Energy loss due to adhesion in longitudinal impact of elastic cylinders

Adhesive interaction between impacting bodies can cause energy loss, even in an otherwise elastic impact. Adhesion force induces tensile stress in the bodies, which modifies the stress wave profile and influences the restitution behavior. We investigate this effect by developing a finite element framework, which incorporates a Lennard-Jones-type potential for modeling the adhesive interaction between volume elements. With this framework, the classical problems in contact mechanics can be revisited without the restrictive surface-force approximation. In this paper, we study the longitudinal impact of an elastic cylinder on a rigid half-space with adhesion. In the absence of adhesion, this problem reduces to the impact between two identical cylinders in which there is no energy loss. Adhesion causes a fraction of energy in the stress waves to remain in the cylinder as residual stress waves. This apparent loss in kinetic energy is shown to be a unique function of maximum tensile strain energy. We have developed a 1-D model in terms of interaction force parameters, velocity and material properties to estimate the tensile stain energy. We show that this model can be used to predict practically important phenomena like capture wherein the impacting bodies stick together. (C) 2013 Elsevier Masson SAS. All rights reserved.

Nonlinear gravity-wave interactions in stratified turbulence

To investigate the dynamics of gravity waves in stratified Boussinesq flows, a model is derived that consists of all three-gravity-wave-mode interactions (the GGG model), excluding interactions involving the vortical mode. The GGG model is a natural extension of weak turbulence theory that accounts for exact three-gravity-wave resonances. The model is examined numerically by means of random, large-scale, high-frequency forcing. An immediate observation is a robust growth of the so-called vertically sheared horizontal flow (VSHF). In addition, there is a forward transfer of energy and equilibration of the nonzero-frequency (sometimes called ``fast'') gravity-wave modes. These results show that gravity-wave-mode interactions by themselves are capable of systematic interscale energy transfer in a stratified fluid. Comparing numerical simulations of the GGG model and the full Boussinesq system, for the range of Froude numbers (Fr) considered (0.05 a parts per thousand currency sign Fr a parts per thousand currency sign 1), in both systems the VSHF is hardest to resolve. When adequately resolved, VSHF growth is more vigorous in the GGG model. Furthermore, a VSHF is observed to form in milder stratification scenarios in the GGG model than the full Boussinesq system. Finally, fully three-dimensional nonzero-frequency gravity-wave modes equilibrate in both systems and their scaling with vertical wavenumber follows similar power-laws. The slopes of the power-laws obtained depend on Fr and approach -2 (from above) at Fr = 0.05, which is the strongest stratification that can be properly resolved with our computational resources.

Transmission of elastic waves through a frictional boundary

Incident energy gets transmitted, reflected and absorbed across an interface in jointed rock mass leading to energy dissipation and alteration of waves. Wave velocities get attenuated during their propagation across joints and this behavior is studied using bender/extender element tests. The velocity attenuation and modulus reduction observed in experimental tests are modeled with three dimensional distinct element code and results are validated. Normal propagation of an incident shear wave through a jointed rock mass cause slip of the rock blocks if shear stress of wave exceeds the shear strength of the joint. As the properties of joint determine the transmission of energy across an interface, a parametric study is then conducted with the validated numerical model by varying the parameters that may determine the energy transmission across a joint using modified Miller's method. Results of the parametric study are analyzed and presented in the paper. (C) 2014 Elsevier Ltd. All rights reserved.

Studies on an improved indigenous pressure wave generator and its testing with a pulse tube cooler

Earlier version of an indigenously developed Pressure Wave Generator (PWG) could not develop the necessary pressure ratio to satisfactorily operate a pulse tube cooler, largely due to high blow by losses in the piston cylinder seal gap and due to a few design deficiencies. Effect of different parameters like seal gap, piston diameter, piston stroke, moving mass and the piston back volume on the performance is studied analytically. Modifications were done to the PWG based on analysis and the performance is experimentally measured. A significant improvement in PWG performance is seen as a result of the modifications. The improved PWG is tested with the same pulse tube cooler but with different inertance tube configurations. A no load temperature of 130 K is achieved with an inertance tube configuration designed using Sage software. The delivered PV power is estimated to be 28.4 W which can produce a refrigeration of about 1 W at 80 K.

Nonequilibrium ``Melting'' of a Charge Density Wave Insulator via an Ultrafast Laser Pulse

We employ an exact solution of the simplest model for pump-probe time-resolved photoemission spectroscopy in charge-density-wave systems to show how, in nonequilibrium, the gap in the density of states disappears while the charge density remains modulated, and then the gap reforms after the pulse has passed. This nonequilibrium scenario qualitatively describes the common short-time experimental features in TaS2 and TbTe3, indicating a quasiuniversality for nonequilibrium ``melting'' with qualitative features that can be easily understood within a simple picture.

