Effective Loss Factor Research Articles

INVERSE ANALYSIS OF THE AMPLITUDE-DEPENDENT DAMPING PROPERTIES OF EPOXY/GLASS FIBER LAMINATES

In this paper, we present the experimental results obtained and corresponding inverse analysis employed to determine the amplitude-dependent damping properties of laminates made of glass fiber reinforced plastic (GFRP). Free damped vibration tests of cantilever beams with different symmetric stacking sequences were performed. Logarithmic decrement analysis was used to evaluate the effective amplitude-dependent loss factor of the samples. Inverse analysis was used to find the single-ply dynamic properties based on the laminated beam theory and the complex moduli approach. It was found that the loss factors of GFRP laminates almost linearly depend on the maximum strain amplitude. The maximum value of the loss factor of unidirectional ply was realized in the transverse direction to the fibers and reached ~ 0.023 for strain amplitudes up to 0.1% in the frequency range of 20-60 Hz.

On Improving the Loss Factors of Aerospace Structures Having Constrained Layer Damping Treatment

The loss factor of a structure can be significantly improved through constrained damping treatment using viscoelastic layer. Even after introducing the constrained damping layer, the effective loss factor achieved is seen to be far less than the loss factor of the basic viscoelastic material. Methods to improve the loss factor of the aerospace structures further are of great practical importance. In this work, two methods are investigated, one is extending the damping treatment to the boundaries and the other is related to the use of stand-offs for the viscoelastic layers. It is shown through experiments and numerical simulation that significant increase in the loss factor can be achieved by extending the damping treatment into the interfaces, especially in the second bending mode of vibration. Stand-offs having good extensional modulus can improve the loss factor of the bending modes further, though its shear modulus does not play any significant role.

An Identification Method for the “Effective Coupling Loss Factor” Based on the Hybrid FE-SEA Model

Due to the limitation of the SEA method, the hybrid FE-SEA method has become a powerful tool to solve the medium-frequency “acoustic-vibration problem”. However, in most cases, the solution process of the hybrid FE-SEA model is often accompanied by ill-posed matrix problems, such as the inverse solution of the matrix, and the calculation accuracy is not high, which affects the overall calculation accuracy of the hybrid FE-SEA model. In this paper, the calculation method for the effective coupling matrix of the hybrid FE-SEA model is further improved. Based on the basic parameter solving method of the hybrid FE-SEA model, the hybrid FE-SEA model for three-coupled systems is established. In this paper, the deterministic subsystem and the random subsystem response solving problem in three-coupled systems is studied. The method is extended to the multi-coupled system, and an improved calculation method for the coupling matrix of the hybrid FE-SEA model is proposed. On the basis of the weighted iterative method of the principal element, intermediate variables and error transfer are introduced. The parameter identification problem of the effective coupling loss factor of the hybrid FE-SEA model is solved, which provides a solution for parameter identification of the hybrid FE-SEA model.

Effective Complex Permittivity of Random Composite Media: PVDF/(Na<sub>1/2</sub>Bi<sub>1/2</sub>)TiO<sub>3</sub>

The present study discusses the fabrication of non-lead ceramic/polymer composites employing (Na1/2Bi1/2)TiO3 (NBT) ceramic powder as a filler and poly(vinylidene fluoride); PVDF as a polymer matrix. The NBT (volume fraction, ϕ = 1) ceramics were synthesized using the conventional mixed-oxide method followed by the high-energy ball milling method whereas (1-ϕ)PVDF/ϕ(Na1/2Bi1/2)TiO3; 0 ≤ ϕ ≤ 0.3 composites were prepared from a melt-mixing process. It was observed that the real and imaginary parts of dielectric permittivity, ac conductivity, and longitudinal piezoelectric charge coefficient increase with the increase in NBT-content. Different dielectric mixing models were presented to determine the effective complex permittivity of the composites. Five dielectric mixture equations have been chosen to test the acceptability of experimental data. It was revealed that theoretical models as given by Bruggman, Rother-Lichtenecker, and modified Rother-Lichtenecker show good agreement with the experimental results of filler-concentration dependent alteration of effective relative permittivity and loss factor of the PVDF/NBT composite. A mathematical model of first-order exponential growth has also been proposed, which fitted excellently the experimental data (r2 > 0.998).

