Maximum Loss Factor Research Articles

Optimum Design of an Unconstrained Viscoelastic Damping Layer under Consideration of Some Modes.

The optimum configuration of the composite plate covered with an unconstrained viscoelastic damping layer is discussed from the viewpoint of the modal loss factor. When the configuration of a damping layer is optimized to an arbitrary mode, it's modal loss factor becomes maximum. In general, however, loss factors of the other modes are much lower than those obtained by optimization to each mode. Therefore, in this study, the optimum configuration of a damping layer is investigated under consideration of modal loss factor to some modes. The optimum distribution of the damping layer is obtained by sequentially changing the position of a section of the layer to another position to optimize the composite modal loss factor. Results are compared with the modal loss factors of (1, 1), (1, 2) and (1, 3) modes, which are optimized to their individual modes. These results indicate that although the maximum loss factor is decreased by 2∼8% compared to those optimized only to each mode, those of the other modes could be increased by 5∼23%. The results are validated by suitable experimental results.

Study of Dynamic Behaviour of Viscoelastic Sandwich Materials. 4th Report. Guideline of Shear Modulus for Viscoelastic Resin.

Characteristics of viscoelastic resin for a vibration damping composite steel sheet (VDCS) were studied numerically using the Ross-Kerwin-Ungar model. The following three conclusions were obtained : i ) magnitude of shear modulus of the resin determines frequency where the VDCS shows the maximum loss factor ; ii ) although there is a limitation of loss factor, the magnitude of loss factor is proportional to tangential loss of the resin ; and iii) loss factor is independent of frequency if the shear modulus of the resin is proportional to frequency. Characteristics of an actual resin for VDCS were shown to agree with the calculated results. The same trends were observed for the calculated results as for the characteristics of the actual resin. Therefore, the results obtained might be useful in the developement of new resin for VDCS. The results obtained are also useful for understanding the behavior of loss factor in terms of frequency dependence and temperature dependence.

Fabrication and damping capacity of CuZnAl matrix composites processed by powder metallurgy route

Cu-26.5Zn-4Al (wt.%) alloy (as a matrix) and each of three different Fe-based ferromagnetic alloy flakes (as a reinforcing material) were processed into three different composites via conventional cold compaction; this was followed by hot isostatic pressing. The sliced sheets of the composites were heat-treated at 1073 K and quenched into ice water to introduce a martensitic structure. The damping capacity and the storage modulus were measured for three different composites as functions of strain amplitude and frequency. The microstructure of the composites was characterized by use of optical microscopy, scanning electron microscopy and scanning transmission electron microscopy in order to examine the martensite, the flake morphologies and the interfaces. In all three composites, the loss factor increased from 0.02 (with a strain of f100 × 10 −6) to approximately 0.05 (with a strain of 300 × 10 −6). In particular, the FeCr flakes/CuZnAl composites exhibited a maximum loss factor near a strain of 165 × 10 −6 , owing to the damping of the FeCr flakes.

Vibration damping with urethane/acrylate simultaneous semi‐interpenetrating polymer networks

AbstractThe vibration damping efficiency of the IPN‐laminated steel sheet, which consisted of a viscoelastic IPN layer sandwiched between two steel sheets, was investigated in this study. The simultaneous semi‐IPN used included an elastomeric urethane phase and a glassy acrylate phase. This study seeks to develop a laminate, with broader damping temperature and frequency ranges, in contrast to the homopolymer‐based laminates studied previously. A vibration damping analysis of the neat IPNs was first conducted using a dynamic rheometer in order to provide basic rheological properties of the neat IPNs. This was followed by the frequency spectrum analysis of the IPN‐based laminates, using a frequency analyzer, utilizing the results derived from the damping analysis of the neat IPNs. The IPN variables studied included the reaction temperature, the amount of the catalyst for urethane phase, the composition in acrylate phase and in urethane phase, and the composition of IPN. The results indicated that, by properly adjusting the IPN parameters, the extent of phase separation in IPN could be controlled. The effect of the network formation in the catalyzed urethane phase on the damping properties of IPNs was also investigated and the possible reaction mechanism was analyzed. The IPNs with catalyzed urethane phase showed single, smooth damping curves with peak values of tan δ = 0.4–0.7 in a broad temperature range. The study was then extended to the analysis of the vibration damping efficiency of the IPN‐based laminated, including the effect of IPN composition, the effect of the urethane composition in IPN, and the effect of the acrylate composition in IPN. The results indicated that the IPN‐based laminates yielded a maximum loss factor in the range of 0.1–0.5, which was below the tan δ value of IPN, but was better than that of the neat steel sheet. In addition, most of the damping properties of the laminates could be derived or predicted from the dynamic rheological properties of the neat IPNs. Thus, knowing the basic dynamic rheological properties of the neat IPNs is vital for a successful design and application of the IPN‐laminated steel sheet. © 1992 John Wiley & Sons, Inc.

