Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

Quasi-simple wave solutions for acoustic gravity waves

The special class of quasi-simple wave solutions is studied for the system of partial differential equations governing inviscid acoustic gravity waves. It is shown that these traveling wave solutions do not admit shocks. Periodic solutions are found to exist when there is no propagation in the vertical direction. The solutions for some particular cases are depicted graphically. Physics of Fluids is copyrighted by The American Institute of Physics.

On plane-wave propagation in a uniform pipe in the presence of a mean flow and a temperature gradient

A theoretical study on the propagation of plane waves in the presence of a hot mean flow in a uniform pipe is presented. The temperature variation in the pipe is taken to be a linear temperature gradient along the axis. The theoretical studies include the formulation of a wave equation based on continuity, momentum, and state equation, and derivation of a general four-pole matrix, which is shown to yield the well-known transfer matrices for several other simpler cases.

Effects of environment on surface-wave characteristics of a dielectric-coated conductor .4.

The problem of excitation of 11zultilayercd-graded-dielectric-coatedc onductor by a magnetic ring source is fornzulated in the ,form of a contour integrul which is rolved by using the method of steepest descent. Numerical evaluation of launching efiiency shows that high value of about 90 percent can be attained by choosing proper dimensions of the launcher with respect to the dimension of the surface wave line.

A Control Strategy for Reference Wave Adaptive Current Generation

Speed control of ac motors requires variable frequency, variable current, or variable voltage supply. Variable frequency supply can be obtained directly from a fixed frequency supply by using a frequency converter or from a dc source using inverters. In this paper a control technique for reference wave adaptive-current generation by modulating the inverter voltage is explained. Extension of this technique for three-phase induction-motor speed control is briefly explained. The oscillograms of the current waveforms obtained from the experimental setup are also shown.

The pulse response of non-linear third order systems

The response of a third order non-linear system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form in which the method of variation of parameters is applicable for the solution of the problem. The method is applied to a single axis gyrostabilized platform subjected to an exponentially decaying pulse. The analytical results are compared with digital and analog computer solutions.

Expansion of high pressure gas into air - A more realistic blast wave model

In this paper, we consider a more realistic model of a spherical blast wave of moderate strength. An arbitrary number of terms for the series solution in each of the regions behind the main shock - the expansion region, the nearly uniform region outside the main expansion and the region between the contact surface and the main shock, have been generated and matched across the boundaries. We then study the convergence of the solution by using Pade approximation. It constitutes a genuine analytic solution for a moderately strong explosion, which, however, does not involve a secondary shock. The pressure distribution behind the shock however shows some significant changes in the location of the tail of the rarefaction and the interface, in comparison to the planar problem. The theory developed for the spherical blasts is also extended to cylindrical blasts. The results are compared with the numerical solution.

Development of Very High Frequency Damped Sine Wave Generator

In order to protect the critical electronic equipment/system against damped sine transient currents induced into its cables due to transient electromagnetic fields, switching phenomena, platform resonances, etc. it is necessary to provide proper hardening. The hardness assurance provided can be evaluated as per the test CS 116 of MIL STD 461E/F in laboratory by generating & inducing the necessary damped sine currents into the cables of the Equipment Under Test (EUT). The need and the stringent requirements for building a damped sine wave current generator for generation of damped sine current transients of very high frequencies (30 MHz & 100 MHz) have been presented. A method using LC discharge for the generation has been considered in the development. This involves building of extremely low & nearly loss less inductors (about 5 nH & 14 nH) as well as a capacitor & a switch with much lower inductances. A technique for achieving this has been described. Two units (I No for 30 MHz. & 100 MHz each) have been built. Experiments to verify the output are being conducted.

Spiral-Wave Turbulence and Its Control in the Presence of Inhomogeneities in Four Mathematical Models of Cardiac Tissue

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control chemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation.

Nonlocal scale effects on wave propagation in multi-walled carbon nanotubes

This paper represents the effect of nonlocal scale parameter on the wave propagation in multi-walled carbon nanotubes (MWCNTs). Each wall of the MWCNT is modeled as first order shear deformation beams and the van der Waals interactions between the walls are modeled as distributed springs. The studies shows that the scale parameter introduces certain band gap region in both flexural and shear wave mode where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite (or group speed tends to zero). The frequency at which this phenomenon occurs is called the ``Escape frequency''. The analysis shows that, for a given N-walled carbon nanotube (CNT). the nonlocal scaling parameter has a significant effect on the shear wave modes of the N - 1 walls. The escape frequencies of the flexural and shear wave modes of the N-walls are inversely proportionl to the nonlocal scaling parameter. It is also shown that the cut-off frequencies are independent of the nonlocal scale parameter. (C) 2009 Elsevier B.V. All rights reserved.

Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements

This paper presents a formulation of an approximate spectral element for uniform and tapered rotating Euler-Bernoulli beams. The formulation takes into account the varying centrifugal force, mass and bending stiffness. The dynamic stiffness matrix is constructed using the weak form of the governing differential equation in the frequency domain, where two different interpolating functions for the transverse displacement are used for the element formulation. Both free vibration and wave propagation analysis is performed using the formulated elements. The studies show that the formulated element predicts results, that compare well with the solution available in the literature, at a fraction of the computational effort. In addition, for wave propagation analysis, the element shows superior convergence. (C) 2007 Elsevier Ltd. All rights reserved.

Vave propagation and bandgaps in a parametrically modulated composite laminate

Wave propagation and its frequency bandgaps in a parametrically modulated composite laminate are reported in this paper. The modulated properties under considerations are due to periodic microstructure, for example honeycomb core sandwich composite, which can be parameterized and homogenized in a suitable scale. Wave equations are derived by assuming a third-order shear deformation theory. Homogenization of the wave equations is carried out in the scale of wavelength. In-plane wave and flexural-shear wave dispersions are obtained for a range of values of a stiffness modulation coefficient (alpha). A clear pattern of stop-bands is observed for alpha >= 4. To validate the band-gap phenomena, we take recourse to time domain response obtained from finite element simulation. As predicted by the proposed analytical technique, a distinct correlation between the chosen frequency band and the simulated wave arrival time and amplitude reduction is found. This promises practical applications of the proposed analytical technique to designing parametrically modulated composite laminate for wave suppression. (C) 2009 Elsevier B.V. All rights reserved.

Inverted slot-mode slow-wave structures for traveling-wave tubes

The dispersion and impedance characteristics of an inverted slot-mode (ISM) slow-wave structure computed by three different techniques, i.e., an analytical model based on a periodic quasi-TEM approach, an equivalent-circuit model, and 3-D electromagnetic simulation are obtained and compared. The comparison was carried out for three different slot-mode structures at S-, C-, and X-bands. The approach was also validated with experimental measurements on a practical X-band ISM traveling-wave tube. The design of ferruleless ISM slow-wave structures, both in circular and rectangular formats, has also been proposed and the predicted dispersion characteristics for these two geometries are compared with 3-D simulation and cold-test measurements. The impedance characteristics for all three designs are also compared.

Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind–Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.