Standing shear waves in rubberlike layered media

Standing shear waves arising in layered media the shear modulus of which varies in a stepwise manner at the plain boundaries between the layers are considered. A general solution is obtained for the shear wave amplitudes in a resonator with an N-layer structure the lower boundary of which performs harmonic vibrations while a finite-mass plate is attached to the upper boundary. Results of calculations and measurements are presented for a resonator with a structure in which nondeformable metal layers alternate with elastic rubberlike polymer layers. It is shown that the resonance frequencies of such a resonator can be controlled by changing the number of layers and their thicknesses. It is demonstrated, both experimentally and theoretically, that, from the resonance curve of a resonator with a two-layer structure, it is possible to determine the shear modulus of one of the layers under the condition that the elasticity of the other layer is known. The method of separation into a finite number of layers is used to analyze the resonance characteristics of a one-dimensional resonator filled with a rubberlike medium the properties of which continuously vary in the direction perpendicular to the shear displacements. The choice of the number of layers depending on the type of inhomogeneity is analyzed.     

Shear waves in a resonator with cubic nonlinearity

Shear waves with finite amplitude in a one-dimensional resonator in the form of a layer of a rubber-like medium with a rigid plate of finite mass at the upper surface of the layer are investigated. The lower boundary of the layer oscillates according to a harmonic law with a preset acceleration. The equation of motion for particles in a resonator is determined using a model of a medium with a single relaxation time and cubical dependence of the shear modulus on deformation. The amplitude and form of shear waves in a resonator are calculated numerically by the finite difference method at shifted grids. Resonance curves are obtained at different acceleration amplitudes at the lower boundary of a layer. It is demonstrated that, as the oscillation amplitude in the resonator grows, the value of the resonance frequency increases and the shape of the resonance curve becomes asymmetrical. At sufficiently large amplitudes, a bistability region is observed. Measurements were conducted with a resonator, where a layer with the thickness of 15 mm was manufactured of a rubber-like polymer called plastisol. The shear modulus of the polymer at small deformations and the nonlinearity coefficient were determined according to the experimental dependence of mechanical stress on shear deformation. Oscillation amplitudes in the resonator attained values when the maximum shear deformations in the layer were 0.4–0.6, which provided an opportunity to observe nonlinear effects. Measured dependences of the resonance frequency on the oscillation amplitude corresponded to the calculated ones that were obtained at a smaller value of the nonlinear coefficient.     

Measurement of shear elasticity and viscosity of rubberlike materials

The method and results of measuring the shear elastic modulus of a rubberlike polymer by the deformation of a plane elastic layer are described. For shear deformations not exceeding 0.5 of the layer thickness, the shear modulus is constant and its value is in agreement with the value determined by pressing a rigid ball against the polymer layer. For deformations exceeding 0.5 of the layer thickness, the stress-strain dependence becomes nonlinear. The coefficient of shear viscosity is determined from the shear wave form generated by focused ultrasound in a homogeneous polymer sample.     

非对称夹芯板隔声量的解析计算模型及影响因素

提出了一种计算上下面板非对称的三明治夹芯板隔声性能的方法.通过对非对称夹芯梁表观抗弯曲刚度的计算,得到对应夹芯板随频率变化的表观抗弯刚度,代入4阶的控制方程,应用模态展开法可以方便地计算简支非对称夹芯板的隔声量.对4种定制的3层非对称碳纤维夹芯板进行了理论计算和实验测试对比,在频率范围100～3150Hz内,计权隔声量...     

Shear elasticity of fluids at low-frequent shear influence

The visco-elastic properties of liquids have been investigated using acoustical resonance method. Piezoquatrz performed tangential oscillations on the main resonance frequency of 74 kHz contacts by the one end of horizontal surface with the studied liquid layer covered by quartz cover-plate. So the stagnant shear waves are installed in layer. The solution of interaction of piezoquartz-liquid layer-cover-plate gives three methods of determination of the real shear modulus (G) and the tangent of mechanical loss angle (tan theta) of liquid. The first method is realized at smaller thickness of liquid layer then the length of shear wave. Liquids of different classes have been studied using this method: polymer liquids, oils, glycols and alcohols. The second method is connected with the propagation of shear wave in liquid layer, parameters of which are determined the G and tan theta. And the third method is based on the determination of limit shift of resonance frequencies at completes damping of shear wave in thick layer of liquid. All these three methods give satisfactory agreement of results.     

