Internal Damping Research Articles

On the notion of a rotating fluid force induced by swirling flow

The Bently/Muszynska (B/M) model shows that oil whirl and oil whip are both self-sustained vibrations associated with two unstable modes of a rotor–fluid system. The model includes a rotating fluid damping and inertia force. In certain configurations, the rotating damping force overcomes the frictional internal damping of the rotor and pushes the rotor into a stable limit cycle of circular orbiting. Such a notion of a rotating fluid force is based on bulk-flow models of fluid-filled clearances that could be approximated as narrow since the tangential velocity of the fluid then translates to one angular velocity at a certain radial distance defined by an average radius. This paper scrutinizes the assumption of a rotating fluid inertia force and pinpoints the additional inertial effects of the swirling flow as the gap width increases. These effects are clarified by deriving the equation of motion of a body with a mass subjected to motion-induced fluid forces of a confined swirling flow. We show that the inertial effects of the swirling flow counteract the destabilizing effect of the rotating damping force. However, if the body mass is larger than the displaced fluid mass, instability follows. The frequency of the unstable mode is unchanged by the additional inertial effects and is always equal to the frequency of the damping that induces the instability.

An Improved Heat Equation for Fully Coupled Thermal-Structural Finite Element Analysis Using Small Strain Formulation

In this paper an improved heat equation for fully coupled thermal structural finite element analysis is presented. In the problem solving process, mathematical formulation appropriate strain measures describing the onset and the growth of ductile and total damage and heat generation rate per unit volume for dissipation-induced heating have been employed. The model was implemented into a finite element code using an improved weak form for fully coupled thermal structural finite element analysis, an extended NoIHKH material model with internal damping for cyclic plasticity of metals capable of modelling ductile material behaviour in wide range of strain rates. A notched aluminium alloy specimen in cyclic tension using 2Hz excitation frequency and linearly increasing amplitude has been studied. The model verification showed excellent agreement with available experiments. A few selected analysis results are presented and briefly discussed.

Experimental study on the dynamic behavior of laterally loaded single pile

To improve the understanding of soil–pile interaction under horizontal dynamic loads and seismic events, a parametric centrifugal study was undertaken. Flexible piles with pile caps of different masses and instrumented with 20 strain gauges on the length of the pile were used for this purpose. The piles were impacted by a new horizontal impact device and the resulting displacement and acceleration for different levels of force were measured. The inherent basic parameters of soil–pile-interaction have been evaluated. An analysis of the damping in relation with depth and during vibration of pile is carried out. The equation of the movement of a beam equivalent to the pile under dynamic loading has been established and all the terms of this equation was determined using the experimental results. It shows that the value of internal damping of pile compared to other terms in the equation is insignificant. The term of inertia was divided into two parts, one related to the mass of the pile and the other related to the mass of the associated soil. The contribution of each term to the equation at different periods (or time of) of vibration was illustrated. Distribution versus time of the displacements and the reactions of the soil at any depth were deduced from the profiles of the bending moments by a double integration and a double derivation respectively. Then the dynamic P–y curves or loops were constructed based on these results. A static test has been performed with the same pile installed in the same conditions so that to obtain the static P–y curves. The procedures of experimental tests and P–y curves construction are explained and a comparison between static and dynamic P–y curves is also indicated.

Flow Behavior of “EPDM” Rubber during Dry Compression

AbstractIn the recent time rubber has emerged as a very useful and suitable material for wider varieties of engineering and other applications which includes but not limited to domestic, sports and many more. It possesses large elasticity compared to metals, has greater damping capability, high internal friction and can accumulate energy to a greater extent compared to steel or other metals. During the deformation of rubber material, particularly by compressive force, internal damping of the material leads to energy dissipation. This is the cause of hysteretic friction of rubber. Friction of rubber has practical importance. At the same time it has many disadvantages tooUse of rubber as engineering material is not new. However, in the recent time its application is gaining renewed importance as well as interest due to several engineering researches and property enhancement too. It is, however, needless to be mentioned that prediction of exact behavior of any viscoelastic material like rubber is very difficult.In the present work compression tests have been carried out to determine the flow characteristics of EPDM rubber of different hardness. Flat mild steel platens have been used to apply axysymetric compressive load on the specimen under dry working condition. The flow behavior like load – elongation curves, true stress – true strain curves and specific energy requirements have been computed from the experimental data. Statical hysteresis and the loss factors have also been obtained.Experimental results reveal that the hardness of EPDM rubber has significant effect on the flow behavior. Thus, it can be stated that the flow behavior can be governed by controlling the carbon black (CB) concentration in EPDM rubber as the hardness depends on it. It is proposed to extend the experiments with the application of different kind of lubricants.

