Maximum Loss Factor Research Articles

Vibration damping characterization of linseed oil‐based elastomers for its effectiveness to attenuate structural vibration

ABSTRACTVibration damping properties of elastomers prepared from linseed oil were characterized by dynamic mechanical analyzer in a temperature range of −50 to 100°C and frequency range of 5 Hz to 1 kHz. The maximum damping loss factor, varies from 0.78 to 1.32, the room temperature (25°C) loss factor, in the range of 0.56–1.08 and the temperature range ( ) for effective damping varies from 63°C to 74.4°C in different elastomers. The elastomers behave as a good vibration damper both in lower and higher frequency range. Thus these elastomers exhibit good damping behavior in a wide range of temperature and frequency, a primary requirement for practical damping applications. A modal constrained layer damping system constructed utilizing these elastomers exhibits its potentiality to attenuate structural vibrations with respect to mild steel bare plate resonator under laboratory fabricated testing methodology. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 3611–3623, 2013

Application of level set method to optimal vibration control of plate structures

Vibration control plays a crucial role in many structures, especially in the lightweight ones. One of the most commonly practiced method to suppress the undesirable vibration of structures is to attach patches of the constrained layer damping (CLD) onto the surface of the structure. In order to consider the weight efficiency of a structure, the best shapes and locations of the CLD patches should be determined to achieve the optimum vibration suppression with minimum usage of the CLD patches. This paper proposes a novel topology optimization technique that can determine the best shape and location of the applied CLD patches, simultaneously. Passive vibration control is formulated in the context of the level set method, which is a numerical technique to track shapes and locations concurrently. The optimal damping set could be found in a structure, in its fundamental vibration mode, such that the maximum modal loss factor of the system is achieved. Two different plate structures will be considered and the damping patches will be optimally located on them. At the same time, the best shapes of the damping patches will be determined too. In one example, the numerical results will be compared with those obtained from the experimental tests to validate the accuracy of the proposed method. This comparison reveals the effectiveness of the level set approach in finding the optimum shape and location of the CLD patches.

The effect of aspect ratios and edge conditions on the optimal damping design of thin soft core sandwich plates and beams

An optimal design is presented to maximize the fundamental damping loss factor of sandwich rectangle plates and beams with general boundary conditions. With an extensive development of the classical laminate theory and energy method, the loss factor of sandwich laminate with a thin viscoelastic core is deduced. For sandwich-laminated plates and beams, the effect of fiber orientation of the orthotropic layer on the loss factor has been studied. The aspect ratio is very important in structural design for plates and beams. In this work, the effects of aspect ratios of sandwich laminates on optimal fundamental loss factors are investigated. The maximum fundamental loss factor and optimal fiber orientation have been obtained and analyzed for different sandwich laminates with the aspect ratio as a variable.

Analysis and optimal design for the damping property of laminated viscoelastic plates under general edge conditions

The present paper is concerned with analysis and optimal design for the damping loss factor of laminated plates under general edge conditions. In the analysis based on the classical lamination theory, the loss factor is deduced from the energy formulation for symmetrically laminated thin plates comprised of fiber reinforced layers and viscoelastic layers. The effects of location and thickness of viscoelastic layers are studied on the loss factor of the plates, and those of the fiber orientation angles are also clarified. In the optimal lay-up design problem, a layerwise optimization (LO) method is applied to the plates comprised of two different orthotropic materials, and the optimal fiber orientation angles are determined to obtain the maximum loss factor in the fundamental mode. These numerical simulation results uncovered that the present approach is quite useful in analyzing and designing the loss factor of the plates.

A combined experiment and molecular dynamics simulation study of hydrogen bonds and free volume in nitrile-butadiene rubber/hindered phenol damping mixtures

By combining experiment and molecular simulation, in this work we have systematically elucidated the fundamental mechanism of the significantly improved damping property of nitrile-butadiene rubber (NBR) contributed by the introduction of hindered phenol (AO-80) small molecules. At the molecular level, through FTIR, 1H-NMR and temperature-dependent FTIR, it is observed that hydrogen bonds (H-bonds) interaction exists between AO-80 small molecules and NBR polymer chains, leading to the formation of a H-bonds network structure. Meanwhile, positron annihilation lifetime spectrometer (PALS) and molecular dynamics simulation were also employed to characterize the fractional free volume for different NBR/AO-80 mixtures and it reached the minimum at the blending mass ratio of 100/60, which also possesses the largest number of H-bonds and the greatest binding energy through quantitative comparison. All of these microscopic analyses just rationalize the maximum dynamic loss factor. Therefore, it was indicated that there was an optimum ratio of rubber to hindered phenol molecules for achieving the maximum damping property. These fundamental studies are expected to provide some useful information to design and fabricate the high-performance polymeric damping materials.