Elastic moduli inheritance and the weakest link in bulk metallic glasses

We show that a variety of bulk metallic glasses (BMGs) inherit their Young's modulus and shear modulus from the solvent components. This is attributed to preferential straining of locally solvent-rich configurations among tightly bonded atomic clusters, which constitute the weakest link in an amorphous structure. This aspect of inhomogeneous deformation, also revealed by our in situ neutron diffraction studies of an elastically deformed BMG, suggests a rubberlike viscoelastic behavior due to a hierarchy of atomic bonds in BMGs.     

General series expression of eddy-current impedance for coil placed above multi-layer plate conductor

This paper presents a closed expression of the layered-plate factor used to calculate the coil eddy-current impedance over the multi-layer plate conductor. By using this expression, the general series of eddy-current impedance can be written directly without solving the undetermined constant equations. The series expression is easy to use for theoretical analysis and programming. Experimental results show that calculated values and measured values are in agreement. As an application, when the bottom layer of the layered plate is a non-ferromagnetic thin layer conductor and the product of the thickness and conductivity of the layer remains unchanged, using the layered-plate factor expression proposed in this paper, it can be theoretically predicted that the eddy-current impedance curves corresponding to different thin layer thickness values will coincide.     

Methodology for rheological testing of engineered biomaterials at low audio frequencies

A commercial rheometer (Bohlin CVO120) was used to mechanically test materials that approximate vocal-fold tissues. Application is to frequencies in the low audio range (20-150 Hz). Because commercial rheometers are not specifically designed for this frequency range, a primary problem is maintaining accuracy up to (and beyond) the mechanical resonance frequency of the rotating shaft assembly. A standard viscoelastic material (NIST SRM 2490) has been used to calibrate the rheometric system for an expanded frequency range. Mathematically predicted response curves are compared to measured response curves, and an error analysis is conducted to determine the accuracy to which the elastic modulus and the shear modulus can be determined in the 20-150-Hz region. Results indicate that the inertia of the rotating assembly and the gap between the plates need to be known (or determined empirically) to a high precision when the measurement frequency exceeds the resonant frequency. In addition, a phase correction is needed to account for the magnetic inertia (inductance) of the drag cup motor. Uncorrected, the measured phase can go below the theoretical limit of -pi. This can produce large errors in the viscous modulus near and above the resonance frequency. With appropriate inertia and phase corrections, +/- 10% accuracy can be obtained up to twice the resonance frequency.     

High friction from a stiff polymer using microfiber arrays

High dry friction requires intimate contact between two surfaces and is generally obtained using soft materials with an elastic modulus less than 10 MPa. We demonstrate that high-friction properties similar to rubberlike materials can also be obtained using microfiber arrays constructed from a stiff thermoplastic (polypropylene, 1 GPa). The fiber arrays have a smaller true area of contact than a rubberlike material, but polypropylene's higher interfacial shear strength provides an effective friction coefficient of greater than 5 at normal loads of 8 kPa. At the pressures tested, the fiber arrays showed more than an order of magnitude increase in shear resistance compared to the bulk material. Unlike softer materials, vertical fiber arrays of stiff polymer demonstrate no measurable adhesion on smooth surfaces due to high tensile stiffness.     

The shear modulus of the human vocal fold in a transverse direction

The aim of this study was to measure the shear modulus of the vocal fold in a human hemilarynx, such that the data can be related to direction of applied stress and anatomical context. Dynamic spring rate data were collected using a modified linear skin rheometer using human hemilarynges, and converted to estimated shear modulus via application of a simple shear model. The measurement probe was attached to the epithelial layer of the vocal fold cover using suction. A sinusoidal force of 3g was applied to the epithelium, and the resultant displacement logged at a rate of 1kHz. Force measurement accuracy was 20microg and position measurement accuracy was 4microm. The force was applied in a transverse direction at the midmembranous point between the vocal process and the anterior commissure. The shear modulus of the three female vocal folds ranged from 814 to 1232Pa. The shear modulus of the three male vocal folds ranged from 1021 to 1796Pa. These data demonstrate that it is possible to obtain estimates for the shear modulus of the vocal fold while preserving anatomical context. The modulus values reported here are higher than those reported using parallel plate rheometry. This is to be expected as the tissue is attached to surrounding structures, and is under natural tension.     