Effects of Locally Distributed Kelvin–Voigt Damping on Parametric Instability of Timoshenko Beams

The effect of partially distributed internal damping of the Kelvin–Voigt type on the parametric instability of a Timoshenko beam subjected to periodic axial loads is studied. To model the dynamic behavior of the beam, a coupled set of second-order linear ordinary differential equations with periodic coefficients is established by the finite element method. A quadratic eigenvalue equation is derived for a parametrically excited damped system to determine the instability regions of the beam of concern based on Bolotin's method. The effects of internal damping, size and location of the damped segment, ratio of thickness to length and static load factor on the parametric instability of the beam are studied, along with the stabilizing effect of the Kelvin–Voigt damping on the primary parametric resonance presented. The results reveal that the beam with a larger damped segment positioned near the fixed end is dynamically more stable.

Estimation of the Damping Matrix in Rotating Machinery for the Calculation of the Stability Threshold Speed

Rotor internal damping is recognized as one of the main causes for instabilities in rotating systems. In a linear speed dependent model, the stability threshold speed can be calculated numerically. However, this threshold depends highly on the modeling choice and mainly on the relation between rotating and nonrotating damping. In this paper, the importance of a well-founded knowledge of the system parameters is highlighted and a method is proposed to estimate the damping of a rotating system not only influenced by the gyroscopic effect but also by rotating damping. With this method, it is possible to reconstruct the physical damping matrix and distinguish between rotating and nonrotating damping. Moreover, the gyroscopic effect can be identified. After a description of the method, a numerical validation is performed.

Dynamics of multiple viscoelastic carbon nanotube based nanocomposites with axial magnetic field

Nanocomposites and magnetic field effects on nanostructures have received great attention in recent years. A large amount of research work was focused on developing the proper theoretical framework for describing many physical effects appearing in structures on nanoscale level. Great step in this direction was successful application of nonlocal continuum field theory of Eringen. In the present paper, the free transverse vibration analysis is carried out for the system composed of multiple single walled carbon nanotubes (MSWCNT) embedded in a polymer matrix and under the influence of an axial magnetic field. Equivalent nonlocal model of MSWCNT is adopted as viscoelastically coupled multi-nanobeam system (MNBS) under the influence of longitudinal magnetic field. Governing equations of motion are derived using the Newton second low and nonlocal Rayleigh beam theory, which take into account small-scale effects, the effect of nanobeam angular acceleration, internal damping and Maxwell relation. Explicit expressions for complex natural frequency are derived based on the method of separation of variables and trigonometric method for the “Clamped-Chain” system. In addition, an analytical method is proposed in order to obtain asymptotic damped natural frequency and the critical damping ratio, which are independent of boundary conditions and a number of nanobeams in MNBS. The validity of obtained results is confirmed by comparing the results obtained for complex frequencies via trigonometric method with the results obtained by using numerical methods. The influence of the longitudinal magnetic field on the free vibration response of viscoelastically coupled MNBS is discussed in detail. In addition, numerical results are presented to point out the effects of the nonlocal parameter, internal damping, and parameters of viscoelastic medium on complex natural frequencies of the system. The results demonstrate the efficiency of the suggested methodology to find the closed form solutions for the free vibration response of multiple nanostructure systems under the influence of magnetic field.

An internal damping formula derived from dispersed elasto-plastic flaws with Weibull-distributed strengths

Internal energy dissipation in many materials, per stress cycle and per unit volume, is frequency-independent and proportional to some power of an equivalent stress amplitude, σeqm. For triaxial stress states, the definition of σeq has so far been ad hoc. In this paper a micromechanically motivated constitutive model for such internal dissipation is developed by assuming a multitude of dispersed microscopic ellipsoidal elasto-plastic flaws. Both detailed ABAQUS simulations and a semi-analytical approach based on formulas given by Eshelby are used. Two limiting special cases are identified where the dissipation in a single flaw is analytically tractable: spherical flaws, and flaws that are flat and thin. For these, Weibull-distributed flaw strengths and spatially homogeneously distributed flaws are assumed. Formulas for the macroscopic dissipation are obtained, analytically for spherical flaws and semi-analytically for flat and thin flaws. For spherical flaws, the averaged macroscopic dissipation is exactly equal to a power of the distortional strain energy. For flat and thin flaws, for 2≤m≤6, the overall dissipation is closely, but not exactly, described by a power of the distortional strain energy alone, even though the dissipation in individual flaws is not governed by distortional strain energy.

