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.

Anomalous plasma heating by an intense laser beam

Heating of laser produced plasmas by an instability is investigated. For intense laser beams anomalous absorption is found. A comparison is made with the experiment.

Decomposition technique for composite signals

A new method for decomposition of compo,.~itsei gnals is presented. It is shown that high freyuency portion of composite signal spectrum possesses information on echo structure. The proposed technique does not assume the shape of basic wavelet and does not place any restrictions on the amplitudes and arrival times of echoes inm the composite signal. In the absence of noise any desirrd resolution can he obtained The effect of sampling rate and jFequency window function on echo resolutio.~ are di.wussed. Voiced speech segment is considered as an example of conzpxite sigrnl to demonstrate the application of the decomposition technique.

Use of transverse beam polarization to probe anomalous V V H interactions at a Linear Collider

We investigate use of transverse beam polarization in probing anomalous coupling of a Higgs boson to a pair of vector bosons, at the International Linear Collider (ILC). We consider the most general form of V V H (V = W/Z) vertex consistent with Lorentz invariance and investigate its effects on the process e(+)e(-) -> f (f) over barH, f being a light fermion. Constructing observables with definite C P and naive time reversal ((T) over tilde) transformation properties, we find that transverse beam polarization helps us to improve on the sensitivity of one part of the anomalous Z Z H Coupling that is odd under C P. Even more importantly it provides the possibility of discriminating from each other, two terms in the general Z Z H vertex, both of which are even under C P and (T) over bar. Use of transversebeam polarization when combined with information from unpolarized and linearly polarized beams therefore, allows one to have completely independent probes of all the different parts of a general ZZH vertex.

The hydrogen bond: a molecular beam microwave spectroscopist's view with a universal appeal

In this manuscript, we propose a criterion for a weakly bound complex formed in a supersonic beam to be characterized as a `hydrogen bonded complex'. For a `hydrogen bonded complex', the zero point energy along any large amplitude vibrational coordinate that destroys the orientational preference for the hydrogen bond should be significantly below the barrier along that coordinate so that there is at least one bound level. These are vibrational modes that do not lead to the breakdown of the complex as a whole. If the zero point level is higher than the barrier, the `hydrogen bond' would not be able to stabilize the orientation which favors it and it is no longer sensible to characterize a complex as hydrogen bonded. Four complexes, Ar-2-H2O, Ar-2-H2S, C2H4-H2O and C2H4-H2S, were chosen for investigations. Zero point energies and barriers for large amplitude motions were calculated at a reasonable level of calculation, MP2(full)/aug-cc-pVTZ, for all these complexes. Atoms in molecules (AIM) theoretical analyses of these complexes were carried out as well. All these complexes would be considered hydrogen bonded according to the AIM theoretical criteria suggested by Koch and Popelier for C-H center dot center dot center dot O hydrogen bonds (U. Koch and P. L. A. Popelier, J. Phys. Chem., 1995, 99, 9747), which has been widely and, at times, incorrectly used for all types of contacts involving H. It is shown that, according to the criterion proposed here, the Ar-2-H2O/H2S complexes are not hydrogen bonded even at zero kelvin and C2H4-H2O/H2S complexes are. This analysis can naturally be extended to all temperatures. It can explain the recent experimental observations on crystal structures of H2S at various conditions and the crossed beam scattering studies on rare gases with H2O and H2S.

Time reversal technique for health monitoring of metallic structure using Lamb waves

Time reversal active sensing using Lamb waves is investigated for health monitoring of a metallic structure. Experiments were conducted on an aluminum plate to study the time reversal behavior of A(0) and S-0 Lamb wave modes under narrow band and broad band pulse excitation. Damage in the form of a notch was introduced in the plate to study the changes in the characteristics of the time reversed Lamb wave modes experimentally. Time-frequency analysis of the time reversed signal was carried out to extract the damage information. A measure of damage based on wavelet transform was derived to quantify the hidden damage information in the time reversed signal. It has been shown that time reversal can be used to achieve temporal recompression of Lamb waves under broadband signal excitation. Further, the broad band excitation can also improve the resolution of the technique in detecting closely located defects. This is demonstrated by picking up the reflection of waves from the edge of the plate, from a defect close to the edge of the plate and from defects located near to each other. This study shows the effectiveness of Lamb wave time reversal for temporal recompression of dispersive Lamb waves for damage detection in health monitoring applications. (C) 2009 Elsevier B.V. All rights reserved.