Low-frequency shear parameters of liquid viscoelastic materials

An experimental study of the shear parameters of viscoelastic liquids is carried out by the acoustic resonance method based on the changes in the natural frequency and Q factor of a piezoelectric quartz resonator. The liquid to be studied is placed between a stationary quartz strap and the piezoelectric quartz crystal vibrating at the resonance frequency. For a set of drilling muds, the values of the real and imaginary shear moduli are obtained at a frequency of 74 kHz. The measurements are performed with a liquid layer thickness much smaller than the shear wavelength. It is shown that the shear modulus decreases with increasing strain amplitude. A cluster model based on the Isakovich-Chaban nonlocal diffusion theory is proposed for explaining the low-frequency viscoelastic relaxation process.     

Granular layers on vibrating plates: effective bending stiffness and particle-size effects

Acoustic methods of land mine detection rely on the vibrations of the top plate of the mine in response to sound. For granular soil (e.g., sand), the particle size is expected to influence the mine response. This hypothesis is studied experimentally using a plate loaded with dry sand of various sizes from hundreds of microns to a few millimeters. For low values of sand mass, the plate resonance decreases with added mass and eventually reaches a minimum without particle size dependence. After the minimum, a frequency increase is observed with additional mass that includes a particle-size effect. Analytical nondissipative continuum models for granular media capture the observed particle-size dependence qualitatively but not quantitatively. In addition, a continuum-based finite element model (FEM) of a two-layer plate is used, with the sand layer replaced by an equivalent elastic layer for evaluation of the effective properties of the layer. Given a thickness of sand layer and corresponding experimental resonance, an inverse FEM problem is solved iteratively to give the effective Young's modulus and bending stiffness that matches the experimental frequency. It is shown that a continuum elastic model must employ a thickness-dependent elastic modulus in order to match experimental values.     

Damping of stiffened plates by multiple layer treatments

It is shown in this paper that the modal damping and resonant frequencies of a stiffened plate structure, with a multiple layer constrained damping treatment attached to the surface, can be predicted from a knowledge of the equivalent complex modulus properties of the treatment. The equations used represent a simple extension of the classical equations of Oberst for a free layer treatment applied to an unstiffened beam or plate, with terms accounting for the effect of the stiffeners. The equivalent complex modulus properties of the treatment depend on a shear parameter, a geometrical parameter, the stiffness of the constraining layer and the loss factor of the adhesive. Experimental results are discussed.     

Slow nonlinearity kinetics of the viscoelastic properties of oil during shear vibrations

Earlier we discovered the slow evolution of viscoelastic moduli of heavy crude oil. The shear modulus was measured at frequencies of 0.5, 5, and 50 Hz at different temperatures over 72 h. New studies of the dependence of the complex shear modulus on the strain amplitude revealed a logarithmic increase in the nonlinearity parameter as a function of time for this oil sample. It was experimentally established that the complex shear modulus is a linear function of the amplitude of shear perturbations. This is possible in the case of a linear dependence of values of the viscoelastic characteristics on the medium modulus of deformation.     

GMM/弹性板/PZT层状复合结构的纵振磁电响应

利用Hamilton原理推导GMM/弹性板/PZT三层层状复合结构的运动方程,在推导中考虑层间胶层的作用,包括其剪切变形和纵向变形产生的效果;应用运动方程,根据层状复合结构的边界条件,推导复合结构的固有频率方程,并结合压磁和压电方程,得到层状复合结构在不同固有频率处的磁电响应.对比磁电响应的频率特性的理论值和实验值,频率误差在9.42%以内,磁电电压转化系数的理论值与实验值符合,并讨论了弹性板的尺寸变化对层状复合结构谐振频率的影响. 关键词： 层状复合结构 磁电响应 Hamilton原理 运动方程     

Material property estimates from ultrasound attenuation in fibre suspensions

An investigation of a new method for measuring fibre material properties from ultrasonic attenuation in a dilute suspension of synthetic fibres of uniform geometry is presented. The method is based on inversely solving an ultrasound scattering and absorption model of suspended fibres in water for the material properties of the fibres. Experimental results were obtained from three suspensions of nylon 66 fibres each with different fibre diameters. A forward solution to the model with reference material values is compared to experimental data to verify the model’s behaviour. Estimates of the shear and Young’s modulus, the compressional wave velocity, Poisson’s ratio and loss tangent from nylon 66 fibres are compared to data available from other sources. Experimental data confirms that the model successfully predicts that the resonance features in the frequency response of the attenuation are a function of diameter. Consistent estimated values for the compressional wave velocity and the Poisson’s ratio were found to be difficult to obtain but in combination gave values of shear modulus within previously reported values and with low sensitivity to noise. Young’s modulus was underestimated by 54% but was consistent and had low sensitivity to noise. The underestimation is believed to be caused by the assumption of isotropic material used in the model. Additional tests on isotropic fibre would confirm this. Further analysis of the model sensitivity and the reasons for the resonance features are required.     

