Influence of the ambient pressure on thin plate and film bending

The distributed lateral load on a plate located in a gas medium has been determined. The difference in the gas pressures of the plate surfaces results in a pressure drop and a lateral force, which depends on the middle surface curvature. It is shown that both these components of the lateral force must be taken into account in the general case. The influence of the second load component is small at a small ratio of the average pressure to the elastic modulus of the plate material and at a large relative thickness of the plate. At a small relative plate thickness and a large ratio of the average pressure of the medium to the elastic modulus of the plate material, the influence of the second component of the lateral load on the bending becomes significant. Cases of both linear and nonlinear plate bending are considered.     

Transient displacement induced in shear wave elastography: comparison between analytical results and ultrasound measurements

It is now accepted that an effective way to investigate the elastic properties of soft tissues is to generate a localized transient acoustic radiation force and to follow the associated displacements in the time/space domain. Shear waves induced by this stress field are particularly interesting in this kind of medium because they are governed by the shear elastic modulus mu, which is directly linked to the Young modulus, and spatial distribution and temporal evolution of the transient motion induced must therefore be obtained in detail. We report here a model based on the elastodynamic Green's function formalism to describe these displacements. 3D simulation of radiation force in homogenous elastic media was performed and the displacement curves computed at different radial distances for different temporal force profiles. Amplitude and duration of displacement were found to be reliable parameters to characterize the elastic properties of the medium. Experimental measurements were performed in a homogeneous agar-gelatin tissue-mimicking phantom, and two transducers were used to generate the radiation force and follow the induced displacements. Displacements obtained from different lateral locations around the applied force axis were then used to reconstruct the shear-wave propagation in a scan plane as a function of time. The experimental displacements/curves agreed with the theoretical profiles obtained by the elastodynamic Green's function formalism.     

Axisymmetric vibrations of a circular plate of linearly varying thickness on an elastic foundation according to Mindlin theory

Free axisymmetric vibrations of an elastic circular plate of linearly varying thickness on an elastic foundation have been studied on the basis of shear theory [1,2]. The transverse displacement and local rotation are expressed as an infinite series. The frequencies corresponding to the first two modes of vibrations are obtained for a circular plate with clamped and simply supported edge conditions for various values of the taper constant and the foundation modulus. The results have been compared with those of reference [3].     

Defect detection and localization in orthotropic wood slabs by inversion of dynamic surface displacements

The nondestructive evaluation inversion and generalized force-mapping techniques developed and demonstrated for isotropic thin plates by Bucaro et al. [(2004). "Detection and localization of inclusions in plates using inversion of point actuated surface displacements," J. Acoust. Soc. Am. 115, 201-206] are extended to the case of orthotropic plates. The extended techniques are applied to a finite-element generated numerical database for point excited wooden slabs with and without an internal defect at 5 and 10 kHz. Operation of the original isotropic algorithms on the wood surface displacements is shown to fail in recovering the uniform elastic parameters or in detecting and locating the defect. The new algorithms based on the wave equation for a thin, orthotropic plate successfully convert the surface displacements on the uniform wooden slab to elastic parameter maps which serve to detect and localize the defect in the flawed plate. The results, particularly at the higher frequency, indicate that the onset of failure in the thin plate approximation impacts both the inversion and the generalized force-mapping accuracy. However, in this case use of the inversion algorithm to obtain modified wave equation coefficients followed by operation of the force-mapping algorithm with these new parameters inserted is shown to successfully mitigate this effect.     

