Ultrasonic wave characteristics of a monolayer graphene on silicon substrate

The present work deals with an ultrasonic type of wave propagation characteristics of monolayer graphene on silicon (Si) substrate. An atomistic model of a hybrid lattice involving a hexagonal lattice of graphene and surface atoms of diamond lattice of Si is developed to identify the carbon-silicon bond stiffness. Properties of this hybrid lattice model is then mapped into a nonlocal continuum framework. Equivalent force constant due to Si substrate is obtained by minimizing the total potential energy of the system. For this equilibrium configuration, the nonlocal governing equations are derived to analyze the ultrasonic wave dispersion based on spectral analysis. From the present analysis we show that the silicon substrate affects only the flexural wave mode. The frequency band gap of flexural mode is also significantly affected by this substrate. The results also show that, the silicon substrate adds cushioning effect to the graphene and it makes the graphene more stable. The analysis also show that the frequency bang gap relations of in-plane (longitudinal and lateral) and out-of-plane (flexural) wave modes depends not only on the y-direction wavenumber but also on nonlocal scaling parameter. In the nonlocal analysis, at higher values of the y-directional wavenumber, a decrease in the frequency band gap is observed for all the three fundamental wave modes in the graphene-silicon system. The atoms movement in the graphene due to the wave propagation are also captured for all the tree fundamental wave modes. The results presented in this work are qualitatively different from those obtained based on the local analysis and thus, are important for the development of graphene based nanodevices such as strain sensor, mass and pressure sensors, atomic dust detectors and enhancer of surface image resolution that make use of the ultrasonic wave dispersion properties of graphene. (C) 2011 Elsevier Ltd. All rights reserved.

Lamb wave based identification and parameter estimation of corrosion in metallic plate structure using a circular PWAS array

A circular array of Piezoelectric Wafer Active Sensor (PWAS) has been employed to detect surface damages like corrosion using lamb waves. The array consists of a number of small PWASs of 10 mm diameter and 1 mm thickness. The advantage of a circular array is its compact arrangement and large area of coverage for monitoring with small area of physical access. Growth of corrosion is monitored in a laboratory-scale set-up using the PWAS array and the nature of reflected and transmitted Lamb wave patterns due to corrosion is investigated. The wavelet time-frequency maps of the sensor signals are employed and a damage index is plotted against the damage parameters and varying frequency of the actuation signal (a windowed sine signal). The variation of wavelet coefficient for different growth of corrosion is studied. Wavelet coefficient as function of time gives an insight into the effect of corrosion in time-frequency scale. We present here a method to eliminate the time scale effect which helps in identifying easily the signature of damage in the measured signals. The proposed method becomes useful in determining the approximate location of the corrosion with respect to the location of three neighboring sensors in the circular array. A cumulative damage index is computed for varying damage sizes and the results appear promising.

Axial wave propagation in coupled nanorod system with nonlocal small scale effects

This article deals with the axial wave propagation properties of a coupled nanorod system with consideration of small scale effects. The nonlocal elasticity theory has been incorporated into classical rod/bar model to capture unique features of the coupled nanorods under the umbrella of continuum mechanics theory. Nonlocal rod model is developed for coupled nanorods. The strong effect of the nonlocal scale has been obtained which leads to substantially different wave behavior of nanorods from those of macroscopic rods. Explicit expressions are derived for wavenumber, cut-off frequency and escape frequency of nanorods. The analysis shows that the wave characteristics of nanorods are highly over estimated by the classical rod model, which ignores the effect of small-length scale. The studies also shows that the nonlocal scale parameter introduces certain band gap region in axial or longitudinal wave mode, where no wave propagation occurs. This is manifested in the spectrum cures as the region, where the wavenumber tends to infinite or wave speed tends to zero. The effect of the coupled spring stiffness is also capture in the present analysis. It has been also shown that the cut-off frequency increases as the stiffness of the coupled spring increases and also the coupled spring stiffness has no effect on escape frequency of the axial wave mode in the nanorod. This cut-off frequency is also independent of the nonlocal small scale parameter. The present study may bring in helpful insights while investigating multiple-nanorod-system-models for future nano-optomechanical systems applications. The results can also provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of coupled single-walled carbon nanotubes or coupled nanorods. (C) 2011 Elsevier Ltd. All rights reserved.

