Modeling and analysis of a tunable piezoelectric structure for transverse shear wave generation

An analytical investigation of the transverse shear wave mode tuning with a resonator mass (packing mass) on a Lead Zirconium Titanate (PZT) crystal bonded together with a host plate and its equivalent electric circuit parameters are presented. The energy transfer into the structure for this type of wave modes are much higher in this new design. The novelty of the approach here is the tuning of a single wave mode in the thickness direction using a resonator mass. First, a one-dimensional constitutive model assuming the strain induced only in the thickness direction is considered. As the input voltage is applied to the PZT crystal in the thickness direction, the transverse normal stress distribution induced into the plate is assumed to have parabolic distribution, which is presumed as a function of the geometries of the PZT crystal, packing mass, substrate and the wave penetration depth of the generated wave. For the PZT crystal, the harmonic wave guide solution is assumed for the mechanical displacement and electric fields, while for the packing mass, the former is solved using the boundary conditions. The electromechanical characteristics in terms of the stress transfer, mechanical impedance, electrical displacement, velocity and electric field are analyzed. The analytical solutions for the aforementioned entities are presented on the basis of varying the thickness of the PZT crystal and the packing mass. The results show that for a 25% increase in the thickness of the PZT crystal, there is ~38% decrease in the first resonant frequency, while for the same change in the thickness of the packing mass, the decrease in the resonant frequency is observed as ~35%. Most importantly the tuning of the generated wave can be accomplished with the packing mass at lower frequencies easily. To the end, an equivalent electric circuit, for tuning the transverse shear wave mode is analyzed.

Fracture analysis of stiffened panels under combined tensile, bending, and shear loads

The objective is to present the formulation of numerically integrated modified virtual crack closure integral technique for concentrically and eccentrically stiffened panels for computation of strain-energy release rate and stress intensity factor based on linear elastic fracture mechanics principles. Fracture analysis of cracked stiffened panels under combined tensile, bending, and shear loads has been conducted by employing the stiffened plate/shell finite element model, MQL9S2. This model can be used to analyze plates with arbitrarily located concentric/eccentric stiffeners, without increasing the total number of degrees of freedom, of the plate element. Parametric studies on fracture analysis of stiffened plates under combined tensile and moment loads have been conducted. Based on the results of parametric,studies, polynomial curve fitting has been carried out to get best-fit equations corresponding to each of the stiffener positions. These equations can be used for computation of stress intensity factor for cracked stiffened plates subjected to tensile and moment loads for a given plate size, stiffener configuration, and stiffener position without conducting finite element analysis.

Approximate solutions for the structure of shock waves

Approximate solutions of the B-G-K model equation are obtained for the structure of a plane shock, using various moment methods and a least squares technique. Comparison with available exact solution shows that while none of the methods is uniformly satisfactory, some of them can provide accurate values for the density slope shock thickness delta n . A detailed error analysis provides explanations for this result. An asymptotic analysis of delta n for largeMach numbers shows that it scales with theMaxwell mean free path on the hot side of the shock, and that their ratio is relatively insensitive to the viscosity law for the gas.

Influence of External Light Waves on the Thermoelectric Power Under Strong Magnetic Field in Ultrathin Films, Quantum Wires and Quantum Dots of Optoelectronic Materials

In this paper, an attempt is made to study the influence of external light waves on the thermoelectric power under strong magnetic field (TPSM) in ultrathin films (UFs), quantum wires (QWs) and quantum dots (QDs) of optoelectronic materials whose unperturbed dispersion relation of the conduction electrons are defined by three and two band models of Kane together with parabolic energy bands on the basis of newly formulated electron dispersion laws in each case. We have plotted the TPSM as functions of film thickness, electron concentration, light intensity and wavelength for UFs, QWs and ODs of InSb, GaAs, Hg1-xCdxTe and In1-xGaxAsyP1-y respectively. It appears from the figures that for UFs, the TPSM increases with increasing thickness in quantum steps, decreases with increasing electron degeneracy exhibiting entirely different types of oscillations and changes with both light intensity and wavelength and these two latter types of plots are the direct signature of light waves on opto-TPSM. For QWs, the opto-TPSM exhibits rectangular oscillations with increasing thickness and shows enhanced spiky oscillations with electron concentration per unit length. For QDs, the opto-TPSM increases with increasing film thickness exhibiting trapezoidal variations which occurs during quantum jumps and the length and breadth of the trapezoids are totally dependent on energy band constants. Under the condition of non-degeneracy, the results of opto-TPSM gets simplified into the well-known form of classical TPSM equation which the function of three constants only and being invariant of the signature of band structure.