Ultrasonic guided wave sensing properties of PVDF thin film with inter digital electrodes

Ultrasonic strain sensing performance of the large area PVDF with Inter Digital Electrodes (IDE) is studied in this work. Procedure to obtain IDE on a beta-phase PVDF is explained. PVDF film with IDE is bonded on a plate structure and is characterized for its directional sensitivity at different frequencies. Guided waves are induced on the IDE-PVDF sensor from different directions by placing a piezoelectric wafer actuator at different angles. Strain induced on the IDE-PVDF sensor by the guided waves in estimated by using a Laser Doppler Vibrometer (LDV) and a wave propagation model. Using measured voltage response from IDE-PVDF sensor and the strain measurements from LDV the piezoelectric coefficient is estimated in various directions. The variation of 11 e at different angles shows directional sensitivity of the IDE-PVDF sensor to the incident guided waves. The present study provides an effective technique to characterize thin film piezoelectric sensors for ultrasonic strain sensing at very high frequencies of 200 kHz. Often frequency of the guided wave is changed to alter the wavelength to interrogate damages of different sizes in Structural Health Monitoring (SHM) applications. The unique property of directional sensitivity combined with frequency tunability makes the IDE-PVDF sensor most suitable for SHM of structures.

Spectral finite element based on an efficient layerwise theory for wave propagation analysis of composite and sandwich beams

In this paper, we present a spectral finite element model (SFEM) using an efficient and accurate layerwise (zigzag) theory, which is applicable for wave propagation analysis of highly inhomogeneous laminated composite and sandwich beams. The theory assumes a layerwise linear variation superimposed with a global third-order variation across the thickness for the axial displacement. The conditions of zero transverse shear stress at the top and bottom and its continuity at the layer interfaces are subsequently enforced to make the number of primary unknowns independent of the number of layers, thereby making the theory as efficient as the first-order shear deformation theory (FSDT). The spectral element developed is validated by comparing the present results with those available in the literature. A comparison of the natural frequencies of simply supported composite and sandwich beams obtained by the present spectral element with the exact two-dimensional elasticity and FSDT solutions reveals that the FSDT yields highly inaccurate results for the inhomogeneous sandwich beams and thick composite beams, whereas the present element based on the zigzag theory agrees very well with the exact elasticity solution for both thick and thin, composite and sandwich beams. A significant deviation in the dispersion relations obtained using the accurate zigzag theory and the FSDT is also observed for composite beams at high frequencies. It is shown that the pure shear rotation mode remains always evanescent, contrary to what has been reported earlier. The SFEM is subsequently used to study wavenumber dispersion, free vibration and wave propagation time history in soft-core sandwich beams with composite faces for the first time in the literature. (C) 2014 Elsevier Ltd. All rights reserved.

Frequency Domain Based Solution for Certain Class of Wave Equations: An exhaustive study of Numerical Solutions

The paper discusses the frequency domain based solution for a certain class of wave equations such as: a second order partial differential equation in one variable with constant and varying coefficients (Cantilever beam) and a coupled second order partial differential equation in two variables with constant and varying coefficients (Timoshenko beam). The exact solution of the Cantilever beam with uniform and varying cross-section and the Timoshenko beam with uniform cross-section is available. However, the exact solution for Timoshenko beam with varying cross-section is not available. Laplace spectral methods are used to solve these problems exactly in frequency domain. The numerical solution in frequency domain is done by discretisation in space by approximating the unknown function using spectral functions like Chebyshev polynomials, Legendre polynomials and also Normal polynomials. Different numerical methods such as Galerkin Method, Petrov- Galerkin method, Method of moments and Collocation method or the Pseudo-spectral method in frequency domain are studied and compared with the available exact solution. An approximate solution is also obtained for the Timoshenko beam with varying cross-section using Laplace Spectral Element Method (LSEM). The group speeds are computed exactly for the Cantilever beam and Timoshenko beam with uniform cross-section and is compared with the group speeds obtained numerically. The shear mode and the bending modes of the Timoshenko beam with uniform cross-section are separated numerically by applying a modulated pulse as the shear force and the corresponding group speeds for varying taper parameter in are obtained numerically by varying the frequency of the input pulse. An approximate expression for calculating group speeds corresponding to the shear mode and the bending mode, and also the cut-off frequency is obtained. Finally, we show that the cut-off frequency disappears for large in, for epsilon > 0 and increases for large in, for epsilon < 0.