Study on the Relationship between the Hydrogen Bond and Damping Properties of Nitrile-Butadiene Rubber/Hindered Phenol Composites by Molecular Dynamics Simulation

This work was try to study the relationship between the damping properties and the hydrogen bonds, fractional free volumes of nitrile-butadiene rubber (NBR)/hindered phenol (AO-80) composites from the microstructural point of view by combining the experimental and molecular simulation studies. The results indicated that the hydrogen bonds (HBs) were formed between AO-80 small molecules and NBR polymer chains. According to simulation results, because of the formed strongest HBs, highest binding energy and the smallest fractional free volume in the NBR/AO-80 composites with the blending ratio of 100/68, it contributed the maximum loss factor and highest modulus. It concluded that there was a suitable proportion of rubber blended with small hindered phenol molecules in the design of damping materials.

Dielectric properties of honey adulterated with sucrose syrup

Sucrose syrup is a common additive in honey adulteration. To provide information for developing a cheap, simple, convenient and rapid sucrose–adulterated honey detector or sucrose content sensor, the permittivities of pure jujube, yellow-locust and milk-vetch flower honey, pure sucrose syrup and honey–sucrose syrup mixtures with sucrose content from 0% (pure honey) to 80% (pure sucrose syrup) were studied from 10 to 4500MHz with open-ended coaxial-line technology and a network analyzer at room temperature. The correlations between permittivities and sucrose contents were regressed. The results showed that the dielectric constants of all samples decreased with increasing frequency, while the pure honey had higher dielectric constant than pure sucrose syrup. Dielectric relaxation existed in all samples. The maximum loss factor decreased with increasing sucrose content. The relaxation frequency changed very little with sucrose content. Strong negative linear correlation, R2>0.98, was found between loss factor around the relaxation frequency and sucrose content.

Research of styrene-butadiene rubber/silicon-aluminum oxides nanotube binary nanocomposites

A novel silicon-aluminum oxides (Si-Al) nanotubes with length ranging from 500 to 1000 nm were introduced to fabricate the styrene-butadiene rubber (SBR)/Si-Al nanotube binary nanocomposites. Scanning electron microscope observation showed the Si-Al nanotubes up to 20 parts per hundred parts of rubber (phr) loading level were dispersed well in SBR matrix. Mechanical properties tests, thermogravimetry analysis and dynamic mechanical thermal analysis revealed that the Si-Al nanotubes have the effects on improving shore A hardness, tensile strength, tear strength, initial decomposition temperature, and storage modulus while lower the maximum loss factor (tan δ) of the SBR/Si-Al nanotube binary nanocomposites. FTIR spectra analysis showed that new SiO bond was generated between the hydroxyl group of Si-Al nanotube and the coupling reagent Si69. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Multi-Objective Optimization Design of Composite I-Beam Embedded with Viscoelastic Layers

Damping capacity and stiffness loss must be considered together in the design of integral damping composite structures. In the present paper, a discrete layer beam finite element is used to model and analyze a damped composite I-beam embedded with viscoelastic layers. Two multi-objective optimization models are developed with maximum natural frequency and modal loss factor. In the first model, only one damping layer is embedded in each flange of the I-beam. Design variables consist of damping layer thickness and its inserting location. In the second model, multiple damping layers of equal thickness are embedded in the flanges. Design variables included the number of damping layers and their inserting locations. Multi-objective genetic algorithm is used to solve optimization problems. It is showed that the analysis method has acceptable accuracy for composite damped I-beams, and it is convenient for optimization design of integral damping composite structures, especially for the cases embedded with multiple damping layers.

Sugar and water contents of honey with dielectric property sensing

The dielectric properties of pure yellow locust, jujube and rape flower honey and their water-adulterated products with water content from 18% to 42.6% were measured with open-ended coaxial-line probe technology and a network analyzer from 10 to 4500 MHz at 25 °C. Dielectric constants of pure honeys and water-added honey samples decreased monotonically with increasing frequency, and increased with increasing water content. Dielectric relaxation was evident in the dielectric loss factors. The critical frequency and the maximum loss factor increased with increasing water content. There were strong linear correlations between the dielectric constant and the total soluble solids and water contents. The linear coefficients of determination were higher than 0.995 from 650 to 960 MHz. The good linear correlations and the sufficient penetration depth >20 mm below 960 MHz, suggest that microwave dielectric properties could be used in developing sensors to determine sugar and water contents.

