Viscoelasticity of Rubber

1952 ◽  
Vol 25 (3) ◽  
pp. 490-499
Author(s):  
Robert B. Blizard
Keyword(s):  
Shear Modulus ◽  
General Expression ◽  
Viscoelastic Behavior ◽  
Viscous Medium ◽  
Modulus Function ◽  
Cross Linking ◽  
Frequency Range ◽  
Frequency Curve ◽  
Low Frequencies ◽  
Single Section

Abstract A theory has been obtained for the viscoelastic behavior of rubber in the frequency range above that at which creep is important and below that at which it behaves like a hard solid. The rubber chains are treated as springs in a viscous medium, and a general expression is obtained for the contribution to modulus of a single section of chain as a function of its length and terminations. A statistical estimate is made of the number of chain segments having given length and terminations. A modulus function is found for the group of chains with each kind of termination, and these are added in the proper amounts to give the form of the modulus vs. frequency curve for any amount of cross-linking. Measurements of shear modulus were made on one apparatus at frequencies between 0.0125 and 750 cps. Agreement is good if a pure viscosity is added to the theory. However, at low frequencies the imaginary part of modulus does not decrease as much as predicted.

Apparatus for the Measurement of the Dynamic Shear Modulus and Hysteresis of Rubber at Low Frequencies

1953 ◽  
Vol 26 (1) ◽  
pp. 181-187 ◽  
Author(s):  
W. P. Fletcher ◽  
A. N. Gent
Keyword(s):  
Shear Modulus ◽  
Simple Shear ◽  
Test Piece ◽  
Dynamic Shear Modulus ◽  
Dynamic Shear ◽  
Frequency Range ◽  
Low Frequencies ◽  
Mechanical Hysteresis ◽  
Cathode Ray Tube ◽  
Instantaneous Values

Abstract An apparatus is described which subjects a rubber test-piece to a force in simple shear, varying sinusoidally with time in the frequency range of 0.0017– 17 c/s, the instantaneous values of force and displacement being measured by photoelectric pickups. From the display on the screen of a cathode-ray tube of the mechanical hysteresis loop described by the vibrating rubber, measurements are made which make possible calculation of the dynamic shear modulus and hysteresis. Typical results are given.

A waveform inversion technique for measuring elastic wave attenuation in cylindrical bars

Geophysics ◽  
1992 ◽  
Vol 57 (6) ◽  
pp. 854-859 ◽  
Author(s):  
Xiao Ming Tang
Keyword(s):  
Elastic Wave ◽  
Wave Attenuation ◽  
Waveform Inversion ◽  
Finite Size ◽  
Low Frequency ◽  
Frequency Range ◽  
Multiple Reflections ◽  
Low Frequencies ◽  
The Time Domain ◽  
Attenuation Values

A new technique for measuring elastic wave attenuation in the frequency range of 10–150 kHz consists of measuring low‐frequency waveforms using two cylindrical bars of the same material but of different lengths. The attenuation is obtained through two steps. In the first, the waveform measured within the shorter bar is propagated to the length of the longer bar, and the distortion of the waveform due to the dispersion effect of the cylindrical waveguide is compensated. The second step is the inversion for the attenuation or Q of the bar material by minimizing the difference between the waveform propagated from the shorter bar and the waveform measured within the longer bar. The waveform inversion is performed in the time domain, and the waveforms can be appropriately truncated to avoid multiple reflections due to the finite size of the (shorter) sample, allowing attenuation to be measured at long wavelengths or low frequencies. The frequency range in which this technique operates fills the gap between the resonant bar measurement (∼10 kHz) and ultrasonic measurement (∼100–1000 kHz). By using the technique, attenuation values in a PVC (a highly attenuative) material and in Sierra White granite were measured in the frequency range of 40–140 kHz. The obtained attenuation values for the two materials are found to be reliable and consistent.