Polarographic and redox potential studies on copper(I) and copper(II) and their complexes. Part III. Copper (I and II)-ethylene diamine and edta complexes and theory of formation of step reduction waves in cupric copper systems

Polarographic and redox potential measurements on the cupric and cuprous complexes of ethylenediamine and EDTA have been carried out. From the ratio of the stability constants of the cupric and cuprous complexes, and the stability constant of the cupric complex, the stability constant of the cuprous-ethylenediamine complex is obtained. In the case of the EDTA complex it has been possible to obtain only βic/β2ous from the equilibrium concentrations of the cuprous and cupric complexes and the disproportionation constant. The inequalities for the appearance of step reduction waves have been given. The values of the stability constants of the cupric and cuprous complexes determined by the polarographic-redox potential method have been used to explain the appearance of step reduction waves in some systems and the non-appearance in other systems.

A note on the measurement of travel times using bender and extender elements

By using the bender and extender elements tests, the travel times of the shear (S) and the primary (P) waves were measured for dry sand samples at different relative densities and effective confining pressures. Three methods of interpretations, namely, (i) the first time of arrival, (ii) the first peak to peak, and (iii) the cross-correlation method, were employed. All the methods provide almost a unique answer associated with the P-wave measurements. On contrary, a difference was noted in the arrival times obtained from the different methods for the S-wave due to the near field effect. The resonant column tests in the torsional mode were also performed to check indirectly the travel time of the shear wave. The study reveals that as compared to the S-wave, it is more reliable to depend on the arrival times' measurement for the P-wave. (C) 2010 Elsevier Ltd. All rights reserved.

A note on the measurement of travel times using bender and extender elements

By using the bender and extender elements tests, the travel times of the shear (S) and the primary (P) waves were measured for dry sand samples at different relative densities and effective confining pressures. Three methods of interpretations, namely, (i) the first time of arrival, (ii) the first peak to peak, and (iii) the cross-correlation method, were employed. All the methods provide almost a unique answer associated with the P-wave measurements. On contrary, a difference was noted in the arrival times obtained from the different methods for the S-wave due to the near field effect. The resonant column tests in the torsional mode were also performed to check indirectly the travel time of the shear wave. The study reveals that as compared to the S-wave, it is more reliable to depend on the arrival times’ measurement for the P-wave.

Effect of relative density and confining pressure on Poisson ratio from bender and extender elements tests

By using the bender and extender elements tests, together with measurements of the travel times of shear (S) and primary (P) waves, the variation of Poisson ratio (nu) was determined for dry sands with respect to changes in relative densities and effective confining pressures (sigma(3)). The tests were performed for three different ranges of particle sizes. The magnitude of the Poisson ratio decreases invariably with an increase in both the relative density and the effective confining pressure. The effect of the confining pressure on the Poisson ratio was found to become relatively more significant for fine-grained sand as compared with the coarse-grained sand. For a given material, at a particular value of sigma(3), the magnitude of the Poisson ratio decreases, almost in a linear fashion, with an increase in the value of maximum shear modulus (G(max)). The two widely used correlations in literature, providing the relationships among G(max), void ratio (e) and effective confining pressure (sigma(3)), applicable for angular granular materials, were found to compare reasonably well with the present experimental data for the fine- and medium-grained sands. However, for the coarse-grained sand, these correlations tend to overestimate the values of G(max).

Relationship between Low Strain Shear Modulus and Standard Penetration Test N Values

A low strain shear modulus plays a fundamental role in the estimation of site response parameters In this study an attempt has been made to develop the relationships between standard penetration test (SPT) N values with the low strain shear modulus (G(max)) For this purpose, field experiments SPT and multichannel analysis of surface wave data from 38 locations in Bangalore, India, have been used, which were also used for seismic microzonation project The in situ density of soil layer was evaluated using undisturbed soil samples from the boreholes Shear wave velocity (V-s) profiles with depth were obtained for the same locations or close to the boreholes The values for low strain shear modulus have been calculated using measured V-s and soil density About 215 pairs of SPT N and G(max) values are used for regression analysis The differences between fitted regression relations using measured and corrected values were analyzed It is found that an uncorrected value of N and modulus gives the best fit with a high regression coefficient when compared to corrected N and corrected modulus values This study shows better correlation between measured values of N and G(max) when compared to overburden stress corrected values of N and G(max)