Study of the bending modulus of individual silicon nitride nanobelts via atomic force microscopy

Analysis of the bending modulus of individual silicon nitride nanobelts in elastic regime is reported here. The nanobelts have the size between 200∼800 nm in width, and thickness 20∼50 nm. Atomic force microscopy was used to image and to perform measurements of force versus bending displacement on individual nanobelts suspending over strips. The bending modulus E_b is deduced by comparison of the measured force curves on the substrate and on the suspending nanobelts. It is shown that the elastic modulus of the silicon nitride nanobelts is about 570 GPa, which is much larger than that of bulk and film of the silicon nitride material. The larger elastic modulus is ascribed to the fact there are less structural defects in the silicon nitride nanobelts. PACS 81.70.Bt; 81.40.Lm; 61.80.+g     

考虑介质膨胀速率的锂离子电池管状电极中扩散诱导应力及轴向支反力分析

硅作为锂离子电池阴极材料相对于传统负极材料具有高比容量,价格低廉等优势.本文针对充电过程中锂离子电池中电极建立力学模型和扩散模型,并在扩散模型引入考虑介质膨胀速率的影响.以硅空心柱形电极为例,分析了恒流充电下介质膨胀速率对电极中扩散诱导应力分布的影响,并研究了不同内外半径比、充电速率、材料参数以及锂化诱导软化系数(lithiation induced softening factor,LISF)对轴向的支反力达到临界欧拉屈曲力所需时间的影响.结果表明,随着电极中锂浓度上升,介质膨胀速率对应力分布的影响增大,对轴向的支反力影响较小.弹性模量和应力成正比,但其与轴向的支反力达到临界欧拉屈曲力所需时间无关;扩散系数与所需时间成反比;偏摩尔体积增大时,达到临界屈曲力所需时间减少;随着LISF绝对值增大,完全锂化时轴向力降低.     

DETERMINATION OF ELASTIC CONSTANTS OF ANISOTROPIC LAMINATED PLATES USING ELASTIC WAVES AND A PROGRESSIVE NEURAL NETWORK

In this paper, a procedure is suggested to inversely determine the elastic constants of anisotropic laminated plates using a progressive neural network (NN). The surface displacement responses are used as the inputs for the NN model. The outputs of the NN are the elastic constants of anisotropic laminated plates. The hybrid numerical method (HNM) is used to calculate the displacement responses of laminated plates to an incident wave for given elastic constants. The NN model is trained using the results from the HNM. A modified back-propagation learning algorithm with a dynamically adjusted learning rate and an additional jump factor is developed to tackle the possible saturation of the sigmoid function and to speed up the training process for the NN model. The concept of orthogonal array was adopted to generate the representative combinations of elastic constants, which reduces significantly the number of training data while maintaining its data completeness. Once trained, the NN model can be used for on-line determination of the elastic constants if the dynamic displacement responses on the surface of the laminated plate can be obtained. The determined elastic constants are then used in the HNM to calculate the displacement responses. The NN model would go through a progressive retraining process until the calculated displacement responses using the determined results are sufficiently close to the actual responses. This procedure is examined for an actual glass/epoxy laminated plate. It is found that the present procedure is very robust and efficient for determining the elastic constants of anisotropic laminated plates.     

Elastic and phonon properties of FeSi and CoSi in the B2 structure

First principles calculations of structural, electronic, elastic, and phonon properties of the intermetallic compounds FeSi and CoSi in the B2 (CsCl) structure are presented, using the pseudopotential plane-wave approach based on density functional theory, within the local density approximation. The optimized lattice constants, independent elastic constants, bulk modulus, and first-order pressure derivative of the bulk modulus are reported for the B2 structure and compared with earlier experimental and theoretical calculations. A linear-response approach to density functional theory is used to derive the phonon dispersion curves, and the vibrational partial and total density of states. Atomic displacement patterns for FeSi at the Γ, X, and R symmetry points are presented. The calculated zone-center optical phonon mode for FeSi is in good agreement with experimental and theoretical data.     

Analytic approximation to nonlinear hydroelastic waves traveling in a thin elastic plate floating on a fluid

An analytic approximation method known as the homotopy analysis method (HAM) is applied to study the nonlinear hydroelastic progressive waves traveling in an infinite elastic plate such as an ice sheet or a very large floating structure (VLFS) on the surface of deep water. A convergent analytical series solution for the plate deflection is derived by choosing the optimal convergencecontrol parameter. Based on the analytical solution the effects of different parameters are considered. We find that the plate deflection becomes lower with an increasing Young’s modulus of the plate. The displacement tends to be flattened at the crest and be sharpened at the trough as the thickness of the plate increases, and the larger density of the plate also causes analogous results. Furthermore, it is shown that the hydroelastic response of the plate is greatly affected by the high-amplitude incident wave. The results obtained can help enrich our understanding of the nonlinear hydroelastic response of an ice sheet or a VLFS on the water surface.     