Nonlinear magneto-viscoelasticity of transversally isotropic magneto-active polymers

Iron-filled magnetorheological polymers, when cured in the presence of a magnetic field, result in having a transversely isotropic structure with iron particles forming chains along the direction of applied magnetic induction. In this work, we model the magneto-viscoelastic deformation (and magnetization) process of such polymers. Components of the deformation gradient and the applied magnetic induction in the direction of anisotropy are considered to be additional arguments of the energy density function. The existence of internal damping mechanisms is considered by performing a multiplicative decomposition of the deformation gradient and an additive decomposition of the magnetic induction into equilibrium and non-equilibrium parts. Energy density functions and evolution laws of the internal variables are proposed that agree with the laws of thermodynamics. In the end, we present solutions of some standard deformation cases to illustrate the theory. In particular, it is shown that the orientation of resultant magnetic field and principal stress directions change with time owing to viscoelastic evolution.

Optimisation of a velocity feedback controller to minimise kinetic energy and maximise power dissipation

In this study the active vibration control of a structure modelled as a single degree of freedom system and excited by a white noise force is considered. The control system consists of an inertial actuator driven with a signal proportional to the velocity of the structure under control measured by an ideal collocated sensor. The optimisation of the physical and control parameters of the control system such as the internal damping of the actuator, its natural frequency and the feedback gain of the controller are considered such that either the kinetic energy of the host structure is minimised or the power dissipated by the control system is maximised. This type of control system is only conditionally stable therefore a stability condition has to be satisfied by the optimisation process. The paper shows that the two optimisation criteria are equivalent.

Effect of non-linear damping on the structural dynamics of flapping beams

In this paper we investigate, through experiment and simulation, the effects of non-linear damping forces on the large amplitude structural dynamics of slender cantilever beams undergoing flapping motion in air. The aluminum beams are set into flapping motion through actuation at the beam base via a 4-bar crank-and-rocker mechanism. The beam strain response dynamics are investigated for two flapping amplitudes, 15° and 30°, and a range of flapping frequencies up to 1.3 times the first modal frequency. In addition to flapping at standard air pressure, flapping simulations and experiments are also performed at reduced air pressure (70% vacuum). In the simulations, linear and non-linear, internal and external damping force models in different functional forms are incorporated into a non-linear, inextensible beam theory. The external non-linear damping models are assumed to depend, parametrically, on ambient air density, beam width, and an empirically determined constant. Periodic solutions to the model equation are obtained numerically with a 1-mode Galerkin method and a high order time-spectral scheme. The effect of different damping forces on the stability of the computed periodic solutions is analyzed with the aid of Floquet theory. The strain-frequency response curves obtained with the various damping models suggest that, when compared to the linear viscous and non-linear internal damping models, the non-linear external damping models better represent the experimental damping forces in regions of primary and secondary resonances. In addition to providing improved correlation with experimental strain response amplitudes over the tested range of flapping frequencies, the non-linear (external) damping models yield stable periodic solutions for each flapping frequency which is consistent with the experimental observations. Changes in both the experimental ambient pressure and flapping amplitude are determined to result in some variation in the non-dimensional parameters associated with each of the non-linear external damping models. This result likely indicates an incomplete description of the model parameter dependence and/or non-linear functional form of the damping force.

Measurements of mechanical thermal noise and energy dissipation in optical dielectric coatings

In recent years, an increasing number of devices and experiments are shown to be limited by mechanical thermal noise. In particular, subhertz laser frequency stabilization and gravitational wave detectors that are able to measure fluctuations of ${10}^{\ensuremath{-}18}\text{ }\text{ }\mathrm{m}/\sqrt{\mathrm{Hz}}$ or less are being limited by thermal noise in the dielectric coatings deposited on mirrors. In this paper, we present a new measurement of thermal noise in low absorption dielectric coatings deposited on microcantilevers, and we compare it with the results obtained from the mechanical loss measurements. The coating thermal noise is measured on the widest range of frequencies with the highest signal-to-noise ratio ever achieved. In addition, we present a novel technique to deduce the coating mechanical losses from the measurement of the mechanical quality factor which does not rely on the knowledge of the coating and substrate Young's moduli. The dielectric coatings are deposited by ion beam sputtering. The results presented here give a frequency-independent loss angle of $(4.7\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ with a Young's modulus of 118 GPa for annealed tantala from 10 Hz to 20 kHz. For as-deposited silica, a weak frequency dependence ($\ensuremath{\propto}{f}^{\ensuremath{-}0.025}$) is observed in this frequency range, with a Young's modulus of 70 GPa and an internal damping of $(6.0\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ at 16 kHz, but this value decreases by one order of magnitude after annealing, and the frequency dependence disappears.