Dynamic Viscoelastic Properties of SBS Modified Asphalt Based on DSR Testing

2012 ◽  
Vol 598 ◽  
pp. 473-476 ◽  
Author(s):  
Yong Mei Guo ◽  
Wei Chen
Keyword(s):  
Complex Modulus ◽  
Superposition Principle ◽  
Asphalt Binder ◽  
Asphalt Binders ◽  
Frequency Range ◽  
Master Curves ◽  
Temperature Property ◽  
Low Frequencies ◽  
High Temperature Property ◽  
Frequency Sweeps

Five SBS modified asphalts and one base asphalt were selected to carry out frequency sweeps over a wider frequency range using the dynamic shear rheometer (DSR). Six asphalt binders were subjected to sinusoidal loading at 30°C-90°C within the linear viscoelastic limits, and master curves of complex modulus (G*) and phase angle (δ) could be constructed by means of the time-temperature superposition principle (TTSP). The results show that the G* values of SBS modified asphalts are significantly greater than those of base asphalt at low frequencies, but are slightly smaller at high frequencies. Compared with the base asphalt, SBS modified asphalts have narrower master curves of complex modulus, and their phase angles are much smaller within the whole frequency range. This indicates that various properties of SBS modified asphalts, such as high-temperature property, low-temperature property, temperature susceptibility and elastic recoverability, are superior to those of the base asphalt. The G* values of the rolling thin-film oven (RTFO) aged asphalt are larger than those of the unaged asphalt in the whole range of frequencies, demonstrating that the anti-rutting performance of asphalt binder is improved after short-term aging.

A Variable Stiffness Vibration Isolation System Based on Magneto-Rheological Elastomer

2012 ◽  
Vol 452-453 ◽  
pp. 659-662
Author(s):  
Wei Wang ◽  
Yi Min Deng
Keyword(s):  
Shear Modulus ◽  
Vibration Isolation ◽  
Variable Stiffness ◽  
Control Area ◽  
Frequency Range ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Vibration Isolators ◽  
Magneto Rheological ◽  
Conventional Type

Vibration isolation is a most widely used vibration protection method.The stiffness of vibration isolators in existing conventional type of vibration isolation system is usually of fixed value. This limits the system in exhibiting its vibration isolation effect in that, it has poor results for lower frequency vibration, especially for resonance frequency. Magneto-rheological elastomer is a new branch of Magneto-rheological materials. It’s an intelligent materials in that it’s shear modulus can be controlled by a magnetic field. It has wide application prospects in the vibration control area. This paper proposes using adjustable stiffness of magneto-rheological elastomer vibration isolation in vibration isolation system. By changing the current of vibration isolators coil to control the shear modulus of magneto-rheological elastomer, it can adjust the stiffness of the isolation system, making the system obtain wider vibration isolation frequency range. By exploying SimuLink software to analyze the vibration isolation system, it is found that such a design is effective and applicable.

Optimally Sensitive and Efficient Compact Loudspeakers for Low Audio Frequencies

2007 ◽  
Vol 38 (7) ◽  
pp. 11-17
Author(s):  
Ronald M. Aarts
Keyword(s):  
Optimality Criterion ◽  
Low Frequency ◽  
Audio Signal ◽  
Design Procedure ◽  
Frequency Range ◽  
Force Factor ◽  
Low Frequencies ◽  
Limited Frequency ◽  
The Cost ◽  
Higher Sensitivity

Conventionally, the ultimate goal in loudspeaker design has been to obtain a flat frequency response over a specified frequency range. This can be achieved by carefully selecting the main loudspeaker parameters such as the enclosure volume, the cone diameter, the moving mass and the very crucial “force factor”. For loudspeakers in small cabinets the results of this design procedure appear to be quite inefficient, especially at low frequencies. This paper describes a new solution to this problem. It consists of the combination of a highly non-linear preprocessing of the audio signal and the use of a so called low-force-factor loudspeaker. This combination yields a strongly increased efficiency, at least over a limited frequency range, at the cost of a somewhat altered sound quality. An analytically tractable optimality criterion has been defined and has been verified by the design of an experimental loudspeaker. This has a much higher efficiency and a higher sensitivity than current low-frequency loudspeakers, while its cabinet can be much smaller.