Anomalous behavior of hydrodynamic modes in the two dimensional shear flow of a granular material

The growth rates of the hydrodynamic modes in the homogeneous sheared state of a granular material are determined by solving the Boltzmann equation. The steady velocity distribution is considered to be the product of the Maxwell Boltzmann distribution and a Hermite polynomial expansion in the velocity components; this form is inserted into them Boltzmann equation and solved to obtain the coeificients of the terms in the expansion. The solution is obtained using an expansion in the parameter epsilon =(1 - e)(1/2), and terms correct to epsilon(4) are retained to obtain an approximate solution; the error due to the neglect of higher terms is estimated at about 5% for e = 0.7. A small perturbation is placed on the distribution function in the form of a Hermite polynomial expansion for the velocity variations and a Fourier expansion in the spatial coordinates: this is inserted into the Boltzmann equation and the growth rate of the Fourier modes is determined. It is found that in the hydrodynamic limit, the growth rates of the hydrodynamic modes in the flow direction have unusual characteristics. The growth rate of the momentum diffusion mode is positive, indicating that density variations are unstable in the limit k--> 0, and the growth rate increases proportional to kslash} k kslash}(2/3) in the limit k --> 0 (in contrast to the k(2) increase in elastic systems), where k is the wave vector in the flow direction. The real and imaginary parts of the growth rate corresponding to the propagating also increase proportional to kslash k kslash(2/3) (in contrast to the k(2) and k increase in elastic systems). The energy mode is damped due to inelastic collisions between particles. The scaling of the growth rates of the hydrodynamic modes with the wave vector I in the gradient direction is similar to that in elastic systems. (C) 2000 Elsevier Science B.V. All rights reserved.

Trapped waves in the neighborhood of a sonic-type singularity

A model equation is derived to study trapped nonlinear waves with a turning effect, occurring in disturbances induced on a two-dimensional steady flow. Only unimodal disturbances under the short wave assumption are considered, when the wave front of the induced disturbance is plane. In the neighbourhood of certain special points of sonic-type singularity, the disturbances are governed by a single first-order partial differential equation in two independent variables. The equation depends on the steady flow through three parameters, which are determined by the variations of velocity and depth, for example (in the case of long surface water waves), along and perpendicular to the wave front. These parameters help us to examine various relative effects. The presence of shocks in a continuously accelerating or decelerating flow has been studied in detail.

A Note on Diffraction of Water Waves by a Nearly Vertical Barrier

A simplified perturbational analysis is employed, together with the application of Green's theorem, to determine the first-order corrections to the reflection and transmission coefficients in the problem of diffraction of surface water waves by a nearly vertical barrier in two basically important cases: (i) when the barrier is partially immersed and (ii) when the barrier is completely submerged. The present analysis produces the desired results fairly easily and relatively quickly as compared with the known integral equation approach to this class of diffraction problems.

Evolution and decay of cylindrical and spherical nonlinear acoustic waves generated by a sinusoidal source

The present work gives a comprehensive numerical study of the evolution and decay of cylindrical and spherical nonlinear acoustic waves generated by a sinusoidal source. Using pseudospectral and predictor–corrector implicit finite difference methods, we first reproduced the known analytic results of the plane harmonic problem to a high degree of accuracy. The non-planar harmonic problems, for which the amplitude decay is faster than that for the planar case, are then treated. The results are correlated with the known asymptotic results of Scott (1981) and Enflo (1985). The constant in the old-age formula for the cylindrical canonical problem is found to be 1.85 which is rather close to 2, ‘estimated’ analytically by Enflo. The old-age solutions exhibiting strict symmetry about the maximum are recovered; these provide an excellent analytic check on the numerical solutions. The evolution of the waves for different source geometries is depicted graphically.

Drained shear strength of fine-grained soil-solid surface interfaces

Herein are reported the results of an investigation on the effective angle of interfacial friction between fine-grained soils and solid surfaces as influenced by the roughness of the material surface, the soil type and the overconsolidation ratio. The ratio of interfacial friction angle to the angle of internal friction (evaluated at constant overconsolidation ratio) of the soil is independent of the overconsolidation ratio. An empirical correlation between this ratio and the roughness of the interface has been proposed.