ブチルアクリレート含有ポリマーをコア材としたラミネーテッド鋼板の制振特性

In general, plastic sheet displays vibration-damping by converting vibration energy into thermal energy. Laminated steel plates were prepared by putting a plastic sheet between two steel plates. The extent of vibration-damping of the laminated steel plate was evaluated for two types of plastics by measuring the loss factor.The resins investigated were acrylonitrile (A)-styrene (S)-butyl acrylate (B) terpolymer and methyl methacrylate (M)-butyl acrylate (B) copolymer. We prepared eight kinds of specimens having different butyl acrylate contents. A cantilever method was adopted for obtaining frequency response spectra, from which the loss factor was derived according to ASTM-E756.Laminated steel plates with AS-B terpolymer gave the maximum loss factor at temperatures above 100°C. The factor was as high as 0.5 at 40°C for the plate prepared from the M-B copolymer having butyl acrylate of 54mol%. The plates with M-B copolymer are expected to be very useful for vibration-damping near room temperature.

ブチルアクリレート含有ポリマーの制振性評価

In general, a plastic sheet displays vibration-damping by converting vibration energy into thermal energy. In this study, the vibration-damping for copolymers including butyl acrylate was evaluated.Copolymer of butyl acrylate (B) grafted onto acrylonitrile (A)-styrene (S) copolymers and methyl methacrylate (M)-butyl acrylate (B) random copolymer were used to prepare eight kinds of specimens having different butyl acrylate contents. A cantilever method was adopted for obtaining frequency response spectra of the specimens. The loss factor of laminated steel plates was also obtained. The loss factor and shear modulus were calculated for copolymers from that of the laminated steel plates.AS-B graft copolymers seemed to give a maximum loss factor at temperatures above 120°C. Therefore the loss factor at room temperature is not sufficiently large. The loss factor for the M-B copolymer having butyl acrylate of 54 mol% was 2.0 in the frequency range from 1Hz to 1kHz at 40°C. Therefore it is expected that M-B copolymer is very useful for vibration-damping at around room temperature.

Effect of the textural characteristics of the new silicas on the dynamic properties of styrene‐butadiene rubber (SBR) vulcanizates

AbstractIt is possible to obtain silicas with different textural characteristics from natural silicates by means of an acid treatment, where the textural characteristics of the new silicas obtained are greatly influenced by the reaction conditions. The mechanodynamical behavior of compounds filled with these silicas and based on Styrenebutadiene rubber (SBR) matrices was studied. The influence of the textural characteristics on dynamic properties is explained in terms of the stiffness, porosity, and structure of the silica particles. Silicas obtained at drastic reaction conditions yield compounds with a higher storage modulus, E′, at low strain amplitudes, but with a lower storage modulus at high strain amplitudes. The maximum loss factor, tanδ, is a function of the silica external surface area.

Analysis of a damped pneumatic spring

The complex dynamic stiffness of a damped spring is determined. The damping is produced by transient pressure feedback from an auxiliary tank connected by a capillary to the spring cylinder. From the complex stiffness, the damping and stiffness are determined as functions of excitation frequency. The behavior of a compound spring, consisting of a damped pneumatic spring in parallel with a stiffer linear spring, is also examined. The analysis shows that the damping loss factor depends only on the tank/cylinder volume ratio, and that the capillary dimensions affect only the frequency at which maximum damping occurs. The compound spring is shown to have a maximum loss factor which quickly reaches an asymptotic value as the tank/cylinder volume ratio increases. From this presentation a clearer understanding of the behavior of a damped air spring, and a better sense of how design parameters affect the component's characteristics are obtained.

Upper bound to coupling loss factor for coupling via a generalized point coupling

In Statistical Energy Analysis (SEA) the coupling loss factor equals the power of energy flux out of one subsystem into another subsystem coupled to it, nondimensionalized by the product of angular frequency and energy stored in the source subsystem. “Generalized point coupling” indicates any coupling mechanism whose dynamic displacement can be characterized by a single generalized coordinate, in the sense of classical mechanics. Without any other specification of the coupling, an upper bound is found for the sum of power dissipated in the coupling, if any, and power delivered to the other subsystem. The maximum loss factor is given by nmax−1 = 2πωn(ω = 2πfn(f), where ω = 2πf, f is frequency in Hz, and n(f) = 2πn(ω) is the modal density of the source subsystem— i.e., the density in f of modal resonance frequencies. The formula for nmax−1 equals 27.3 times the number of resonances in a tenth‐decade (⅓‐octave) hand. The upper bound is achieved in the case of two parallel thin plates of the same thickness, connected by a rigid, massless, point connection.