Wave dispersion in a cellular composite with modulated microstructure

In this paper we report a modeling technique and analysis of wave dispersion in a cellular composite laminate with spatially modulated microstructure, which can be modeled by parameterization and homogenization in an appropriate length scale. Higher order beam theory is applied and the system of wave equations are derived. Homogenization of these equations are carried out in the scale of wavelength and frequency of the individual wave modes. Smaller scale scattering below the order of cell size are filtered out in the present approach. The longitudinal dispersion relations for different values of a modulation parameter are analyzed which indicates the existence of stop and pass band patterns. Dispersion relations for flexural-shear case are also analyzed which indicates a tendency toward forming the stop and pass bands for increasing values of a shear stiffness modulation parameter. The effect the phase angle (θ) of the incident wave indicates the existence more number of alternative stop bands and pass bands for θ = 45°.

Ultrasonic Lamb wave based monitoring of corrosion type of damage in plate using a circular array of piezoelectric transducers

In this paper we propose a concept and report experimental results based on a circular array of Piezoelectric Wafer Active Sensors (PWASs) for rapid localization and parametric identification of corrosion type damage in metallic plates. Implementation of this circular array of PWASs combines the use of ultrasonic Lamb wave propagation technique and an algorithm based on symmetry breaking in the signal pattern to locate and monitor the growth of a corrosion pit on a metallic plate. Wavelet time-frequency maps of the sensor signals are employed to obtain an insight regarding the effect of corrosion growth on the Lamb wave transmission in time-frequency scale. We present here a method to eliminate the time scale, which helps in identifying easily the signature of damage in the measured signals. The proposed method becomes useful in determining the approximate location of the damage with respect to the location of three neighboring sensors in the circular array. A cumulative damage index is computed from the wavelet coefficients for varying damage sizes and the results appear promising. Damage index is plotted against the damage parameters for frequency sweep of the excitation signal (a windowed sine signal). Results of corrosion damage are compared with circular holes of various sizes to demonstrate the applicability of present method to different types of damage. (C) 2011 Elsevier Ltd. All rights reserved.

Effect of pairing fluctuations on low-energy electronic spectra in cuprate superconductors

We describe here a minimal theory of tight-binding electrons moving on the square planar Cu lattice of the hole-doped cuprates and mixed quantum mechanically with their own Cooper pairs. The superconductivity occurring at the transition temperature T(c) is the long-range, d-wave symmetry phase coherence of these Cooper pairs. Fluctuations, necessarily associated with incipient long-range superconducting order, have a generic large-distance behavior near T(c). We calculate the spectral density of electrons coupled to such Cooper-pair fluctuations and show that features observed in angle resolved photoemission spectroscopy (ARPES) experiments on different cuprates above T(c) as a function of doping and temperature emerge naturally in this description. These include ``Fermi arcs'' with temperature-dependent length and an antinodal pseudogap, which fills up linearly as the temperature increases toward the pseudogap temperature. Our results agree quantitatively with experiment. Below T(c), the effects of nonzero superfluid density and thermal fluctuations are calculated and compared successfully with some recent ARPES experiments, especially the observed bending or deviation of the superconducting gap from the canonical d-wave form.