Application of bandlimited anelastic models to wave propagation in highly attenuative media

1995 ◽  
Vol 85 (5) ◽  
pp. 1359-1372
Author(s):  
Hsi-Ping Liu
Keyword(s):  
Wave Propagation ◽  
Quality Factor ◽  
Lower Limit ◽  
Relaxation Function ◽  
Function Approach ◽  
Creep Function ◽  
Frequency Range ◽  
Quality Factors ◽  
Low Frequencies ◽  
Near Surface

Abstract Because of its simple form, a bandlimited, four-parameter anelastic model that yields nearly constant midband Q for low-loss materials is often used for calculating synthetic seismograms. The four parameters used in the literature to characterize anelastic behavior are τ1, τ2, Qm, and MR in the relaxation-function approach (s1 = 1/τ1 and s2 = 1/τ2 are angular frequencies defining the bandwidth, MR is the relaxed modulus, and Qm is approximately the midband quality factor when Qm ≫ 1); or τ1, τ2, Qm, and MR in the creep-function approach (s1 = 1/τ1 and s2 = 1/τ2 are angular frequencies defining the bandwidth, and Qm is approximately the midband quality factor when Qm ≫ 1). In practice, it is often the case that, for a particular medium, the quality factor Q(ω0) and phase velocity c(ω0) at an angular frequency ω0 (s1 < ω0 < s2; s1 < ω0 < s2) are known from field measurements. If values are assigned to τ1 and τ2 (τ2 < τ1), or to τ1 and τ2 (τ2 < τ1), then the two remaining parameters, Qm and MR, or Qm and MR, can be obtained from Q(ω0). However, for highly attenuative media, e.g., Q(ω0) ≦ 5, Q(ω) can become highly skewed and negative at low frequencies (for the relaxation-function approach) or at high frequencies (for the creep-function approach) if this procedure is followed. A negative Q(ω) is unacceptable because it implies an increase in energy for waves propagating in a homogeneous and attenuative medium. This article shows that given (τ1, τ2, ω0) or (τ1, τ2, ω0), a lower limit of Q(ω0) exists for a bandlimited, four-parameter anelastic model. In the relaxation-function approach, the minimum permissible Q(ω0) is given by ln [(1 + ω20τ21)/(1 + ω20τ22)]/{2 arctan [ω0(τ1 − τ2)/(1 + ω20τ1τ2)]}. In the creep-function approach, the minimum permissible Q(ω0) is given by {2 ln (τ1/τ2) − ln [(1 + ω20τ21)/(1 + ω20τ22)]}/{2 arctan [ω0(τ1 − τ2)/(1 + ω20τ1τ2)]}. The more general statement that, for a given set of relaxation mechanisms, a lower limit exists for Q(ω0) is also shown to hold. Because a nearly constant midband Q cannot be achieved for highly attenuative media using a four-parameter anelastic model, a bandlimited, six-parameter anelastic model that yields a nearly constant midband Q for such media is devised; an expression for the minimum permissible Q(ω0) is given. Six-parameter anelastic models with quality factors Q ∼ 5 and Q ∼ 16, constant to 6% over the frequency range 0.5 to 200 Hz, illustrate this result. In conformity with field observations that Q(ω) for near-surface earth materials is approximately constant over a wide frequency range, the bandlimited, six-parameter anelastic models are suitable for modeling wave propagation in highly attenuative media for bandlimited time functions in engineering and exploration seismology.

scholarly journals THE PECULIARITIES OF THE SOUND FIELD ENERGY DECAY IN A ROOM WITH THE USE OF DIFFERENT PULSED SOUND SOURCES/GARSO LAUKO ENERGIJOS SLOPIMO PATALPOJE YPATUMAI, NAUDOJANT SKIRTINGUS IMPULSINIUS GARSO ŠALTINIUS