Evaluation of elastic modulus of cantilever beam by TA-ESPI

The paper proposes an evaluation technique for the elastic modulus of a cantilever beam by vibration analysis based on time average electronic speckle pattern interferometry (TA-ESPI) and Euler-Bernoulli equation. General approaches for the measurement of elastic modulus of a thin film are the Nano indentation test, Buldge test, Micro-tensile test, and so on. They each have strength and weakness in the preparation of the test specimen and the analysis of experimental results. ESPI is a type of laser speckle interferometry technique offering non-contact, high-resolution and whole-field measurement. The technique is a common measurement method for vibration mode visualization and surface displacement. Whole-field vibration mode shape (surface displacement distribution) at resonance frequency can be visualized by ESPI. And the maximum surface displacement distribution from ESPI can be used to find the resonance frequency for each vibration mode shape. And the elastic modules of a test material can be easily estimated from the measured resonance frequency and Euler-Bernoulli equation. The TA-ESPI vibration analysis technique can be used to find the elastic modulus of a material requiring simple preparation process and analysis.     

Temporal analysis of tissue displacement induced by a transient ultrasound radiation force

One of the stress sources that can be used in dynamic elastography imaging methods is the acoustic radiation force. However, displacements of the medium induced by this stress field are generally not fully understood in terms of spatial distribution and temporal evolution. A model has been developed based on the elastodynamic Green's function describing the different acoustic waves generated by focused ultrasound. The function is composed of three terms: two far-field terms, which correspond to a purely longitudinal compression wave and a purely transverse shear wave, and a coupling near-field term which has a longitudinal component and a transverse component. For propagation distances in the shear wavelength range, the predominant term is the near field term. The displacement duration corresponds to the propagation duration of the shear wave between the farthest source point and the observation point. This time therefore depends on the source size and the local shear modulus of the tissue. Evolution of the displacement/time curve profile, which is directly linked to spatial and temporal source profiles, is computed at different radial distances, for different durations of force applications and different shear elastic coefficients. Experimental results performed with an optical interferometric method in a homogeneous tissue-mimicking phantom agreed with the theoretical profiles.     

The peculiarities of cross-correlation between two secondary precursors – Radon and magnetic field variations,induced by stress transfer changes

A model of precursor manifestation mechanisms, stimulated by tectonic activity and some peculiarities of observer strategy, whose main task is the effective measurement of precursors in the spatial area of their occurrence on the Earth's daylight, are considered. In particular, the applicability of Dobrovolsky's approximation is analyzed, when an unperturbed medium (characterized by the simple shear state) and the area of tectonic activity (local inhomogeneity caused by the change only of shear modulus) are linearly elastic, and perturbation, in particular, surface displacement is calculated as a difference of the solutions of two independent static problems of the theory of elasticity with the same boundary condition on the surface. Within the framework of this approximation a formula for the spatial distribution (of first component) of magnetic field variations caused by piezomagnetic effect in the case of perturbed regular medium, which is in simple shear state is derived. Cogent arguments in favor of linear dependence between the radon spatial distribution and conditional deformation are obtained.Changes in magnetic field strength and radon concentrations were measured along a tectonomagnetic profile of the total length of 11 km in the surroundings of the ”Academician Vernadsky” Station on the Antarctic Peninsula (W 64°16′, S 65°15′). Results showed a positive correlation between the annual surface radon concentration and annual changes of magnetic field relative to a base point, and also the good coincidence with theoretical calculation.     