Influence of particle size and compaction pressure on the magnetic properties of iron-phenolic soft magnetic composites

This paper investigates the effect of particle size and compaction pressure on the magnetic properties of iron-phenolic soft magnetic composites (50 Hz–1000 kHz). The results showed that the optimum amount of phenolic resin to attain maximum permeability and minimum loss factor at 10 kHz is 0.7 wt% for samples containing iron powder with average particle size ∼150 μm compacted at 800 MPa. In accordance with this resin content, at high frequencies (>300 kHz), the sample with lower particle size ∼10 μm exhibits higher magnetic permeability, higher operating frequencies and lower imaginary part of permeability. With increase in the compaction pressure, specific resistivity decreases and imaginary and real parts of permeability increase at low frequencies.

Analysis of Constrained Damping Layers, Including Normal-Strain Effects

A beam partially covered with a constrained damping layer is analyzed. The longitudinal normal strain and shear strain in the viscoelastic layer are considered. Hamilton's principle is used to derive equations of motion and boundary conditions. A sixth-order equation is used to describe the portion of the beam covered with a constrained damping layer. The characteristic equations are solved numerically to determine normalized natural frequency and loss factor values. The loss parameter (normalized loss factor) is shown to be a function of the shear parameter gr; the geometric parameter Y T ; the normalized coverage length L c /L; dimensionless coefficients B 1 , B 2 , and B 3 ; and the core loss factor n 2 .It is shown that traditional constrained-layer damping theory that includes only shearing in the damping layer is inadequate for very small or very large values of the shear parameter. Optimal shear-parameter and coverage-length values are determined for a variety of boundary conditions. Results demonstrate the optimal values for the shear parameter and coverage length to obtain maximum damping levels. Plots are derived to determine the optimal coverage length for any shear-parameter value for maximum loss factor.

Identification of Viscoelastic Fractional Complex Modulus

An examination is made of a graphical method and derived techniques to characterize the fractional complex modulus of simple and complex viscoelastic materials, by a fit of experimental data, as well as from all of the various states of a material, that is, rubbery, transition, and glassy regions, rather than from that limited just to the sole transition domain, a situation that often occurs in materials investigation. Concrete results of some useful materials are illustrated. Nomenclature D β = fractional derivative of order β Einf = inflexion magnitude E(ω) = magnitude of complex modulus E0 = static Young’s modulus E ∗ (ω) = complex modulus E � (ω) = real part of complex modulus E �� (ω) = imaginary part of complex modulus j 2 = −1 s = Laplace variable t = time z1, z2 = complex numbers (model parameters) α, β, a, b, c = model parameters (real numbers) � =g amma function e(t) = strain e ∗ (ω) =F ourier transform of e(t) ηmax = maximum loss factor

Vitrification and dielectric relaxation during the isothermal curing of an epoxy–amine resin

The isothermal curing of an epoxy resin based on diglycidyl ether of bisphenol A (DGEBA) with a diamine based on 4,4′-diamino-3,3′-dimethyldicyclohexylmethane (3DCM) was analysed by dielectric relaxation spectroscopy (DRS), conventional differential scanning calorimetry (DSC) and temperature modulated DSC (TMDSC). The chemical kinetics corresponds to an autocatalytic model with an apparent activation energy of 58 kJ mol −1. The vitrification was analysed by TMDSC, between 40 and 140 °C, using the modulus of the complex heat capacity, |C p ∗|. A mobility factor based on the evolution of |C p ∗| was used to study the reaction step controlled by diffusion. The permittivity and loss factor were measured by DRS as a function of time in the frequency range between 10 Hz and 100 kHz. The dipolar relaxation, analysed by the peak of the maximum loss factor, was correlated with the vitrification determined by TMDSC. The analysis of the logarithm of the frequency against the conversion degree allows the characterisation of the molecular dynamics of the crosslinking reaction up until the vitrification of the system.

Studies on damping characteristics and parameter optimization of anisotropic laminated damped structure

An anisotropic design is introduced to the laminated damped plates in this paper. The parameter effects on the loss factor of anisotropic laminated damped plates have been analyzed in detail. The damping analyses and control mechanism of laminated anisotropic damped plates have been carried out theoretically. Finally, through the software developed here, the parameter optimization has been conducted on the loss factors of the anisotropic laminated damped plates. The results indicate it may provide scientific basis for the new optimization anisotropic design of laminated damped plates used in Aircraft cabin structure for obtaining the maximum loss factor.