Investigation on the influence of the structural characteristics of particle dampers on its damping performance

Under the condition of vertical harmonic excitation, the influence of two structural characteristics of the damping rod and the inner wall on the damping characteristics of the damper is studied. The force signal and acceleration signal of the damper under different excitation conditions are measured through experiments.The damping characteristics such as effective mass, loss power and loss factor of the damper are analyzed by the steady-state energy flow method. The experiment results indicate that, on the basis of ordinary particle dampers, adding damping rods can intensify the friction and extrusion of particles and rods, thereby enhancing the energy dissipation performance. By pasting rubber material on the inner wall of the damper, the soft inner wall can consume the acoustic energy during collision, enhance the energy consumption during collision, and improve the damping effect.

Enhanced vibration absorption of plates with circular metasurface composed of lossy acoustic black hole subunits

Metasurfaces and acoustic black holes (ABHs), as two kinds of emerging structures exhibiting extraordinary performances in steering and trapping waves, respectively, both have attracted extensive attention of researchers due to their potential applications in vibration control. However, studies combining the merits of them are rarely reported. In this paper, we propose a lossy circular ABH metasurface (LCAM) composed of gradient ABH subunits pasted with damping layers to realize the enhanced omnidirectional vibration absorption of plates in broadband, which is attributed to the introduced multiple reflection effect in the lossy ABH subunits. The phase shifts of the lossy ABH subunits are derived by using the transfer matrix method and integral method, and the effective loss factors are obtained through the effective medium theory. Based on the theoretical analyses, the LCAM is designed, and the results of simulations and experiments show that the designed LCAM realizes enhanced omnidirectional vibration absorption of the plate. The LCAM is applied to plates with different dimensions and boundary conditions to show its strong adaptability. Our design improves the ABH effect by taking advantages of the multiple reflection effect in metasurfaces, which provides an effective method for passive structural vibration control.

Energy flow analysis of equivalent fluid models for porous media.

Based on a heat conduction analogy that enables the energy flow analysis (EFA) to describe the smoothed energy variations, the EFA has been applied to a variety of structures to predict vibrational responses at high-frequency regions. In this paper, energy equations in the form of heat conduction laws are derived to represent dilatational waves in rigid- and limp-frame porous media using equivalent fluid models. Homogeneous and inhomogeneous waves are considered. Within the EFA framework, the group velocity and loss factor included in the energy models for structures are replaced with the energy velocity and effective loss factor, respectively. The capabilities of the energy models are illustrated using configurations in which the porous layer backed by a rigid wall is in a normal and oblique incident sound field. The results of the numerical simulations confirm the feasibility of the energy model. From an energy perspective, the adequacy of using rigid- and limp-frame equivalent fluid models is also discussed. It is shown that the use of a rigid-frame equivalent model for predicting the energy distribution is more restrictive than predicting acoustic performance such as sound absorption.

High temperature microwave dielectric and thermochemical properties of waste LixMn2O4 battery cathode materials reduced by moso bamboo

It is important to effectively and in an environmentally friendly manner, recover metallic elements such as lithium and manganese from waste lithium-manganese batteries. In this work, the changes in the dielectric and thermochemical properties of mixtures of waste LixMn2O4 battery cathode materials and moso bamboo during a microwave heating process were studied in detail using moso bamboo as the reducing agent. The dielectric properties of the mixed materials were measured by the cylindrical cavity perturbation method.The results of the high-temperature reduction process demonstrated that the reduction process could be divided into five temperature ranges (e.g., <120 °C, 120°C–220 °C, 220°C–380 °C, 380°C–600 °C, and >600 °C), and the reduction reaction mainly occurred in the third and fourth stages, especially in the ranges of 300–330 °C and 410–430 °C.The results of the microwave absorption characteristics under different conditions demonstrated that high temperatures were favorable for microwave penetration, and the microwave penetration depth (Dp) was 4 cm at 900 °C. In addition, when the moso bamboo content exceeded 16%, the εr" (effective loss factor) and tan δ (loss angle tangent) of the mixtures suddenly dropped to lower levels by approximately 0.064 and 0.087, respectively. It was also found that when the moso bamboo content was 12%, the mixture had better thermal reduction and microwave dielectric properties.