Hypersonic wave drag reduction in re-entry capsules using concentrated energy deposition

Experiments are carried out in a shock tunnel at a nominal Mach number of 5.75 in order to study the effect of concentrated energy deposition on the drag force experienced by a 120° blunt cone. Electrical energy was deposited along the stagnation streamline of the model using a high voltage DC discharge circuit (1.5 – 3.5KW) and the drag force was measured by a single component accelerometer balance. Numerical simulations were also carried complimenting the experiments. These simulations showed a substantial drag reduction (20% ~ 65%) whereas the experiments show no appreciable reduction in drag

Study of non-local wave properties of nanotubes with surface effects

In macroscopic and even microscopic structural elements, surface effects can be neglected and classical theories are sufficient. As the structural size decreases towards the nanoscale regime, the surface-to-bulk energy ratio increases and surface effects must be taken into account. In the present work, the terahertz wave dispersion characteristics of a nanotube are studied with consideration of the surface effects as well as the non-local small scale effects. Non-local elasticity theory is used to derive the general governing differential equation based on equilibrium approach to include those scale effects. Scale and surface property dependent wave characteristic equations are obtained via spectral analysis. For the present study the material properties of an anodic alumina nanotube with crystallographic of < 111 > direction are considered. The present analysis shows that the effect of surface properties (surface integrated residual stress and surface integrated modulus) on the flexural wave characteristics of anodic nanotubes are more significant. It has been found that the flexural wavenumbers with surface effects are high as compared to that without surface effects. It has also been shown that, with consideration of surface effects the flexural wavenumbers are under compressive nature. The effect of the small scale and the size of the nanotube on wave dispersion properties are also captured in the present work. (C) 2012 Elsevier B.V. All rights reserved.

A Revisit to Capture the Entire Behavior of Ultrasonic Wave Dispersion Characteristics of Single Walled Carbon Nanotubes Based on Nonlocal Elasticity Theory and Flugge Shell Model

In this paper, an ultrasonic wave propagation analysis in single-walled carbon nanotube (SWCNT) is re-studied using nonlocal elasticity theory, to capture the whole behaviour. The SWCNT is modeled using Flugge's shell theory, with the wall having axial, circumferential and radial degrees of freedom and also including small scale effects. Nonlocal governing equations for this system are derived and wave propagation analysis is also carried out. The revisited nonlocal elasticity calculation shows that the wavenumber tends to infinite at certain frequencies and the corresponding wave velocity tends to zero at those frequencies indicating localization and stationary behavior. This frequency is termed as escape frequency. This behavior is observed only for axial and radial waves in SWCNT. It has been shown that the circumferential waves will propagate dispersively at higher frequencies in nonlocality. The magnitudes of wave velocities of circumferential waves are smaller in nonlocal elasticity as compared to local elasticity. We also show that the explicit expressions of cut-off frequency depend on the nonlocal scaling parameter and the axial wavenumber. The effect of axial wavenumber on the ultrasonic wave behavior in SWCNTs is also discussed. The present results are compared with the corresponding results (for first mode) obtained from ab initio and 3-D elastodynamic continuum models. The acoustic phonon dispersion relation predicted by the present model is in good agreement with that obtained from literature. The results are new and can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of single-walled carbon nanotubes.

Spectral Element Approach to Wave Propagation in Uncertain Composite Beam Structures

This paper presents a study of the wave propagation responses in composite structures in an uncertain environment. Here, the main aim of the work is to quantify the effect of uncertainty in the wave propagation responses at high frequencies. The material properties are considered uncertain and the analysis is performed using Neumann expansion blended with Monte Carlo simulation under the environment of spectral finite element method. The material randomness is included in the conventional wave propagation analysis by different distributions (namely, the normal and the Weibul distribution) and their effect on wave propagation in a composite beam is analyzed. The numerical results presented investigates the effect of material uncertainties on different parameters, namely, wavenumber and group speed, which are relevant in the wave propagation analysis. The effect of the parameters, such as fiber orientation, lay-up sequence, number of layers, and the layer thickness on the uncertain responses due to dynamic impulse load, is thoroughly analyzed. Significant changes are observed in the high frequency responses with the variation in the above parameters, even for a small coefficient of variation. High frequency impact loads are applied and a number of interesting results are presented, which brings out the true effects of uncertainty in the high frequency responses. [DOI: 10.1115/1.4003945]

