Effective Loss Factor Research Articles

Dependence of the dynamic properties of Voigt and Reuss composites on the Poisson's ratios and bulk loss factors of the constituent materials

Materials possessing both high stiffness and high damping would be beneficial in many structural applications. Composites that combine a stiff material, which usually has low damping, with a soft and lossy material have been proposed to engender both high dynamic modulus and high loss factor. In this article, we investigate the effective dynamic moduli and loss factors of Reuss and Voigt composites in response to a uniaxial harmonic load. The constituent materials are characterized by multiaxial viscoelastic models in the frequency domain. Using the viscoelastic correspondence principle, we derive formulae for Reuss and Voigt composites of infinite dimensions taking into account Poisson effects. We show that the effective loss factor of a Reuss composite is sensitive to the values of the Poisson's ratio and bulk loss factors of the constituent materials. Finally we simulate, using finite element analysis, the response of cylindrical Reuss composite rods of finite radius to an axial load. We demonstrate that the effective dynamic properties of these rods is highly sensitive to the ratio of the radius to the layer thickness of the composite.

Effect of filler waviness and orientation on the damping behavior of CNF-reinforced epoxy composites

An ever increasing demand for material performance coupled with recent advances in the production and availability of nanoscale materials has led to a significant interest in the use of nanoscale fillers to augment and tailor material performance in nanocomposites. Specifically, the use of high aspect ratio fillers, such as carbon nanotubes and carbon nanofibers (CNF) to augment the viscoelastic performance of nanocomposites has been the focus of many studies. Previous study has shown the use of high aspect ratio fillers to significantly enhance the damping capacity at low frequencies by more than 100 %, relative to the neat epoxy. In light of the promise, this technology holds for use in engineered applications, requiring specific damping performance, there remains a fundamental lack in understanding of the precise mechanisms and thereby a lack of ability to accurately predict material performance, which is limiting application of the technology. This study looks at both the effect of the random filler orientation and the effect of filler waviness in examining the viscoelastic response of CNF-reinforced nanocomposites. Using a fundamental approach, this study employs experimental, analytical, and numerical modeling techniques to characterize the amount of strain energy transferred to the filler and the matrix, and to indirectly estimate the effective loss factor of the filler. Utilizing experimental investigation coupled with parametric inquiries using strain energy methods relative to both filler orientation and waviness, this study provides fundamental insight into the effect of imperfect geometries and random filler distributions seen in nanocomposites utilizing high aspect ratio fillers, such as CNF.

Effect of functionalization of single-wall carbon nanotubes (SWNTs) on the damping characteristics of SWNT-based epoxy composites via multiscale analysis

The influence of carbon nanotube functionalization on damping characteristics of SWNT-based composites is investigated for the first time with a sequential multiscale approach. The process consists of two parts. First, the interfacial shear strength between the functionalized nanotube and the epoxy is calculated by simulating a SWNT pull-out test using the molecular dynamics method. The strength values obtained from atomic simulation are then applied to a micromechanical damping model of a representative unit cell of a SWNT/epoxy composite under cyclic loading. The analysis results indicate that the nanotube functionalization increases the interfacial shear strength. Due to the stick–slip motion at the interfacial surface, the effective loss factor of the epoxy with functionalized nanoropes is sensitive to the applied load/stress. The increased shear strength can either enhance or reduce the damping ability of the composite, depending on the operational load/stress range and nanotube aspect ratio.

Vibration and damping characteristics of beams with active constrained layer treatments under parametric variations