Synthetic Turbulence Generators for RANS-LES Interfaces in Zonal Simulations of Aerodynamic and Aeroacoustic Problems

The paper presents the detailed formulation and validation results of simple and robust procedures for the generation of synthetic turbulence aimed at providing artificial turbulent content at the RANS-to-LES interface within a zonal Wall Modelled LES of attached and mildly separated wall-bounded flows. There are two versions of the procedure. The aerodynamic version amounts to a minor modification of a synthetic turbulence generator developed by the authors previously, but the acoustically adapted version is new and includes an internal damping layer, where the pressure field is computed by “weighting” of the instantaneous pressure fields from LES and RANS. This is motivated by the need to avoid creating spurious noise as part of the turbulence generation. In terms of pure aerodynamics, the validation includes canonical shear flows (developed channel flow, zero pressure gradient boundary layer, and plane mixing layer), as well as a more complex flow over the wall-mounted hump with non-fixed separation and reattachment, with emphasis on a rapid conversion from modeled to resolved Reynolds stresses. The aeroacoustic applications include the flow past a trailing edge and over a two-element airfoil configuration. In all cases the methodology ensures a very acceptable accuracy for the mean flow, turbulent statistics and, also, the near- and far-field noise.

Enhanced characteristics of fused silica fibers using laser polishing

The search for gravitational wave signals from astrophysical sources has led to the current work to upgrade the two largest of the long-baseline laser interferometers, the LIGO detectors. The first fused silica mirror suspensions for the Advanced LIGO gravitational wave detectors have been installed at the LIGO Hanford and Livingston sites. These quadruple pendulums use synthetic fused silica fibers produced using a CO2 laser pulling machine to reduce thermal noise in the final suspension stage. The suspension thermal noise in Advanced LIGO is predicted to be limited by internal damping in the surface layer of the fibers, damping in the weld regions, and the strength of the fibers. We present here a new method for increasing the fracture strength of fused silica fibers by laser polishing of the stock material from which they are produced. We also show measurements of mechanical loss in laser polished fibers, showing a reduction of 30% in internal damping in the surface layer.

Series expansion of complex ground amplifications with a sequence of simple transfer functions

SUMMARYAmplification of earthquake ground motions at actual deposit sites is an important factor to consider when assessing the risk of an earthquake disaster. In order to identify the amplification properties, several preprocessings such as the Fourier transform are required. I propose a series expansion of the amplification with simple ground transfer functions as a new preprocessing. I define a sequence of transfer functions based on a two‐layered structure excluding an internal damping and a function space spanned by the set of the functions. I mathematically prove that the function space is equal to L2 space. This indicates that all the functions belonging to L2 space, that is, an arbitrary ground amplification, have a unique series expansion. This expansion is applied to the physics‐based decomposition of the amplification. Some numerical examples indicate that the similarity between a target complex structure and a simple model is measured by the absolute value of each coefficient in the series expansion. Copyright © 2014 John Wiley & Sons, Ltd.

Seismic base-isolation mechanism in liquefied sand in terms of energy

Seismic base isolation effect in a liquefied sand layer was investigated based on soil properties measured in a series of undrained cyclic triaxial tests. Transmission of seismic wave in a soil model consisting of a liquefied surface layer and an underlying nonliquefied layer was analyzed in terms of energy, considering liquefaction-induced changes in S-wave velocity and internal damping. It was found that, between two different base-isolation mechanisms, a drastic increase in wave attenuation in the liquefied layer due to shortening wave length gives a greater impact on the base isolation with increasing thickness of the liquefied layer than the change of seismic impedance between the liquefied and nonliquefied layer. Also indicated was that cyclic mobility behavior in dilative clean sand tends to decrease the seismic isolation effect to a certain extent.