1999 ◽  
Vol 5 (2) ◽  
pp. 135-140
Author(s):  
Vytautas Stauskis
Keyword(s):  
Noise Level ◽  
Sound Field ◽  
Maximum Energy ◽  
Reverberation Time ◽  
Frequency Range ◽  
Sound Sources ◽  
Low Frequencies ◽  
High Frequencies ◽  
The Difference ◽  
Field Decay

The paper deals with the differences between the energy created by four different pulsed sound sources, ie a sound gun, a start gun, a toy gun, and a hunting gun. A knowledge of the differences between the maximum energy and the minimum energy, or the signal-noise ratio, is necessary to correctly calculate the frequency dependence of reverberation time. It has been established by investigations that the maximum energy excited by the sound gun is within the frequency range of 250 to 2000 Hz. It decreases by about 28 dB at the low frequencies. The character of change in the energy created by the hunting gun differs from that of the sound gun. There is no change in the maximum energy within the frequency range of 63–100 Hz, whereas afterwards it increases with the increase in frequency but only to the limit of 2000 Hz. In the frequency range of 63–500 Hz, the energy excited by the hunting gun is lower by 15–30 dB than that of the sound gun. As frequency increases the difference is reduced and amounts to 5–10 dB. The maximum energy of the start gun is lower by 4–5 dB than that of the hunting gun in the frequency range of up to 1000 Hz, while afterwards the difference is insignificant. In the frequency range of 125–250 Hz, the maximum energy generated by the sound gun exceeds that generated by the hunting gun by 20 dB, that by the start gun by 25 dB, and that by the toy gun—by as much as 35 dB. The maximum energy emitted by it occupies a wide frequency range of 250 to 2000 Hz. Thus, the sound gun has an advantage over the other three sound sources from the point of view of maximum energy. Up until 500 Hz the character of change in the direct sound energy is similar for all types of sources. The maximum energy of direct sound is also created by the sound gun and it increases along with frequency, the maximum values being reached at 500 Hz and 1000 Hz. The maximum energy of the hunting gun in the frequency range of 125—500 Hz is lower by about 20 dB than that of the sound gun, while the maximum energy of the toy gun is lower by about 25 dB. The maximum of the direct sound energy generated by the hunting gun, the start gun and the toy gun is found at high frequencies, ie at 1000 Hz and 2000 Hz, while the sound gun generates the maximum energy at 500 Hz and 1000 Hz. Thus, the best results are obtained when the energy is emitted by the sound gun. When the sound field is generated by the sound gun, the difference between the maximum energy and the noise level is about 35 dB at 63 Hz, while the use of the hunting gun reduces the difference to about 20–22 dB. The start gun emits only small quantities of low frequencies and is not suitable for room's acoustical analysis at 63 Hz. At the frequency of 80 Hz, the difference between the maximum energy and the noise level makes up about 50 dB, when the sound field is generated by the sound gun, and about 27 dB, when it is generated by the hunting gun. When the start gun is used, the difference between the maximum signal and the noise level is as small as 20 dB, which is not sufficient to make a reverberation time analysis correctly. At the frequency of 100 Hz, the difference of about 55 dB between the maximum energy and the noise level is only achieved by the sound gun. The hunting gun, the start gun and the toy gun create the decrease of about 25 dB, which is not sufficient for the calculation of the reverberation time. At the frequency of 125 Hz, a sufficiently large difference in the sound field decay amounting to about 40 dB is created by the sound gun, the hunting gun and the start gun, though the character of the sound field curve decay of the latter is different from the former two. At 250 Hz, the sound gun produces a field decay difference of almost 60 dB, the hunting gun almost 50 dB, the start gun almost 40 dB, and the toy gun about 45 dB. At 500 Hz, the sound field decay is sufficient when any of the four sound sources is used. The energy difference created by the sound gun is as large as 70 dB, by the hunting gun 50 dB, by the start gun 52 dB, and by the toy gun 48 dB. Such energy differences are sufficient for the analysis of acoustic indicators. At the high frequencies of 1000 to 4000 Hz, all the four sound sources used, even the toy gun, produce a good difference of the sound field decay and in all cases it is possible to analyse the reverberation process at varied intervals of the sound level decay.