Hybrid damping designs with active piezoelectric materials and passive viscoelastic materials (VEMs) combine the advantages of both active and passive constrained layer damping (ACLD/PCLD) treatments. Researchers have established the standards for the extent and placement of the PCLD treatment for common structures. However for ACLD treatment, such detailed studies are not available. This study is aimed to examine, the effect of parametric variation of active constrained layer on the vibration control of the beams treated with optimally placed active or passive constrained layer damping patches. Finite element model is developed to model the open-loop and close-loop dynamics of active/passive constrained layer damping treated beam. The placement strategies of ACLD patches are devised using the modal strain energy (MSE) approach. Extensive experimentation studies are conducted by making twenty one separate samples of ACLD/PCLD treated beams with variations in viscoelastic material layer thickness, ACLD/PCLD patch coverage and location of the patch. Effects of key parameters, such as control gain, viscoelastic material thickness, coverage and location variation of ACLD patch on the system loss factor have been investigated. The careful analysis of results from partially covered ACLD treated beam suggests that the maximum damping of the first mode can be achieved by attaching the ACLD patch only up to 50% coverage. It also reveals that with proper choice of the control voltage and thickness, the effective loss factor can be almost doubled. The present study suggests the potential use of parametric studies that establish some guide lines for the extent and placement of the ACLD patches on the cantilevered beam.

Dynamics and Performance of a Harmonically Excited Vertical Impact Damper

Particle impact dampers (PIDs) have been shown to be effective in vibration damping. However, our understanding of such dampers is still limited, based on the theoretical models existing today. Predicting the performance of the PID is an important problem, which needs to be investigated more thoroughly. This research seeks to understand the dynamics of a PID as well as those parameters which govern its behavior. The system investigated is a particle impact damper with a ceiling, under the influence of gravity. The base is harmonically excited in the vertical direction. A two-dimensional discrete map is obtained, wherein the variables at one impact uniquely dictate the variables at the next impact. This map is solved using a numerical continuation procedure. Periodic impact motions and “irregular” motions are observed. The effects of various parameters such as the gap clearance, coefficient of restitution, and the base acceleration are analyzed. The dependence of the effective damping loss factor on these parameters is also studied. The loss factor results indicate peak damping for certain combinations of parameters. These combinations of parameters correspond to a region in parameter space where two-impacts-per-cycle motions are observed over a wide range of nondimensional base accelerations. The value of the nondimensional acceleration at which the onset of two-impacts-per-cycle solutions occurs depends on the nondimensional gap clearance and the coefficient of restitution. The range of nondimensional gap clearances over which two-impacts-per-cycle solutions are observed increases as the coefficient of restitution increases. In the regime of two-impacts-per-cycle solutions, the value of nondimensional base acceleration corresponding to onset of these solutions initially decreases and then increases with increasing nondimensional gap clearance. As the two-impacts-per-cycle solutions are associated with high loss factors that are relatively insensitive to changing conditions, they are of great interest to the designer.

Investigation of beam-plate systems including indirect Coupling in terms of Statistical Energy Analysis

Statistical Energy Analysis (SEA) is generally used for the high frequency analysis in various areas. In the present paper a SEA-related study concerning coupled structures consisting of beams and plates is discussed. Firstly, the Fourier technique is explained to obtain the energies and power flows for excitation on the beam and the plate. Then, these are used in the Power Injection Method (PIM) to obtain the effective Coupling Loss Factors (CLFs) of the single beam-plate system. Overlapping octave bands are used in a frequency average approach. Based on the analysis for the beam-plate structure, the beam-plate-beam structure is also investigated in the SEA framework. It is found that the indirect coupling in an SEA sense may exist for such a beam-plate-beam coupled structure. The numerical result shows that its effect is larger when the dimensions of beams are similar.

Dielectric spectroscopy of osmotic solutions and osmotically dehydrated tomato products

Complex permittivity is the physical property that describes the interaction between matter and an electromagnetic field. This property is related to the structural and physico-chemical properties such as water and soluble solids content or water activity of the material. The complex permittivity of different aqueous solutions, fresh and osmotically dehydrated cherry tomatoes was measured and related to the products’ composition. Results showed that fruits osmotically dehydrated with sucrose solutions reached the lowest loss factors but the maximum penetration depth ( D p). On the other hand, fruits immersed in binary salt solutions showed the inverse tendency. For products impregnated with ternary solutions an intermediate behaviour was observed. Calcium lactate addition had no significant effects on complex permittivity at 2.45 GHz, but its presence increased the effective loss factor at low frequency. The dielectric properties of fruits and vegetables can be modified by controlling osmotic process variables (time, temperature, pressure and osmotic solution composition) in order to improve their further drying with microwaves.