Hopf bifurcation analysis of asymmetrical rotating shafts

The Hopf and double Hopf bifurcations analysis of asymmetrical rotating shafts with stretching nonlinearity are investigated. The shaft is simply supported and is composed of viscoelastic material. The rotary inertia and gyroscopic effect are considered, but, shear deformation is neglected. To consider the viscoelastic behavior of the shaft, the Kelvin–Voigt model is used. Hopf bifurcations occur due to instability caused by internal damping. To analyze the dynamics of the system in the vicinity of Hopf bifurcations, the center manifold theory is utilized. The standard normal forms of Hopf bifurcations for symmetrical and asymmetrical shafts are obtained. It is shown that the symmetrical shafts have double zero eigenvalues in the absence of external damping, but asymmetrical shafts do not have. The asymmetrical shaft in the absence of external damping has a saddle point, therefore the system is unstable. Also, for symmetrical and asymmetrical shafts, in the presence of external damping at the critical speeds, supercritical Hopf bifurcations occur. The amplitude of periodic solution due to supercritical Hopf bifurcations for symmetrical and asymmetrical shafts for the higher modes would be different, due to shaft asymmetry. Consequently, the effect of shaft asymmetry in the higher modes is considerable. Also, the amplitude of periodic solutions for symmetrical shafts with rotary inertia effect is higher than those of without one. In addition, the dynamic behavior of the system in the vicinity of double Hopf bifurcation is investigated. It is seen that in this case depending on the damping and rotational speed, the sink, source, or saddle equilibrium points occur in the system.

Periodic and quasiperiodic galloping of a wind-excited tower under parametric damping

The effect of internal parametric damper on periodic and quasi-periodic (QP) galloping of a wind-excited tower is studied analytically in this paper. We use a simple degree of freedom model and consider the cases where the turbulent wind activates external excitation, parametric one or both. The method of three stage perturbation analysis is performed to obtain an approximation of periodic and QP solutions as well as the QP modulation envelope. We explore the effect of internal parametric damping (PD) on the amplitude and the onset of periodic and QP galloping. It is revealed that for specific turbulent wind excitation, the PD significantly influences the critical wind speed above which periodic and QP galloping occurs. In the case where external and parametric excitations are activated simultaneously, QP galloping persists for all ranges of wind velocity. The results also show that the modulation frequency of the QP galloping depends strongly on the type of excitation induced by the turbulent wind.

Finite element based vibration analysis of functionally graded spinning shaft system

The present work deals with the study of vibration and stability analysis of a functionally graded spinning shaft system using three-noded beam element based on the Timoshenko beam theory. Material properties are assumed to be graded in radial direction according to power law gradation. In the present analysis, the mixture of aluminum oxide (Al2O3) and stainless steel (SUS304) has been considered as functionally graded material where metal (SUS304) content decreases towards the outer diameter of the shaft. The functionally graded shafts has been modeled as a Timoshenko beam, which contains discrete isotropic rigid disks supported by flexible bearing. The functionally graded shaft has been modeled based on first-order shear deformation beam theory with transverse shear deformation, rotary inertia, gyroscopic effect, strain and kinetic energy of shafts by adopting three-dimensional constitutive relations. The derivation of governing equations of motion has been obtained using Hamilton’s principle. Three-noded beam element with four degrees of freedom per node has been used to solve the govering equations. In this work, the effects of both internal viscous and hysteretic damping have also been incorporated in the finite element model. Various results have been obtained such as Campbell diagram, stability speed limit, damping ratio, and time responses for functionally graded shaft and also compared with conventional steel shaft. It has been found that the responses of the functionally graded spinning shaft are significantly influenced by material properties, radial thickness, power law gradient index, and internal (viscous and hysteretic) damping. The obtained results also show the advantages of functionally graded shaft over conventional steel shaft.

Description of phenomena vibration in hyperdeform polymers materials

The issue of vibration damping occurs in many mechanical problems in the operation of various devices, in the automotive industry engineering, aerospace. In the case where damping by selection of the masses and dimensions is not possible due to various reasons or for other reasons it was abandoned, vibration dampers are used. Minimization of adverse impact of dynamic interaction effects is an important research and technical problem. Passive energy absorbers used today (complex of bumpers, passenger lifts buffers typically allows to the safe dissipation of energy within a certain range of loads. In the case of high-impact loading variability is desirable to use an adaptive energy absorption system capable of rapid change their dynamic characteristics. The main issue in the analysis of interactions impact of dynamic loads on objects is dispersion (dissipation) of kinetic energy during impact. In paper a description of model of internal damping was proposed with the proof the influence of component part of polynomial. For example elastomer material EPUNIT will be used to present prepare the buildings of model hyperdeform material. Was present conclusion of analyses systems hyperdeform composite materials.