A microwave fracturability index (MFI) of hard igneous rocks

Microwave has been regarded as a promising technique to break hard igneous rocks. However, there is no criterion to evaluate the ease with which commonly found hard rocks can be fractured by microwave. In this study, 15 hard rocks were treated by a 2.45 GHz single mode microwave cavity at 3 kW for 1 min. The effect of rock properties including the average grain size, the volume inhomogeneity coefficient, the effective dielectric loss factor and the initial P-wave velocity on the P-wave velocity reduction (which is defined as the microwave fracturability index-MFI) was investigated. The first three parameters can be obtained from the petrographic images whereas the last one is easy to assess. The results found positive linear relationships between MFI and the average grain size, the effective dielectric loss factor and the initial P-wave velocity, and a negative linear relationship between MFI and the volume inhomogeneity coefficient. In addition, the study revealed that the most significant factors according the entropy weight method are the effective dielectric loss factor and the average grain size, followed by the volume inhomogeneity coefficient, and finally the initial P-wave velocity. A multi-parameter linear regression model for MFI of igneous rocks was proposed and validated. This work provides an easy and straightforward method to assess the microwave fracturability of a specific rock based on petrographic photomicrographs and P-wave velocity measurement.

Experimental and numerical analysis of the complex permittivity of open-cell ceramic foams

Open-cell ceramic foams are promising materials in the field of microwave heating. They can be manufactured from susceptor materials and can, therefore, be used as selective heating elements. In this study, the complex permittivities of ceramic foam materials, including silicon-infiltrated silicon carbide (SiSiC), pressureless sintered silicon carbide (SSiC), silicate-bonded silicon carbide (SBSiC), and cordierite were determined. The dielectric properties of the foams were determined by the cavity perturbation technique using a TE104 WR340 waveguide resonator at 2.45 GHz. Samples were preheated in a tubular furnace, enabling temperature-dependent permittivity measurements up to 200 °C. The effective dielectric constant and effective loss factor were found to depend on the porosity and material composition of the foam. The SiSiC material had a higher effective dielectric constant than the SSiC and SBSiC ceramics. The effective dielectric constant of the foams showed a trend of gradual increase with increasing temperature. Some selected dielectric mixing relations were then applied to describe the effective permittivity of the foams and compare them with predictions from finite element simulations performed using the CST Studio Suite. The foam morphologies and simple block inclusions were used in the simulations.

Improved damping in sandwich beams through the inclusion of dispersed graphite particles within the viscoelastic core

In this work, the passive damping in a sandwich beam is investigated for the inclusion of dispersed graphite particles within the viscoelastic core. The effective material properties of the viscoelastic particulate composite (VEPC) are estimated using a differential scheme and the elastic–viscoelastic correspondence principle. The corresponding results reveal increased effective storage moduli and decreased effective loss factor of a viscoelastic medium for the inclusion of graphite particles. As it implies both the possibilities of augmentation and deterioration of passive damping in the sandwich beam, the subsequent study is carried out on the variation of damping characteristics of the sandwich beam especially for different volume fractions of inclusion. It is found that the passive damping in the sandwich beam increases significantly for the inclusion of graphite particles within the viscoelastic core, and also an optimal volume fraction of inclusion corresponding to the maximum damping in the sandwich beam appears. Further study on the optimal utilization of VEPC patches within the core of the sandwich beam reveals a minimal change of weight of the overall beam for the replacement of patches of conventional viscoelastic material by VEPC patches while this replacement yields a remarkable improvement of passive damping in the sandwich beam.

Vibration damping materials with enhanced loss due to microstructural nonlinearity

One conventional approach to attenuating structure-borne waves or reduce the ringdown time of modes in structural elements is to attach damping layers or patches to vibrating components. Common patch and layer materials are specially formulated polymers or engineered polymeric composites that demonstrate elevated viscoelastic loss factors in the frequency range of interest. Recent research has shown that small volume fractions of negative stiffness inclusions embedded in a lossy material generate effective loss factors that exceed that of the host material. The ability to generate negative stiffness behavior, however, is often the result of nonlinear inclusion material response. Presented here is a multiscale model of a particulate composite material consisting of a nearly incompressible host material containing small-scale heterogeneities with a nonlinear elastic stress-strain response. We investigate the nonlinear dynamic behavior of the heterogeneous medium for small harmonic perturbations about several pre-strain states to demonstrate the influence of the microscale dynamic response on the macroscopically observable mechanical loss. Of primary interest is the energy dissipation capabilities of the composite which can be tuned using inclusion pre-strain. Loss for composites with nonlinear inclusions is compared to conventional composites containing air voids or steel inclusions. [Work supported by ONR.]