Ultrasonic Wave Dispersion Characteristics of Fluid-Filled Single-Walled Carbon Nanotubes Based on Nonclassical Shell Model

In this paper, ultrasonic wave propagation analysis in fluid filled single-walled carbon nanotube (SWCNT) is studied using nonlocal elasticity theory. The SWCNT is modeled using Flugge's shell theory, with the wall having axial, circumferential and radial degrees of freedom and also including small scale effects. The fluid inside the SWCNT is assumed as water. Nonlocal governing equations for this system are derived and wave propagation analysis is also carried out. The presence of fluid in SWCNT alters the ultrasonic wave dispersion behavior. The wavenumber and wave velocity are smaller in presence of fluid as compared to the empty SWCNT. The nonlocal elasticity calculation shows that the wavenumber tends to reach the continuum limit at certain frequencies and the corresponding wave velocity tends to zero at those frequencies indicating localization and stationary behavior. It has been shown that the circumferential. waves will propagate non-dispersively at higher frequencies in nonlocality. The magnitudes of wave velocities of circumferential waves are smaller in nonlocal elasticity as compared to local elasticity. We also show that the cut-off frequency depend on the nonlocal scaling parameter and also on the density of the fluid inside the SWCNT, and the axial wavenumber, as the fluid becomes denser the cut-off frequency decreases. The effect of axial wavenumber on the ultrasonic wave behavior in SWCNTS filled with water is also discussed.

Effect of Grain Size on Structural and Magnetic Properties of CuFe2O4 Nanograins Synthesized by Chemical Co-Precipitation

CuFe2O4 nanograins have been prepared by the chemical co-precipitation technique and calcined in the temperature range of 200-1200 degrees C for 3 h. A wide range of grain sizes has been observed in this sintering temperature range, which has been determined to be 4 to 56 nm. Formation of ferrite has also been confirmed by FTIR measurement through the presence of wide band near 600 and 430 cm(-1) for the samples in the as-dried condition. Systematic variation of wave number has been observed with the variation of the calcination temperature. B-H loops exhibit transition from superparamagnetic to ferrimagnetic state above the calcination temperature of 900 degrees C. Coercivity of the samples at lower calcination temperature of 900 degrees C reduces significantly and tends towards zero coercivity, which is suggestive of superparamagnetic transition for the samples sintered below this temperature. Frequency spectrum of the real and imaginary part of complex initial permeability have been measured for the samples calcined at different temperature, which shows wide range of frequency stability. Curie temperature, T-c has been measured from temperature dependence initial permeability at a fixed frequency of 100 kHz. Although there is small variation of T-c with sintering temperature, the reduction of permeability with temperature drastically reduce for lower sintering temperature, which is in conformity with the change of B-H loops with the variation of sintering temperatures.

Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler-Bernoulli beam theory

In the present work, the effect of longitudinal magnetic field on wave dispersion characteristics of equivalent continuum structure (ECS) of single-walled carbon nanotubes (SWCNT) embedded in elastic medium is studied. The ECS is modelled as an Euler-Bernoulli beam. The chemical bonds between a SWCNT and the elastic medium are assumed to be formed. The elastic matrix is described by Pasternak foundation model, which accounts for both normal pressure and the transverse shear deformation. The governing equations of motion for the ECS of SWCNT under a longitudinal magnetic field are derived by considering the Lorentz magnetic force obtained from Maxwell's relations within the frame work of nonlocal elasticity theory. The wave propagation analysis is performed using spectral analysis. The results obtained show that the velocity of flexural waves in SWCNTs increases with the increase of longitudinal magnetic field exerted on it in the frequency range: 0-20 THz. The present analysis also shows that the flexural wave dispersion in the ECS of SWCNT obtained by local and nonlocal elasticity theories differ. It is found that the nonlocality reduces the wave velocity irrespective of the presence of the magnetic field and does not influences it in the higher frequency region. Further it is found that the presence of elastic matrix introduces the frequency band gap in flexural wave mode. The band gap in the flexural wave is found to independent of strength of the longitudinal magnetic field. (C) 2011 Elsevier Inc. All rights reserved.