Wave propagation analysis in laminated composite plates with transverse cracks using the wavelet spectral finite element method

This paper presents a newly developed wavelet spectral finite element (WFSE) model to analyze wave propagation in anisotropic composite laminate with a transverse surface crack penetrating part-through the thickness. The WSFE formulation of the composite laminate, which is based on the first-order shear deformation theory, produces accurate and computationally efficient results for high frequency wave motion. Transverse crack is modeled in wavenumber-frequency domain by introducing bending flexibility of the plate along crack edge. Results for tone burst and impulse excitations show excellent agreement with conventional finite element analysis in Abaqus (R). Problems with multiple cracks are modeled by assembling a number of spectral elements with cracks in frequency-wavenumber domain. Results show partial reflection of the excited wave due to crack at time instances consistent with crack locations. (C) 2014 Elsevier B.V. All rights reserved.

Diffusing-wave spectroscopy in an inhomogeneous object: Local viscoelastic spectra from ultrasound-assisted measurement of correlation decay arising from the ultrasound focal volume

We demonstrate diffusing-wave spectroscopy (DWS) in a localized region of a viscoelastically inhomogeneous object by measurement of the intensity autocorrelation g(2)(tau)] that captures only the decay introduced by the temperature-induced Brownian motion in the region. The region is roughly specified by the focal volume of an ultrasound transducer which introduces region specific mechanical vibration owing to insonification. Essential characteristics of the localized non-Markovian dynamics are contained in the decay of the modulation depth M(tau)], introduced by the ultrasound forcing in the focal volume selected, on g(2)(tau). The modulation depth M(tau(i)) at any delay time tau(i) can be measured by short-time Fourier transform of g(2)(tau) and measurement of the magnitude of the spectrum at the ultrasound drive frequency. By following the established theoretical framework of DWS, we are able to connect the decay in M(tau) to the mean-squared displacement (MSD) of scattering centers and the MSD to G*(omega), the complex viscoelastic spectrum. A two-region composite polyvinyl alcohol phantom with different viscoelastic properties is selected for demonstrating local DWS-based recovery of G*(omega) corresponding to these regions from the measured region specific M(tau(i))vs tau(i). The ultrasound-assisted measurement of MSD is verified by simulating, using a generalized Langevin equation (GLE), the dynamics of the particles in the region selected as well as by the usual DWS experiment without the ultrasound. It is shown that whereas the MSD obtained by solving the GLE without the ultrasound forcing agreed with its experimental counterpart covering small and large values of tau, the match was good only in the initial transients in regard to experimental measurements with ultrasound.

Role of Crosslinking and Entanglements in the Mechanics of Silicone Networks

The goal of this study is to investigate the applicability of different constitutive models for silicone networks using comprehensive multiaxial experimental tests, including non-equibiaxial mechanical tests which introduce differential constraints on the networks in the two orthogonal directions, on samples prepared using various crosslinking densities. Uniaxial stress-strain experiments show that a decrease in crosslinker amounts used in the preparation of silicone networks lead to more compliant material response as compared to that obtained using higher amounts of crosslinker. Biaxial data were used to obtain fits to the neo- Hookean, Mooney-Rivlin, Arruda-Boyce and the Edward-Vilgis slip-link constitutive models. Our results show that the slip-link model, based on separation of the individual contributions of chemical crosslinks and physical entanglements, is better at describing the stress-strain response of highly crosslinked networks at low stretches as compared to other constitutive models. Modulus obtained using the slip-link model for highly crosslinked networks agrees with experimentally determined values obtained using uniaxial tension experiments. In contrast, moduli obtained using coefficients to the other constitutive models underpredict experimentally determined moduli by over 40 %. However, the slip-link model did not predict the experimentally observed stiffening response at higher stretches which was better captured using the Arruda-Boyce model.

Shear-imposed falling film

The study of a film falling down an inclined plane is revisited in the presence of imposed shear stress. Earlier studies regarding this topic (Smith, J. Fluid Mech., vol. 217, 1990, pp. 469-485; Wei, Phys. Fluids, vol. 17, 2005a, 012103), developed on the basis of a low Reynolds number, are extended up to moderate values of the Reynolds number. The mechanism of the primary instability is provided under the framework of a two-wave structure, which is normally a combination of kinematic and dynamic waves. In general, the primary instability appears when the kinematic wave speed exceeds the speed of dynamic waves. An equality criterion between their speeds yields the neutral stability condition. Similarly, it is revealed that the nonlinear travelling wave solutions also depend on the kinematic and dynamic wave speeds, and an equality criterion between the speeds leads to an analytical expression for the speed of a family of travelling waves as a function of the Froude number. This new analytical result is compared with numerical prediction, and an excellent agreement is achieved. Direct numerical simulations of the low-dimensional model have been performed in order to analyse the spatiotemporal behaviour of nonlinear waves by applying a constant shear stress in the upstream and downstream directions. It is noticed that the presence of imposed shear stress in the upstream (downstream) direction makes the evolution of spatially growing waves weaker (stronger).

