverses over part of the annulus, a situation which cannot easily be modelled theoretically. These effects of eccentricity have been investigated experimentally on a vibration rig where the fluid forces on a centrebody fixed or forced to vibrate over a range of frequencies and amplitudes within an annular diffuser have been measured directly. It has been discovered that the flow in the annulus can exist in two distinct states characterized by the existence or absence of a Strouhal type of aerodynamic instability. With the instability present and the centrebody held fixed, large forces can be measured at a frequency proportional to flow velocity, but if the centrebody is shaken with sufficient amplitude the frequency of the instability can lock-on to the vibration in the classic fashion. A novel feature of this particular flow, however, is that the instability can be completely suppressed by carefully adjusting the imposed vibration amplitude and frequency, leaving the flow in its nonoscillatory state. It is found that the periodic instability can be reinitiated by increasing the forced vibration amplitude above a frequency-dependent threshold. Furthermore, by examining the phase relationships between the self-induced forces on the centrebody and its displacement, it is shown that the second state gives rise to negative fluid dynamic damping, the first to positive damping.

Forced oscillations. (Student experiment)

One of the most attractive experiments with forced oscillations was described by Burchell (1975). He describes measurement of the logarithmic decrement as a function of damping, and of the amplitude of forced vibrations as a function of damping and of frequency. However, in common with most descriptions of mechanical systems, the examination of the phase relationship is very sketchy indeed. The present author describes a technique to simplify the measurement of the phase angle and so add to the completeness of a truly elegant experiment.

Vibration of rigid bodies in the visco-elastic Hook-Maxwell model

In this paper the self-excited and forced vibrations of rigid bodies fastened to visco-elastic beam are considered. Two parameters solutions of motion equations of third order are found in the asymptotic series and their stability is investigated. It was shown that in comparison with Hook material the Hook-Maxwell material of beam limits the growth of amplitudes of both self-excited and forced vibrations. The theoretical results agree well with experimental ones.

Vibrations of parametrically excited systems

The paper is concerned with a set of linear differential equations with time-dependent parameters given by trigonometrical series. Derived formulas make it possible to examine stability, to find boundaries of the regions of instability and to estimate the steady state response amplitude of forced vibrations.

On the Vibrational Properties of High-Elastic Gels

A new method is presented for determining dynamic mechanical properties of high-elastic gels by measuring the amplitude and phase of forced longitudinal vibrations excited in get blocks themselves. It is shown that the Young's modulus and viscosity can be determined by analysing these quantities. Theoretical analyses are also made for the vibrations excited in the vertical cylindrical samples with no viscosity by horizontal oscillations of the bottom ends. The calculated results are illustrated by strains (displacement, inclination and shearing angle) for various values of cylinder diameters and frequencies used. It is shown that an approximate value of rigidity can be obtained from the frequency dependence of the strains. On an basis of this method the dependence of dynamic mechanical constants of agar-agar gels on cylinder diameters, concentrations and frequencies is studied, and reasonable values are obtained.

Forced Vibration and Chatter in Horizontal Milling: An Investigation Using a Structural Model

This paper describes an investigation into the characteristics of, and interaction between, forced vibration and chatter in horizontal milling. The machine tool structure was simulated by a single-degree-of-freedom structural model. The results show that forced vibration amplitudes: (1) vary with cutter speed in a series of resonance peaks; (2) are similar for plain and climb milling, but vary with orientation between the machining direction and the axis of vibration in a different way for the two processes; (3) increase approximately linearly with feed, except at low feeds; (4) pass through maxima and minima as depth of cut is increased. The amplitudes and frequencies of chatter are distinct from, and depend on machining conditions differently from, those of forced vibration. Peak chatter amplitudes exceed those of forced vibration, but the latter can, under certain machining conditions, exceed chatter amplitudes. Forced vibration can thus be as much of a limitation as chatter when a good surface finish is required. It was found that the discontinuous cutting of milling suppresses the onset of chatter relative to that for continuous cutting, for otherwise identical machining conditions. This is the reverse of previous contention.

On equilibrium modes of a rubber spherical shell under internal pressure: PMM vol. 32, no. 2, 1968, pp. 339–344

We study the influence of residual stress on the static and dynamic characteristics of a spherical structure. We consider a shrink-fitted compound sphere, where residual stress is developed due to the interference between outer and inner spherical layers. We calculate this residual stress and model the residually stressed material with suitable hyperelastic strain energy satisfying Initial Stress Reference Independence (ISRI). Under the action of inhomogeneous residual stress, the compound sphere behaves as an anisotropic, functionally graded composite sphere, which is reflected by the model. We apply this model to obtain stress distributions and inflation characteristics of the compound sphere. Our results demonstrate the hypothesis that residual stress moderates the stress concentration and reduces the stress gradient in biological/engineering structures. We obtain critical stretch and pressure for spherically symmetric deformations. An increase in interference/residual stress increases the critical stretch/pressure and improves the structural stability. We then apply an analytical approach to calculate the natural frequency of the compound sphere for small amplitude radial vibration. We observe that an increase in residual stress increases the natural frequency and widens the range of stable free vibration. We numerically investigate the free and forced vibration of the compound sphere. Forced vibration amplitude reduces as interference/residual stress increases, which is reflected in the frequency–amplitude plots. The frequency response shows a small hardening non-linearity. We investigate the subharmonic and superharmonic responses for small and large amplitude vibration.

Calculating the frequencies of natural vibrations and the amplitudes of forced vibrations in three-column centrifuges

Calculating the frequencies of natural vibrations and the amplitudes of forced vibrations in three-column centrifuges

Axially Symmetric Vibrations of a Thick Cylindrical Shell in an Acoustic Medium

This paper treats the dynamic behavior of infinitely long thick cylindrical shells surrounded by water. The shell is excited by axially symmetric forces. The solution is formed by coupling the three-dimensional elastic solution with the expression for the fluid pressure in cylindrical coordinates. Curves are presented which give the forced vibration amplitude and acoustic pressure in the water as a function of frequency for various modes of vibration of the cylinder.

Transverse vibrations of power transmission chains

In this paper the natural frequencies of a travelling chain are determined by treating the chain as a uniform string. For a constant chain tension the natural frequencies decrease progressively to zero as the chain speed approaches the velocity of transverse wave propagation. In practice such a condition is not obtained since the chain tension increases with speed owing to centrifugal effects. Formulae are obtained for the amplitude of forced vibration of the chain when excited by a transverse displacement at one end. The effect of damping is considered and exact and approximate methods of determining resonant amplitudes are given.

Dynamic Behavior of Reinforced Cylindrical Shells in a Vacuum and in a Fluid

Abstract The vibrations of an infinite cylindrical shell reinforced with periodically spaced septa and stiffening rings are studied in a vacuum and in a fluid medium. Lagrange equations are used to derive the dynamic equations; the fluid reaction is obtained from the solution of the wave equation. The solution gives the dynamic characteristics of the shell, the amplitude of forced vibration, and the sound field generated thereby. The theory can be extended to shells embodying complex stiffening structures and load distributions. Certain features of the fluid reaction suggest interesting applications: Its inertial component becomes extremely large under certain conditions, thus tending to eliminate some modes of vibration; also, the resistive, i.e., damping, component may vanish for certain modes, which therefore do not radiate any sound.