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°.

Linear stability, transient growth and the role of viscosity stratification in compressible Couette flow

Linear stability and the nonmodal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the uniform shear flow with constant viscosity, and (b) the nonuniform shear flow with stratified viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers (M). For a given M, the critical Reynolds number (Re) is significantly smaller for the uniform shear flow than its nonuniform shear counterpart; for a given Re, the dominant instability (over all streamwise wave numbers, α) of each mean flow belongs to different modes for a range of supersonic M. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean flow to perturbations. It is shown that the energy transfer from mean flow occurs close to the moving top wall for “mode I” instability, whereas it occurs in the bulk of the flow domain for “mode II.” For the nonmodal transient growth analysis, it is shown that the maximum temporal amplification of perturbation energy, Gmax, and the corresponding time scale are significantly larger for the uniform shear case compared to those for its nonuniform counterpart. For α=0, the linear stability operator can be partitioned into L∼L̅ +Re2 Lp, and the Re-dependent operator Lp is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: G(t∕Re)∼Re2. In contrast, the dominance of Lp is responsible for the invalidity of this scaling law in nonuniform shear flow. An inviscid reduced model, based on Ellingsen-Palm-type solution, has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and nonmodal instability, it is shown that the viscosity stratification of the underlying mean flow would lead to a delayed transition in compressible Couette flow.

Synthesis, Structure, Negative Thermal Expansion, and Photocatalytic Property of Mo Doped ZrV(2)O(7)

A new series of compounds identified in the phase diagram of ZrO(2)-V(2)O(8)-MoO(3) have been synthesized via the solution combustion method. Single crystals of one of the compounds in the series, ZrV(1.50)Mo(0.50)O(7.25), were grown by the melt-cool technique from the starting materials with double the MoO(3) quantity. The room temperature average crystal structure of the grown crystals was solved using the single crystal X-ray diffraction technique. The crystals belong to the cubic crystal system, space group Pa (3) over bar (No. 205) with a = 8.8969 (4) angstrom, V = 704.24 (6) angstrom(3), and Z = 4. The final R(1) value of 0.0213 was achieved for 288 independent reflections during the structure refinement. The Zr(4+) occupies the special position (4a) whereas V(5+) and Mo(6+) occupy two unique (8c) Wyckoff positions. Two fully occupied O atoms, (24d) and (4b), one partially occupied 0 atom (8c) have been identified for this molybdovanadate, which is a unique feature for these crystals. The structure is related to both ZrV(2)O(7) and cubic ZrMo(2)O(8). The temperature dependent single crystal studies show negative thermal expansion above 370 K. The compounds have been characterized by powder X-ray diffraction, solid-state UV-vis diffuse reflectance spectra, scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The photocatalytic activity of these compounds has been investigated for the degradation of various dyes, and these compounds show specificity toward the degradation of non-azoic dyes.

Generalized asymptotic expansions for the wavenumbers in infinite flexible in vacuo orthotropic cylindrical shells

Analytical expressions are found for the wavenumbers and resonance frequencies in flexible, orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders n. The Donnell-Mushtari shell theory is used to model the dynamics of the cylindrical shell. Initially, an in vacuo cylindrical isotropic shell is considered and expressions for all the wavenumbers (bending, near-field bending, longitudinal and torsional) are found. Subsequently, defining a suitable orthotropy parameter epsilon, the problem of wave propagation in an orthotropic shell is posed as a perturbation on the corresponding problem for an isotropic shell. Asymptotic expressions for the wavenumbers in the in vacuo orthotropic shell are then obtained by treating epsilon as an expansion parameter. In both cases (isotropy and orthotropy), a frequency-scaling parameter (eta) and Poisson's ratio (nu) are used to find elegant expansions in the different frequency regimes. The asymptotic expansions are compared with numerical solutions in each of the cases and the match is found to be good. The main contribution of this work lies in the extension of the existing literature by developing closed-form expressions for wavenumbers with arbitrary circumferential orders n in the case of both, isotropic and orthotropic shells. Finally, we present natural frequency expressions in finite shells (isotropic and orthotropic) for the axisymmetric mode and compare them with numerical and ANSYS results. Here also, the comparison is found to be good. (C) 2011 Elsevier Ltd. All rights reserved.

Model track studies on fouled ballast using ground penetrating radar and multichannel analysis of surface wave

Ballast fouling is created by the breakdown of aggregates or outside contamination by coal dust from coal trains, or from soil intrusion beneath rail track. Due to ballast fouling, the conditions of rail track can be deteriorated considerably depending on the type of fouling material and the degree of fouling. So far there is no comprehensive guideline available to identify the critical degree of fouling for different types of fouling materials. This paper presents the identification of degree of fouling and types of fouling using non-destructive testing, namely seismic surface-wave and ground penetrating radar (GPR) survey. To understand this, a model rail track with different degree of fouling has been constructed in Civil engineering laboratory, University of Wollongong, Australia. Shear wave velocity obtained from seismic survey has been employed to identify the degree of fouling and types of fouling material. It is found that shear wave velocity of fouled ballast increases initially, reaches optimum fouling point (OFP), and decreases when the fouling increases. The degree of fouling corresponding after which the shear wave velocity of fouled ballast will be smaller than that of clean ballast is called the critical fouling point (CFP). Ground penetrating radar with four different ground coupled antennas (500 MHz, 800 MHz, 1.6 GHz and 2.3 GHz) was also used to identify the ballast fouling condition. It is found that the 800 MHz ground coupled antenna gives a better signal in assessing the ballast fouling condition. Seismic survey is relatively slow when compared to GPR survey however it gives quantifiable results. In contrast, GPR survey is faster and better in estimating the depth of fouling. (C) 2011 Elsevier B.V. All rights reserved.

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.