Frequencies and Loss Factors of Multicored Sandwich Beams

The sandwich beam analyzed in the present paper consists of layers of elastic and viscoelastic material of arbitrary thickness and material. No restrictive assumptions are made on the bending and shear rigidities of the cores. Higher-order effects like rotatory inertia, bending, and extension of the core, which were ignored in previous theories, are included in the equations of motion presented herein. Exact equations for finding resonant frequencies and loss factors are given for simply-supported beams, while for other boundary conditions, these quantities are computed by variational method. Analysis of numerical results indicates that unsymmetricizing the face layers is superior to unsymmetricizing the core layers. It also showed that uniformly high damping over a wide frequency range can be obtained only by the use of stiff cores, but this is followed by a reduction in the maximum loss factor.

Transverse vibrations of pre-twisted sandwich beams

A set of equations of motion governing the bending and extensional displacements of a pre-twisted sandwich beam of rectangular cross-section are derived by using Hamilton's principle. The middle viscoelastic core is assumed to deform mainly through the classical shearing mechanism. The eigenvalues and loss factors of simply supported pre-twisted sandwich beams are computed by using the variational method. Analysis of the results revealed that pre-twisting the beam increases the real part of the eigenvalue by as much as 20% while reducing the loss factor by as much as 30 %. The loss factor of very soft, thickcored beams is especially sensitive to even small angles of pre-twist: e.g., a 22· 5° pre-twist may reduce the loss factor by as much as 80%. The effect of pre-twist is, however, shown not to be appreciable for soft, thin-cored beams. In any case, pre-twisting of the beam has a detrimental effect on the maximum loss factor that one can obtain for a specific size of the beam when only the shear parameter of the beam is changed.

Investigation of the interaction of bis-phenols with tertiary amines under conditions of low-temperature polycondensation

(3) It has been shown that the static dielectric permeability and the maximum loss factor in the PPG oligomers investigated decreases in inverse proportion to the degree of polymerization. (4) It has been established that the activation energy for the dipole relaxation processes in solutions of PPG in toluene decreases with dilution from 22.5 to 8-0 keal/mole, the corresponding figures for ED-5 being 39.5 and 8.0 keal/mole. It has been suggested that the observed decrease in the activation energy for dipole relaxation is caused in the substances investigated by a decrease in the energy of intermoleeular interactions.

A theoretical analysis of the mechanical relaxation of single-crystalline ice

Kneser, Magun & Ziegler (1955) have found a mechanical relaxation of single crystals of ice. Torsional vibrations of cylindrical specimens, cut parallel to the c -axis, were employed and the logarithmic decrement showed the characteristic maximum associated with a single relaxation time. Similar results have since beer obtained by Schiller (yet unpublished) for various modes of vibration and various crystallographic orientations. The frequency for maximum loss factor and the energy of activation are approximately equal for the mechanical and dielectric relaxation. It seems obvious to associate both relaxations with movements of the hydrogen atoms. In the mechanical case, this may be done in two different ways. As a first possibility I have assumed that an equilibrium exists between a large number of possible hydrogen arrangements and that this equilibrium is disturbed by and mechanical deformation of the crystal lattice. The rearrangement of the hydrogen atoms throughout the lattice then gives rise to the observed relaxation. A second possible mechanism is connected with the distribution of lattice defects such as doubly occupied and vacant bonds between neighbouring oxygen atoms. Normally the probability of finding a given type of defect on a given bond would be approxi­mately the same for all bonds. In the deformed lattice, bonds with a certain orientation would be preferred and the resulting rearrangement of the defects would cause the observed relaxation. With the first mechanism, lattice defects can serve as catalysts in bringing about configurational changes and their presence (in small numbers) will thus affect the relaxation time, but not the magnitude of the decrement. With the second mechanism, however, the magnitude of the decrement is proportional to the number of defects present. I have calculated the maximum value of the decrement for the first mechanism, which implies a general rearrange­ment of the hydrogen atoms, and shall show that the result agrees well with the measurements. On the other hand, estimates based on the second mechanism are clearly inconsistent with the experimental evidence.

DIELECTRIC RELAXATION IN CELLULOSE CONTAINING SORBED VAPORS

The dielectric constant and dielectric loss factor were measured in a dispersion region for a paper of high cellulose content. The complex arrangement of the paper in the measuring condenser did not effectively alter the position of the dispersion region of the paper itself, as shown by electrical analysis. From this analysis equations were derived from which the dielectric constant and maximum dielectric loss factor of the cellulose fiber were evaluated for varying amounts of sorbed water, methanol, and ethanol. The effect of each of these vapors on the position of the dispersion region was studied, measurements being performed over a range of frequency of 10 to 1000 kc.p.s., and a range of temperature of −58 to 26 °C. A typical plasticizing action was observed in all three cases. This was confirmed from an analysis of the data using the theory of absolute reaction rates.