Influence of adhesive layer properties on laser-generated ultrasonic waves in thin bonded plates

This paper studies quantitatively the generation of Lamb waves in thin bonded plates subjected to laser illumination, after considering the viscoelasticity of the adhesive layer. The displacements of such plates have been calculated in the frequency domain by using the finite element method, and the time domain response has been reconstructed by applying an inverse fast Fourier transform. Numerical results are presented showing the normal surface displacement for several configurations: a single aluminum plate, a three-layer bonded plate, and a two-layer plate. The characteristics of the laser-generated Lamb waves for each particular case have been investigated. In addition, the sensitivity of the transient responses to variations of material properties (elastic modulus, viscoelastic modulus, and thickness) of the adhesive layer has been studied in detail.     

Generation of waves in an elastic plate by a torsional moment and a horizontal force

An approximate solution is determined for the motion of an infinite elastic plate, excited by a torsional moment (with the axis of the moment normal to the plate) and by a horizontal force (parallel to the plate). The driving moment and force are sinusoidal in time and applied to a small rigid indenter with a circular base, fixed to the plate. The solution is obtained from a three-dimensional approach but is evaluated only for low frequencies, where the wavelengths of the quasi-longitudinal, tranverse and bending waves are much larger than the thickness of the plate. For the case of excitation with a torsional moment, the solution contains two parts, one describing a travelling transverse wave and the other a local reaction. The local reaction is built up of two infinite sums of Love waves with imaginary wave numbers. The driving-point admittance due to the local reaction is larger than the admittance due to the tranverse wave when the diameter of the indenter is smaller than about twice the thickness of the plate. For the case of excitation with a horizontal force, the solution contains three parts that describe travelling waves (quasi-longitudinal, transverse and bending) and two parts that describe the local reaction (infinite sums of Lamb and Love waves). The admittances due to the three types of travelling waves are all of the same order of magnitude. The admittance due to the local reaction is of importance when the frequency is relatively high and the diameter of the identer much smaller than the thickness of the plate. For both cases of excitation, the admittance due to the local reaction increases with increasing thickness of the plate and tends to the value found for a semi-infinite medium.     

Internal field of an insonified elastic plate

The displacement field within an infinite, fluid-loaded elastic plate insonified by a plane wave at arbitrary incidence angle is examined. For a water-immersed steel plate which is 0·55 shear wavelengths thick extensive graphical data are presented showing the evolution of the displacement field with variation of incidence angle from very close to normal incidence to very close to grazing incidence. Particular attention is paid to the behaviour at angles at which Lamb modes are excited, and it is incidentally shown by the decomposition of the normal boundary motions into antisymmetrical and symmetrical constituents that at the coincidence angles these motions are neither totally antisymmetrical nor totally symmetrical. New expressions derived for the displacement components at the critical angles illustrate the transition between oscillatory and exponentially decaying waves within the plate. Some clarification is obtained of the physical behaviour at transmission nulls.     

Simulation of elastic displacement of surface during laser short pulse heating of gold

The laser short pulse heating initiates nonequilibrium heating of the substrate material, which in turn results in the thermal stresses developing in the region below the surface. The surface temperature can be measured possibly through the monitoring of the resulting surface displacement. This requires in detail investigation into the surface displacement and surface temperature rises across the heated spot during the laser short pulse heating process. In the present study, the laser short pulse heating of gold surface is considered and the temperature rise at the surface and elastic displacement of the surface are investigated. The spatial and temporal distributions of surface displacement and surface temperature are predicted and the elastic response of the substrate material due to temperature rise is explored. It is found that the temporal and spatial distributions of the surface displacement do not follow the temperature rise at the surface. Consequently, care should be taken when measuring the temperature rise at the surface by means of monitoring the surface displacement during a laser short pulse heating process.     