Determination of effective loss factors in reduced SEA models

The definition of Statistical Energy Analysis (SEA) models for large complex structures is highly conditioned by the classification of the structure elements into a set of coupled subsystems and the subsequent determination of the loss factors representing both the internal damping and the coupling between subsystems. The accurate definition of the complete system can lead to excessively large models as the size and complexity increases. This fact can also rise practical issues for the experimental determination of the loss factors. This work presents a formulation of reduced SEA models for incomplete systems defined by a set of effective loss factors. This reduced SEA model provides a feasible number of subsystems for the application of the Power Injection Method (PIM). For structures of high complexity, their components accessibility can be restricted, for instance internal equipments or panels. For these cases the use of PIM to carry out an experimental SEA analysis is not possible. New methods are presented for this case in combination with the reduced SEA models. These methods allow defining some of the model loss factors that could not be obtained through PIM. The methods are validated with a numerical analysis case and they are also applied to an actual spacecraft structure with accessibility restrictions: a solar wing in folded configuration.

Homogenization theory for designing graded viscoelastic sonic crystals**Project supported by the National Basic Research Program of China (Grant No. 2011CB610301).

In this paper, we propose a homogenization theory for designing graded viscoelastic sonic crystals (VSCs) which consist of periodic arrays of elastic scatterers embedded in a viscoelastic host material. We extend an elastic homogenization theory to VSC by using the elastic-viscoelastic correspondence principle and propose an analytical effective loss factor of VSC. The results of VSC and the equivalent structure calculated by using the finite element method are in good agreement. According to the relation of the effective loss factor to the filling fraction, a graded VSC plate is easily and quickly designed. Then, the graded VSC may have potential applications in the vibration absorption and noise reduction fields.

Comparison of Microwave and Radio-Frequency Heating of Dealuminated Zeolites and Al2O3

In the present study, the dielectric heating option was investigated for various dry materials: USY zeolite, ZSM-5 zeolite, and α- & γ-alumina. These materials are characterized by low effective dielectric loss factors; therefore they are often considered as not accessible for direct dielectric heating. Applying technically relevant volumes up to 20 L, dielectric heating could be demonstrated for all these materials when employing radio waves (RW) whereas heating with microwaves (MW) was difficult or even impossible. Dielectric heating experiments were also simulated with the CST electromagnetic simulation software.It could be shown that for all tested materials RW heating is more suitable than MW heating with regard to heating rates, temperature rise (both at equal power input) and homogeneity of the temperature pattern. The comparison of experimental data and simulation shows an excellent agreement. Thus, dielectric heating utilizing frequencies in the MHz range (radio-frequencies, RF) was demonstrated to be well applicable, even for materials with low loss factors, up to technically relevant temperatures and scales.This study also includes the evaluation of the energy efficiency for RW heating on the basis of the heating and power input data. Reasons for lower efficiencies, even under optimal fitting conditions applying an electronic matching network, are discussed and interpreted using literature and own experimental results, namely temperature-programmed desorption (TPD).

Nonlinear behavior of heterogeneous materials containing snapping acoustic metamaterial inclusions

This work studies the forced dynamical behavior of a heterogeneous material containing metamaterial inclusions undergoing large deformations. The inclusions exhibit non-monotonic stress-strain behavior, modeled with an expansion to third order in volume strain, where the coefficients of the expansion depend on the metamaterial structure. The resulting constitutive behavior of interest displays regimes of both positive and negative stiffness and the inclusion therefore exhibits hysteretic snapping when forced by an acoustic pressure. Two cases are explored using a generalized Rayleigh-Plesset analysis to model the large-deformation dynamics of the metamaterial inclusion following an approach similar to Emelianov et al. [J. Acoust. Soc. Am., 115, 581 (2004)]. The first case focuses on the forced dynamics of a single inclusion embedded in a weakly compressible elastic medium. The second case broadens the model to analyze the behavior of a heterogeneous material comprised of a low volume fraction of non-interacting metamaterial inclusions embedded in a weakly compressible material. Finally, estimates of the effective bulk modulus and loss factor of the heterogeneous medium are presented for instances of the forcing pressure inducing either large or small inclusion deformation. [Work supported by the ARL:UT McKinney Fellowship in Acoustics and the Office of Naval Research.]