Dynamic strength behavior of a Zr-based bulk metallic glass under shock loading

Dynamic strength behavior of Zr51Ti5Ni10Cu25Al9 bulk metallic glass(BMG) up to 66 GPa was investigated in a series of plate impact shock-release and shock-reload experiments.Particle velocity profiles measured at the sample/Li F window interface were used to estimate the shear stress,shear modulus,and yield stress in shocked BMG.Beyond confirming the previously reported strain-softening of shear stress during the shock loading process for BMGs,it is also shown that the softened Zr-BMG still has a high shear modulus and can support large yield stress when released or reloaded from the shocked state,and both the shear modulus and the yield stress appear as strain-hardening behaviors.The work provides a much clearer picture of the strength behavior of BMGs under shock loading,which is useful to comprehensively understand the plastic deformation mechanisms of BMGs.     

Shear modulus of shock-compressed LY12 aluminium up to melting point

Asymmetric plate impact experiments are conducted on LY12 aluminium alloy in a pressure range of 85-131 GPa. The longitudinal sound speeds axe obtained from the time-resolved particle speed profiles of the specimen measured with Velocity Interferometer System for Any Reflector （VISAR） technique, and they are shown to be good agreement with our previously reported data of this alloy in a pressure range of 20-70 GPa, and also with those of 2024 aluminium reported by McQueen. Using all of the longitudinal speeds and the corresponding bulk speeds calculated from the Gruneisen equation of state （EOS）, shear moduli of LY12 aluminium alloy are obtained. A comparison of the shear moduli in the solid phase region with those estimated from the Steinberg model demonstrate that the latter are systematically lower than the measurements. By re-analysing the pressure effect on the shear modulus, a modified equation is proposed, in which the pressure term of P/η^1/3 in the Steinberg model is replaced by a linear term. Good agreement between experiments and the modified equation is obtained, which implies that the shear modulus of LY12 aluminium varies linearly both with pressure and with temperature throughout the whole solid phase region. On the other hand, shear modulus of aluminium in a solid-liquid mixed phrase region decreases gradually and smoothly, a feature that is very different from the drastic dropping at the melting point under static conditions.     

Shear modulus of shock-compressed LY12 aluminium up to melting point

Asymmetric plate impact experiments are conducted on LY12 aluminium alloy in a pressure range of 85--131\,GPa. The longitudinal sound speeds are obtained from the time-resolved particle speed profiles of the specimen measured with Velocity Interferometer System for Any Reflector (VISAR) technique, and they are shown to be good agreement with our previously reported data of this alloy in a pressure range of 20--70\,GPa, and also with those of 2024 aluminium reported by McQueen. Using all of the longitudinal speeds and the corresponding bulk speeds calculated from the Gruneisen equation of state (EOS), shear moduli of LY12 aluminium alloy are obtained. A comparison of the shear moduli in the solid phase region with those estimated from the Steinberg model demonstrate that the latter are systematically lower than the measurements. By re-analysing the pressure effect on the shear modulus, a modified equation is proposed, in which the pressure term of $P/\eta^{1/3}$ in the Steinberg model is replaced by a linear term. Good agreement between experiments and the modified equation is obtained, which implies that the shear modulus of LY12 aluminium varies linearly both with pressure and with temperature throughout the whole solid phase region. On the other hand, shear modulus of aluminium in a solid-liquid mixed phrase region decreases gradually and smoothly, a feature that is very different from the drastic dropping at the melting point under static conditions.     

Impedance method for measuring shear elasticity of liquids

Experimental results of studying low-frequency (74 kHz) shear elasticity of polymer liquids by the impedance method (analogous to the Mason method) are presented. A free-volume thick liquid layer is placed on the horizontal surface of a piezoelectric quartz crystal with dimensions 34.7 × 12 × 5.5 cm. The latter performs tangential vibrations at resonance frequency. The liquid layer experiences shear strain, and shear waves should propagate in it. From the theory of the method, it follows that, with an increase in the layer thickness, both real and imaginary resonance frequency shifts should exhibit damped oscillations and tend to limiting values. For the liquids under study, the imaginary frequency shift far exceeds the real one, which testifies to the presence of bulk shear elasticity.