Surface adhesion and demolding force dependence on resist composition in ultraviolet nanoimprint lithography

Demolding, the process to separate stamp from molded resist, is most critical to the success of ultraviolet nanoimprint lithography (UV-NIL). In the present study we investigated adhesion and demolding force in UV-NIL for different compositions of a model UV-curable resist system containing a base (either tripropyleneglycol diacrylate with shorter oligomer length or polypropyleneglycol diacrylate with longer oligomer length), a cross-linking agent (trimethylolpropane triacrylate) and a photoinitiator (Irgacure 651). The demolding force was measured using a tensile test machine with homemade fixtures after imprinting the UV resist on a silicon stamp. While decreasing the cross-linking agent content from 49 to 0 wt% has little effect on the resist surface energy, it reduces the resist's elastic modulus drastically. The decrease in elastic modulus results in a decreased adhesion force at the resist/stamp interface thereby facilitating the demolding. The decrease in elastic modulus and, therefore, demolding force by lowering the cross-linking agent content was markedly less pronounced in tripropyleneglycol diacrylate-based resists due to its shorter oligomer length. These general findings will be useful in designing new resists for UV-NIL process.     

First-principles study of the structural and thermodynamic properties of AsNMg3 antiperovskite

The structural and elastic properties of the antiperovskite semiconductor AsNMg₃ are investigated using the full-potential linearized augmented plane wave plus local orbital (FP-LAPW+lo) method within the generalized gradient in the frame of the density functional theory. The ground state properties such as lattice constant, bulk modulus, pressure derivative of the bulk modulus and elastic constants are in good agreement with numerous experimental and theoretical data. Through the quasi-harmonic Debye model, in which the phononic effects are considered, we have obtained successfully the thermodynamic properties such as the thermal expansion coefficient, Debye temperature and specific heats in the whole pressure range from 0 to 30 GPa and temperature range from 0 to 1200 K.     

Contact mechanics analysis of oscillatory sliding of a rigid fractal surface against an elastic–plastic half-space

Oscillatory sliding contact between a rigid rough surface and an elastic–plastic half-space is examined in the context of numerical simulations. Stick-slip at asperity contacts is included in the analysis in the form of a modified Mindlin theory. Two friction force components are considered – adhesion (depending on the real area of contact, shear strength and interfacial adhesive strength) and plowing (accounting for the deformation resistance of the plastically deformed half-space). Multi-scale surface roughness is described by fractal geometry, whereas the interfacial adhesive strength is represented by a floating parameter that varies between zero (adhesionless surfaces) and one (perfectly adhered surfaces). The effects of surface roughness, apparent contact pressure, oscillation amplitude, elastic–plastic properties of the half-space and interfacial adhesion on contact deformation are interpreted in the light of numerical results of the energy dissipation, maximum tangential (friction) force and slip index. A non-monotonic trend of the energy dissipation and maximum tangential force is observed with increasing surface roughness, which is explained in terms of the evolution of the elastic and plastic fractions of truncated asperity contact areas. The decrease of energy dissipation with increasing apparent contact pressure is attributed to the increase of the elastic contact area fraction and the decrease of the slip index. For a half-space with fixed yield strength, a lower elastic modulus produces a higher tangential force, whereas a higher elastic modulus yields a higher slip index. These two competing effects lead to a non-monotonic dependence of the energy dissipation on the elastic modulus-to-yield strength ratio of the half-space. The effect of interfacial adhesion on the oscillatory contact behaviour is more pronounced for smoother surfaces because the majority of asperity contacts deform elastically and adhesion is the dominant friction mechanism. For rough surfaces, higher interfacial adhesion yields less energy dissipation because more asperity contacts exhibit partial slip.     

ZrH_2结构与热力学性质

基于密度泛函理论,采用全势线性缀加平面波加局域轨道方法和广义梯度近似研究了ZrH2的结构与弹性性质。结果表明:在基态条件下,ZrH2的晶格常数计算值与实验值及其它理论值相当吻合。在考虑声子作用的前提下,采用准谐德拜模型成功获得了不同条件下(0~50 GPa,0~1 300 K)ZrH2的热容、热膨胀系数和德拜温度等热力学性质。结果表明:定压热容预测值随温度升高而增大,并逐渐接近佩蒂特-杜隆极限;随压强增加,德拜温度呈增加趋势;随温度增加,德拜温度呈减小趋势;在压强一定的条件下,热膨胀系数随温度的升高而增大,且在高温高压条件下,热膨胀系数的增加趋势变缓。