Electrical characteristics of Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt; and Ta&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;5&lt;/sub&gt; nanoparticles synthesized by DC anodic ARC-discharge in water

Because of the length scale and high specific surface area of nanometer-sized particles, they exhibit novel properties as compared with their bulk counterpart materials. Furthermore, the incorporation of well-characterized nanoparticles in various organic matrices provides dielectrics with improved electrical, mechanical and thermal features. Alumina and tantalum-pentoxide nanoparticles have been proved efficient fillers in such nanocomposites. These specific particles are herein produced by DC anodic arc-discharge immersed in water and they are probed by means of broadband dielectric spectroscopy in a wide temperature range (-100 to 100 °C). Different formalisms (effective dielectric constant, loss factor and specific conductivity) are combined, providing the possibility to determine the frequency and temperature dependence of the dielectric characteristics of the synthesized nanoparticles. The knowledge of the latter should be determinant for potential application of alumina and tantalum-pentoxide fillers to two-phase heterogeneous nanodielectrics.

Electrical characteristics of Al2O3 and Ta2O5 nanoparticles synthesized by DC anodic ARC-discharge in water

Because of the length scale and high specific surface area of nanometer-sized particles, they exhibit novel properties as compared with their bulk counterpart materials. Furthermore, the incorporation of well-characterized nanoparticles in various organic matrices provides dielectrics with improved electrical, mechanical and thermal features. Alumina and tantalum-pentoxide nanoparticles have been proved efficient fillers in such nanocomposites. These specific particles are herein produced by DC anodic arc-discharge immersed in water and they are probed by means of broadband dielectric spectroscopy in a wide temperature range (-100 to 100 °C). Different formalisms (effective dielectric constant, loss factor and specific conductivity) are combined, providing the possibility to determine the frequency and temperature dependence of the dielectric characteristics of the synthesized nanoparticles. The knowledge of the latter should be determinant for potential application of alumina and tantalum-pentoxide fillers to two-phase heterogeneous nanodielectrics.

Recent Developments in the Microwave Processing of Ceramics

Highly absorbing ceramics can be heated in a standard multimode microwave oven. However, most of the microwave energy is dissipated in their ceramic surfaces and heat is transported slowly throughout the sample volume by the usual thermal conduction mechanisms. As with conventional methods, this process leads to non-uniform heating. In contrast, ceramics that are fairly transparent to microwave energy are difficult to heat in standard microwave ovens. When they can be heated, reverse temperature gradients often develop. Reverse temperature gradients can be beneficial in some processes, e.g., combustion synthesis, chemical vapor infiltration (CVI) and binder burnout, but in most ceramic processes, temperature gradients are undesirable. These characteristics have presumably been partially responsible for the ceramic industry's failure to examine microwave processing more closely.The ability of dipoles to respond to the oscillating electric field and their subsequent inability to keep up with rapid reversals in the field result in dielectric losses that are manifested as heat. While some of the mechanisms by which electromagnetic radiation interacts with ceramics are well known, interaction mechanisms in the microwave frequency range are less well understood. Since several mechanisms, including electrical conductivity, can operate simultaneously, the total energy dissipation and heat generation depends on the effective loss factor. The effective loss factor (e″eff) is described bywhere e′ is the dielectric constant and is a measure of the extent of polarization, and tan δ indicates how responsive the dipoles are to the oscillating field.

Analysis and optimal design of layered composites with high stiffness and high damping

In this paper we investigate the design of composite materials with simultaneously high stiffness and high damping. We consider layered composite materials with parallel plane layers made of a stiff constituent and a lossy polymer. We analyze the response of these composites to a dynamic load with an arbitrary direction. Using the viscoelastic correspondence principle and linear frequency domain viscoelastic models, we derive an expression for the effective complex modulus of layered composites of infinite size at infinitesimal strains. The dependence of the effective dynamic modulus and loss factor on the geometrical parameters and on the tensile and bulk loss factors of the lossy constituent is analyzed. Moreover we determine the magnitude of the strains in the lossy constituent and demonstrate that the combination of high stiffness and high damping of these composites is due to the high normal and/or shear strains in the lossy material. We use nonlinear constrained optimization to design layered composites with simultaneously high stiffness and high damping while constraining the strains in the polymer. To determine the range of validity of the linear viscoelastic model, simulations using finite deformations models are compared to the theoretical results. Finally, we compute the effective properties of composites of finite size using finite element methods and determine the minimum size required to approach the formulae derived for composites of infinite size.