Influence of excitation amplitude on the characteristics of nonlinear butyl rubber isolators

The purpose of this study is to explore the advantages and characteristics of nonlinear butyl rubber (type IIR) isolators in vibratory shear by comparison with linear isolators. It is known that the mechanical properties of viscoelastic materials exhibit significant frequency and temperature dependence, and in some cases, nonlinear dynamic behavior as well. Nonlinear characteristics in shear deformation are reflected in mechanical properties such as stiffness and damping. Furthermore, even when the excitation amplitude is small the response amplitude may often be large enough that nonlinearities cannot be ignored. The treatment involves developing phenomenological models of the effective storage modulus and effective loss factor of a rubber isolator material as a function of excitation amplitude. The transmissibility of a nonlinear viscoelastic isolator is compared with that of a linear isolator using an equivalent linear damping coefficient. Forced resonance vibration and impedance tests are used to characterize nonlinear parameters and to measure the normalized transmissibility. It is found that as the excitation amplitude of the nonlinear viscoelastic isolator increases, the response amplitude decreases and the transmissibility is improved over that of the linear isolator for excitation frequency that exceeds a particular value governed by the temperature and excitation amplitude. The method of multiple scales and numerical simulations are used to predict the response characteristics of the isolator based on the phenomenological modeling under different values of system parameters.

Improved volume-averaged model for steady and pulsed-power electronegative discharges

An improved volume-averaged global model is developed for a cylindrical (radius R, length L) electronegative (EN) plasma that is applicable over a wide range of electron densities, electronegativities, and pressures. It is applied to steady and pulsed-power oxygen discharges. The model incorporates effective volume and surface loss factors for positive ions, negative ions, and electrons combining three electronegative discharge regimes: a two-region regime with a parabolic EN core surrounded by an electropositive edge, a one-region parabolic EN plasma, and a one-region flat-topped EN plasma, spanning the plasma parameters and gas pressures of interest for low pressure processing (below a few hundred millitorr). Pressure-dependent effective volume and surface loss factors are also used for the neutral species. A set of reaction rate coefficients, updated from previous model calculations, is developed for oxygen for the species O2, O2(Δg1), O, O2+, O+, and O−, based on the latest published cross-section sets and measurements. The model solutions yield all of the quantities above together with such important processing quantities such as the neutral/ion flux ratio ΓO∕Γi, with the discharge aspect ratio 2R∕L and pulsed-power period and duty ratio (pulse on-time/pulse period) as parameters. The steady discharge results are compared to an experiment, giving good agreement. For steady discharges, increasing 2R∕L from 1 to 6 leads to a factor of 0.45 reduction in ΓO∕Γi. For pulsed discharges with a fixed duty ratio, ΓO∕Γi is found to have a minimum with respect to pulse period. A 25% duty ratio pulse reduces ΓO∕Γi by a factor of 0.75 compared to the steady-state case.

Design Method of Sound Absorber for Anti Acoustic Resonance in Tube Bundles Based on Acoustic FEM

Equipment of sound absorbers mid-air in the duct is an effective countermeasure for anti acoustic resonance in tube bundles of heat exchangers. Its design method, including the number or placement of absorbers in the duct space for efficient performance, was developed based on acoustic FEM. Here, the acoustic characteristics of absorbers, such as effective bulk modulus, loss factor or density of the air within the absorbers are needed. These parameters are evaluated by flow resistance method or impedance tube method. Complex eigenvalue analysis with acoustic FEM is executed which yields the increase of modal damping ratio by the equipment of absorbers. In order to verify the above-mentioned method, the acoustic experiment with the scale model of coal-fired boilers was conducted and experimental and analytical results are in good agreement. Finally this method was applied to the actual boiler plant and based on these results, it was confirmed that the proposed method is the effective countermeasure for the and acoustic resonance in heat exchangers.