Nonlocal continuum mechanics formulation for axial, flexural, shear and contraction coupled wave propagation in single walled carbon nanotubes

This paper presents the effect of nonlocal scaling parameter on the coupled i.e., axial, flexural, shear and contraction, wave propagation in single-walled carbon nanotubes (SWCNTs). The axial and transverse motion of SWCNT is modeled based on first order shear deformation theory (FSDT) and thickness contraction. The governing equations are derived based on nonlocal constitutive relations and the wave dispersion analysis is also carried out. The studies shows that the nonlocal scale parameter introduces certain band gap region in all wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. Explicit expressions are derived for cut-off and escape frequencies of all waves in SWCNT. It is also shown that the cut-off frequencies of shear and contraction mode are independent of the nonlocal scale parameter. The results provided in this article are new and are useful guidance for the study and design of the next generation of nanodevices that make use of the coupled wave propagation properties of single-walled carbon nanotubes.

Nonlocal continuum mechanics based ultrasonic flexural wave dispersion characteristics of a monolayer graphene embedded in polymer matrix

Wave propagation in graphene sheet embedded in elastic medium (polymer matrix) has been a topic of great interest in nanomechanics of graphene sheets, where the equivalent continuum models are widely used. In this manuscript, we examined this issue by incorporating the nonlocal theory into the classical plate model. The influence of the nonlocal scale effects has been investigated in detail. The results are qualitatively different from those obtained based on the local/classical plate theory and thus, are important for the development of monolayer graphene-based nanodevices. In the present work, the graphene sheet is modeled as an isotropic plate of one-atom thick. The chemical bonds are assumed to be formed between the graphene sheet and the elastic medium. The polymer matrix is described by a Pasternak foundation model, which accounts for both normal pressure and the transverse shear deformation of the surrounding elastic medium. When the shear effects are neglected, the model reduces to Winkler foundation model. The normal pressure or Winkler elastic foundation parameter is approximated as a series of closely spaced, mutually independent, vertical linear elastic springs where the foundation modulus is assumed equivalent to stiffness of the springs. For this model, the nonlocal governing differential equations of motion are derived from the minimization of the total potential energy of the entire system. An ultrasonic type of flexural wave propagation model is also derived and the results of the wave dispersion analysis are shown for both local and nonlocal elasticity calculations. From this analysis we show that the elastic matrix highly affects the flexural wave mode and it rapidly increases the frequency band gap of flexural mode. The flexural wavenumbers obtained from nonlocal elasticity calculations are higher than the local elasticity calculations. The corresponding wave group speeds are smaller in nonlocal calculation as compared to local elasticity calculation. The effect of y-directional wavenumber (eta(q)) on the spectrum and dispersion relations of the graphene embedded in polymer matrix is also observed. We also show that the cut-off frequencies of flexural wave mode depends not only on the y-direction wavenumber but also on nonlocal scaling parameter (e(0)a). The effect of eta(q) and e(0)a on the cut-off frequency variation is also captured for the cases of with and without elastic matrix effect. For a given nanostructure, nonlocal small scale coefficient can be obtained by matching the results from molecular dynamics (MD) simulations and the nonlocal elasticity calculations. At that value of the nonlocal scale coefficient, the waves will propagate in the nanostructure at that cut-off frequency. In the present paper, different values of e(0)a are used. One can get the exact e(0)a for a given graphene sheet by matching the MD simulation results of graphene with the results presented in this article. (c) 2012 Elsevier Ltd. All rights reserved.