Nonclassical Paths in Quantum Interference Experiments

In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.

Dynamic Site Characterization and Correlation of Shear Wave Velocity with Standard Penetration Test `N' Values for the City of Agartala, Tripura State, India

Seismic site characterization is the basic requirement for seismic microzonation and site response studies of an area. Site characterization helps to gauge the average dynamic properties of soil deposits and thus helps to evaluate the surface level response. This paper presents a seismic site characterization of Agartala city, the capital of Tripura state, in the northeast of India. Seismically, Agartala city is situated in the Bengal Basin zone which is classified as a highly active seismic zone, assigned by Indian seismic code BIS-1893, Indian Standard Criteria for Earthquake Resistant Design of Structures, Part-1 General Provisions and Buildings. According to the Bureau of Indian Standards, New Delhi (2002), it is the highest seismic level (zone-V) in the country. The city is very close to the Sylhet fault (Bangladesh) where two major earthquakes (M (w) > 7) have occurred in the past and affected severely this city and the whole of northeast India. In order to perform site response evaluation, a series of geophysical tests at 27 locations were conducted using the multichannel analysis of surface waves (MASW) technique, which is an advanced method for obtaining shear wave velocity (V (s)) profiles from in situ measurements. Similarly, standard penetration test (SPT-N) bore log data sets have been obtained from the Urban Development Department, Govt. of Tripura. In the collected data sets, out of 50 bore logs, 27 were selected which are close to the MASW test locations and used for further study. Both the data sets (V (s) profiles with depth and SPT-N bore log profiles) have been used to calculate the average shear wave velocity (V (s)30) and average SPT-N values for the upper 30 m depth of the subsurface soil profiles. These were used for site classification of the study area recommended by the National Earthquake Hazard Reduction Program (NEHRP) manual. The average V (s)30 and SPT-N classified the study area as seismic site class D and E categories, indicating that the city is susceptible to site effects and liquefaction. Further, the different data set combinations between V (s) and SPT-N (corrected and uncorrected) values have been used to develop site-specific correlation equations by statistical regression, as `V (s)' is a function of SPT-N value (corrected and uncorrected), considered with or without depth. However, after considering the data set pairs, a probabilistic approach has also been presented to develop a correlation using a quantile-quantile (Q-Q) plot. A comparison has also been made with the well known published correlations (for all soils) available in the literature. The present correlations closely agree with the other equations, but, comparatively, the correlation of shear wave velocity with the variation of depth and uncorrected SPT-N values provides a more suitable predicting model. Also the Q-Q plot agrees with all the other equations. In the absence of in situ measurements, the present correlations could be used to measure V (s) profiles of the study area for site response studies.

Improved quasiparticle wave functions and mean field for G(0)W(0) calculations: Initialization with the COHSEX operator

The GW approximation to the electron self-energy has become a standard method for ab initio calculation of excited-state properties of condensed-matter systems. In many calculations, the G W self-energy operator, E, is taken to be diagonal in the density functional theory (DFT) Kohn-Sham basis within the G0 W0 scheme. However, there are known situations in which this diagonal Go Wo approximation starting from DFT is inadequate. We present two schemes to resolve such problems. The first, which we called sc-COHSEX-PG W, involves construction of an improved mean field using the static limit of GW, known as COHSEX (Coulomb hole and screened exchange), which is significantly simpler to treat than GW W. In this scheme, frequency-dependent self energy E(N), is constructed and taken to be diagonal in the COHSEX orbitals after the system is solved self-consistently within this formalism. The second method is called off diagonal-COHSEX G W (od-COHSEX-PG W). In this method, one does not self-consistently change the mean-field starting point but diagonalizes the COHSEX Hamiltonian within the Kohn-Sham basis to obtain quasiparticle wave functions and uses the resulting orbitals to construct the G W E in the diagonal form. We apply both methods to a molecular system, silane, and to two bulk systems, Si and Ge under pressure. For silane, both methods give good quasiparticle wave functions and energies. Both methods give good band gaps for bulk silicon and maintain good agreement with experiment. Further, the sc-COHSEX-PGW method solves the qualitatively incorrect DFT mean-field starting point (having a band overlap) in bulk Ge under pressure.