Modeling the electrical characteristics of periodic dielectric media

The dispersion of the effective permittivities of two inhomogeneous matrix systems with unidirectional fiber inclusions with a square cross section is studied. Interpolation formulas for the effective permittivity as a function of the frequency are obtained, whose range of applicability is determined through physical modeling and comparison with known systems of equations admitting exact solutions. It is established that the effective loss factor exhibits anomalous behavior in the vicinity of the critical concentration of inclusions.

Unequalized Currents in Coaxial AC Bridges

In a coaxial ac bridge with imperfect current equalization, the comparison of two standard resistors shows a linear frequency dependence. Unequalized currents load the magnetic cores in the coaxial bridge and result in effective loss factors of certain capacitances of the compared resistors. To avoid this systematic effect in any coaxial bridge used for the precise calibration of impedance standards, a correct arrangement of current equalizers is absolutely necessary.

Electrical Properties of Soils at ISM Radio Frequencies, From 1 to 40 MHz

Soil electrical properties, conductivity and permittivity, vary with moisture content and temperature. The goal of the work was to generate working correlative functions of the electrical properties of soil over practical ISM radio frequencies (6.78 to 40.68 MHz) from the Kirtland Air Force Base RF soil remediation project, and its constituent soil types, to facilitate numerical model studies. Correlates were developed to facilitate numerical model temperature and moisture dependence of the electrical properties. Measurements were made in continuous spectra from 1 to 40 MHz for varying moisture content and temperatures of sand, kaolinite, Austin land fill clay, sandy loam and Kirtland Air Force Base soil samples. The measurements were conducted in a 1 5/8”coaxial sample holder with flush mounted center conductor. Impedance data were collected with a Hewlett-Packard 4194A Impedance Analyzer from which calculations of permittivity were made. In general, the relative permittivity and effective loss factor are sensitive functions of water content and temperature.

A hybrid mode/Fourier-transform approach for estimating the vibrations of beam-stiffened plate systems

In this paper, a hybrid Mode/Fourier-transform approach is described for estimating the vibration response of a structure such as a beam-stiffened plate with excitation applied to the beam. The beam is defined deterministically in terms of its modes, whereas the plate is treated approximately by assuming it extends to infinity. Equilibrium and continuity conditions are approximated along the interface between the beam and the plate in the wavenumber domain by a Fourier transform method. Consequently, both the dynamic response of the beam and the power transmitted to the plate can be simply estimated. Meanwhile, the dynamic interactions of the coupled system can be determined. These depend on the correlations between the modal properties of the beam and the wave motions of the plate. Expressions are given for the effective mass (density) and effective loss factor the plate applies to each mode of the beam. When a locally reacting plate approximation is incorporated into the Mode/Fourier-transform procedure, a simpler ‘locally reacting impedance method’ can be developed. The results are discussed and compared to those of fuzzy structure theory. Numerical examples are presented.

Damping as a result of piezoelectric energy harvesting

Systems that harvest or scavenge energy from their environments are of considerable interest for use in remote power supplies. A class of such systems exploits the motion or deformation associated with vibration, converting the mechanical energy to electrical, and storing it for later use; some of these systems use piezoelectric materials for the direct conversion of strain energy to electrical energy. The removal of mechanical energy from a vibrating structure necessarily results in damping. This research addresses the damping associated with a piezoelectric energy harvesting system that consists of a full-bridge rectifier, a filter capacitor, a switching DC–DC step-down converter, and a battery. Under conditions of harmonic forcing, the effective modal loss factor depends on: (1) the electromechanical coupling coefficient of the piezoelectric system; and (2) the ratio of the rectifier output voltage during operation to its maximum open-circuit value. When the DC–DC converter is maximizing power flow to the battery, this voltage ratio is very nearly 1/2, and the loss factor depends only on the coupling coefficient. Experiments on a base-driven piezoelectric cantilever, having a system coupling coefficient of 26%, yielded an effective loss factor for the fundamental vibration mode of 2.2%, in excellent agreement with theory.