Dynamic and creep analysis of polyvinyl alcohol based films blended with starch and protein

2018 ◽  
Vol 39 (1) ◽  
pp. 35-47 ◽  
Author(s):  
Naman Jain ◽  
Vinay K. Singh ◽  
Sakshi Chauhan
Keyword(s):  
Polyvinyl Alcohol ◽  
Moisture Absorption ◽  
Viscoelastic Behavior ◽  
Mechanical Analysis ◽  
Cross Linking ◽  
Mechanical And Thermal Properties ◽  
Blend Films ◽  
Creep And Recovery ◽  
Degradation Temperature ◽  
Creep Analysis

Abstract The present study focuses on the fabrication and analyses of polyvinyl alcohol (PVA) based films blended with polymers, such as starch and protein. The aim is to improve the moisture absorption, solubility, mechanical and thermal properties of PVA by blending it with various polymers. The thermal cross-linking of the films has been studied by heating the films at 120°C for 4 h. The result shows that PVA was completely soluble in water, while post-blending solubility and moisture absorption of blended films decreased. The tensile strength of blended films was significantly higher (4%–29%) as compared to neat PVA, while thermally cross-linked films showed much higher strength (8%–174%). Blended films were characterized using Fourier transform infrared spectroscopy (FTIR) to confirm the formation of hydrogen bonds. Thermogravimetric analysis showed the increase in degradation temperature post-blending as compared to neat PVA. The viscoelastic behavior of the material as well as glass transition temperature was studied using dynamic mechanical analysis. Creep and recovery behavior were examined to study the effect of stress and temperature on creep strain. The biodegradability of the blended films was increased post-blending. This study showed that PVA based blend films can replace non-biodegradable plastics and hence are necessary for the development of environmentally friendly materials.

Spectra of quarry blasts and microearthquakes recorded at local distances in Israel

1993 ◽  
Vol 83 (6) ◽  
pp. 1799-1812
Author(s):  
Yefim Gitterman ◽  
Torild van Eck
Keyword(s):  
Time Delays ◽  
Spectral Characteristics ◽  
Open Pit ◽  
Frequency Range ◽  
Simple Method ◽  
Low Frequencies ◽  
Event Identification ◽  
Routine Basis ◽  
Seismograph Network ◽  
Discrimination Method

Abstract In northern Israel, quarry blasts and microearthquakes occur in a region with complicated tectonics. Therefore correct event identification, preferably based on a simple method that can be applied on a routine basis, is essential for accurate and detailed seismotectonic studies. Spectral analysis of quarry blasts and microearthquakes recorded at local distances (5 < Δ < 2000 km) by stations of the Israel Seismograph Network revealed spectral characteristics in the frequency range less than 12.5 Hz that can be used routinely for event identification. Most quarry blasts in northern Israel are ripple-fired, open pit blasts, consequently we chose an event discrimination method based on the recognition of ripple-firing patterns in the signal. A simple model for ripple firing parameters, based on interference theory of linear systems and including random effects, predicts spectral minima at low frequencies identical for different seismic phases. We compared the spectra of complete seismogram signals of 52 events recorded by the ISN at different distances and azimuths, including both microearthquakes and quarry blasts in a selected region of northern Israel. Consistent spectral modulation was found in a band from about 2 to 8 Hz for 18 of 21 reliably identified, i.e., reported, quarry blasts with time delays of 20 to 40 msec. The spectral minima frequencies correspond to those predicted by the theory.

Sign in / Sign up

Export Citation Format

Share Document