Constrained polymer layers to reduce noise: reality or fiction?—An experimental inquiry into their effectiveness

The frequency and temperature dependent noise radiation properties of constrained polymer layered oil pans are examined through mobility and intensity measurements. Four metal/polymer/metal sandwich composites of varied thermo-plastic elastomer systems of polystyrene–polybutadiene–polystyrene triblock copolymers are investigated within a wide frequency range covering 1000–5000 Hz, and over a wide temperature range covering 20–100 °C, with results compared to those of an ordinary steel oil pan. The mobility and intensity are found to be strongly frequency and temperature dependent, displaying a substantial mobility reduction as compared to that of the ordinary pan, while using the constrained layer damping configurations at their maximum loss factor temperatures. However, the reduction of noise radiation is smaller than that of the mobility at those temperatures, mainly due to the increased radiation efficiency while adding damping materials.

Geometry and surface treatment dependence of the light collection from LSO crystals

We study the relative light collection efficiency for narrow LSO crystals as a function of surface finish and geometry. We explore both a specular and diffuse surface reflector finish, using LSO crystals that are either polished or etched. The crystals have a square cross-section with widths of 1.8, 2.2, 2.5, or 2.6 mm and lengths of 10, 20 or 30 mm. When optically coupled to a PMT on a square end and wrapped with Teflon on 5 sides, we excite them at 5 mm incremental depths with 511 keV photons and measure the photopeak position. The light collection is characterized by a maximum output (based on the photopeak position when excited at the PMT end) and a depth-dependent loss factor. Both the maximum output and loss factor are effectively independent of width, and the maximum output is only weakly dependent on length (6696±612, 5796±432, and 5328±288 photons for 10, 20, and 30 mm lengths). The loss factor is effectively independent of length, with a 0, 18, 27, and 22% reduction at excitation depths of 0, 10, 20, and 30 mm. The light collection is only weakly dependent on surface finish if it is polished or etched beyond a minimum time.

A Study of Viscoelastic Damped Sandwich Disk Vibration.

Vibration analysis of the viscoelastic damped sandwich disk is studied. Analytical results are as follows. (1) Analytical method of natural frequency coupled with loss factor for the sandwich disk is presented. (2) Loss factor of the sandwich disk is the function of parameters which arc elasticity, damping and thickness of the viscoelastic layer. And, maximum loss factor is obtained using suitable value of these parameters. (3) Natural frequencies coupled with loss factor are higher than the case of without loss factor. Especially, this tendency is remarkable at maximum loss factor.

Polystyrene-glass bead composites: Maxwell-Wagner-sillars relaxations and percolation

Dielectric spectrometry experiments are performed on a series of polystyrene-glass bead composites with volume filler content from 0 to 50% and with three particle diameters ( 5μm, 20 μm, and 90 μm) in order to study the Maxwell-Wagner-Sillars (MWS) relaxations and the percolation phenomena. In the high-temperature region (130 to 220°C ), the experimental data give evidence of MWS relaxations for all the composite systems, whatever the bead size and the filler content are. A good agreement is found between the experimental values of the maximum loss factor frequency and the theoretical ones drawn from the van Beek formula, especially for low contents. A percolation phenomenon is shown in the low-temperature region (40 to 120°C for high-content/low-size composites. The percolation threshold, determined by considering the critical interparticle distance, is below 15.0% for the 5 μm glass bead composites and above 47.3% for the 90 μm composites; it lies between 20.5 and 28.6% for the 20 μm composites. Two schematic models, based on a distribution of the sizes and on a random dispersion of the beads, are developed to show how MWS and percolation phenomena can both be observed for the high-content/low-size composites.

Maxwell–Wagner–Sillars relaxations in polystyrene–glass-bead composites

The Maxwell–Wagner–Sillars (MWS) relaxation is studied for glass-bead–polystyrene (PS) composites having compositions from 0% to ∼50% in volume, in the range 20 Hz–1 MHz and for temperatures varying from room temperature to 280 °C. For the PS matrix, the complex permittivities and ac conductivities are within the limits of 3.3–3.7 and 2–3×10−9 Ω−1 cm−1, respectively, at 1 kHz in a 120–180 °C temperature interval. For the glass, these parameters vary between 20 and 300 for the complex permittivity, and between 9×10−9 and 4×10−8 Ω−1 cm−1 for the ac conductivity, in the same conditions. Good agreement is found between the calculated values of the maximum loss factor frequencies and the experimental ones. The relaxation found in the composite at temperatures above the α relaxation of the PS is ascribed to the trapping of conductive carriers at the interface between the glass spheres and the polymer matrix. This MWS relaxation is showed to have an activation energy of 20 kcal mol−1 and a relaxation time of 10−13.6 s. From the Argand representations it is observed that the MWS phenomenum deviates from a simple Debye-like process for composites having glass volume fractions from 12.5% upward.