Numerical analysis of microwave heating of a dielectric

AbstractMicrowave heating of a dielectric in a cavity was analyzed numerically with the FDTD method with the aim of devising new methods for reducing uneven heating typical of microwaving. The dielectric was assumed to be water and the frequency of a microwave was taken to be 1 GHz. It was found that the electric field is highly dependent on the position of the dielectric in a cavity. The temperature distribution reflects the profile of the RMS value of the electric field in the dielectric, although there appears to be no effect of the short wavelength typical of the electric field. The heating rate depends on the position of the dielectric. In the case of a higher effective loss factor a microwave decays immediately after entering the dielectric, and the temperature of the interior remains low. These results indicate that the uneven heating is due to at least two causes: standing wave and rapid decay of a microwave. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(3): 227–236, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10087

Boundary damping of flexural vibrations in beams and plates

The damping of resonantly enhanced flexurally vibrating beams and plates is typically accomplished with surface treatments, viz. constrained or unconstrained damping layers. Alternatively, damping may be achieved at boundaries. In some sense this is a more fundamental approach in that for homogeneous plates, it is the boundaries that are solely responsible for resonant behavior. The theoretical performance of boundary treatments is unbounded, provided the treatment is full, that is continuous along the extent of the boundary. This is not the case however with partial coverage, where a portion of the boundary is left bare. The bounds for such treatments are explored in this paper. The treatment itself is defined in terms of a single bounce reflection coefficient (RC). It is found that for boundary damping in one dimension, viz., beams, the effective loss factor for individual modes is frequently invariant with either one or both ends treated, assuming RC constant. This is in contrast to the two-dimensional case, viz., thin plates, where analogous loss factor values are frequency dependent. Illustrative examples are presented and analyzed. [Work partially performed at CAA/Anteon Corp. and supported by NSWCCD and NSSC, Code 93R.]

Dielectric dispersion of three-and four-component matrix media

The dielectric dispersion of heterogeneous matrices containing dissimilar cylindrical inclusions is studied. Conditions for the dispersion in multicomponent media are found and explained from the physical standpoint. It is shown that the effective loss factor may have several maxima with their number depending on the number of dissimilar inclusions in the composite. Effective permittivity diagrams in the complex plane are constructed. For media with a low inclusion concentration, an approximate method for finding the frequency of the maxima is suggested.

Large coated plates under random excitation: Spatial-domain insights into radiation efficiency

A formal spatial-domain analysis of a large plate’s cross-spectral response to TBL-like excitations yields the following two results, unified and in closed form: (1) a part that contains a moderate area effect (from the acoustic field’s point of view, despite the plate being below coincidence by choice) and a stronger edge effect; and (2) a second part with a weak edge effect and a potentially strong area effect. The strong-edge/moderate-area part contains as coefficient the inverse of the plate’s effective loss factor. The strong-area part does not, enabling it to dominate the former with rising frequency particularly over that range in the frequency spectrum encompassing the typically broad (lossy) thickness resonances of the plate’s coating. Use of this unified cross-spectral response function to compute the plate’s acoustic field confirms the expected rise in radiation efficiency at higher loss factors and frequencies, as brought about by the relative growth of the strong-area effect under both of those conditions. [Work supported by NSWC/Carderock Division.]

Linear hydrodynamics and viscoelasticity of nematic elastomers

: We develop a continuum theory of linear viscoelastic response in oriented monodomain nematic elastomers. The expression for the dissipation function is analogous to the Leslie-Ericksen version of anisotropic nematic viscosity; we propose the relations between the anisotropic rubber moduli and new viscous coefficients. A new dimensionless number is introduced, which describes the relative magnitude of viscous and rubber-elastic torques. In an elastic medium with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics, the model shows a dramatic decrease in the dynamic modulus in certain deformation geometries. The degree to which the storage modulus does not altogether drop to zero is shown to be both dependent on frequency and to be proportional to the semi-softness, the non-ideality of a nematic network. We consider the most interesting geometry for the implementation of the theory, calculating the dynamic response to an imposed simple shear and making predictions for effective moduli and (exceptionally high) loss factors.