High Resolution Surface Imaging Using a Carbon Nanotube Array with Pointed Height distribution

In this paper we discuss a new technique to image the surfaces of metallic substrates using field emission from a pointed array of carbon nanotubes (CNTs). We consider a pointed height distribution of the CNT array under a diode configuration with two side gates maintained at a negative potential to obtain a highly intense beam of electrons localized at the center of the array. The CNT array on a metallic substrate is considered as the cathode and the test substrate as the anode. Scanning the test Substrate with the cathode reveals that the field emission current is highly sensitive to the surface features with nanometer resolution. Surface features of semi-circular, triangular and rectangular geometries (projections and grooves) are considered for simulation. This surface scanning/mapping technique can be applied for surface roughness measurements with nanoscale accuracy. micro/nano damage detection, high precision displacement sensors, vibrometers and accelerometers. among other applications.

EIT as a tool to observe dual wavelength operation of a semiconductor laser

We propose a simplified technique for dual wavelength operation of an extended cavity semiconductor laser, and its characterization using electromagnetically induced transparency (EIT). In this laser cavity scheme light beam is made converging before it incidences on the cavity grating. The converging angle of the beam creates two longitudinal oscillating modes of resonating cavity. Frequency separation between the longitudinal modes are measured with the help of beat frequency generation in a photodiode and creating pair of EIT spectra in Rb vapor. The pair of EIT dips that are generated due to dual wavelength of this laser (that is used as control laser) can be used to estimate frequency difference between the generated wavelengths. Width of EIT spectra can be used to estimate line width of individual wavelength components.

A Novel Bandwidth Enhancement Technique for Cascode Amplifier

In this paper, a new technique is presented to increase the bandwidth for a single stage amplifier. Usually, -3 dB bandwidth of single stage amplifier is in few MHz. High output impedance and subsequent capacitive loading decrease the bandwidth of amplifier. The presented technique uses a load which itself acts as bandwidth enhancer. This high speed amplifier is designed on 180 nm CMOS technology, operates at 2.5 V power supply. This amplifier is succeeded by an output buffer to achieve a better linearity, high output swing and required output impedance for matching.

A one-step technique to prepare aligned arrays of carbon nanotubes

A simple effective pyrolysis technique has been developed to synthesize aligned arrays of multi-walled carbon nanotubes (MWCNTs) without using any carrier gas in a single-stage furnace at 700 °C. This technique eliminates nearly the entire complex and expensive machinery associated with other extensively used methods for preparation of CNTs such as chemical vapour deposition (CVD) and pyrolysis. Carbon source materials such as xylene, cyclohexane, camphor, hexane, toluene, pyridine and benzene have been pyrolyzed separately with the catalyst source material ferrocene to obtain aligned arrays of MWCNTs. The synthesized CNTs have been characterized by scanning electron microscopy (SEM), x-ray diffraction (XRD), transmission electron microscopy (TEM), thermogravimetric analysis (TGA) and Raman spectroscopy. In this technique, the need for the tedious and time-consuming preparation of metal catalysts and continuously fed carbon source material containing carrier gas can be avoided. This method is a single-step process where not many parameters are required to be monitored in order to prepare aligned MWCNTs. For the production of CNTs, the technique has great advantages such as low cost and easy operation.

Asymptotic analysis for the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell: The beam mode

Using asymptotics, the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell vibrating in the beam mode (viz. circumferential wave order n = 1) are studied. Initially, the uncoupled wavenumbers of the acoustic fluid and the cylindrical shell structure are discussed. Simple closed form expressions for the structural wavenumbers (longitudinal, torsional and bending) are derived using asymptotic methods for low- and high-frequencies. It is found that at low frequencies the cylinder in the beam mode behaves like a Timoshenko beam. Next, the coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic fluid, with an added fluid-loading term involving a parameter mu due to the coupling. An asymptotic expansion involving mu is substituted in this equation. Analytical expressions are derived for the coupled wavenumbers (as modifications to the uncoupled wavenumbers) separately for low- and high-frequency ranges and further, within each frequency range, for large and small values of mu. Only the flexural wavenumber, the first rigid duct acoustic cut-on wavenumber and the first pressure-release acoustic cut-on wavenumber are considered. The general trend found is that for small mu, the coupled wavenumbers are close to the in vacuo structural wavenumber and the wavenumbers of the rigid-acoustic duct. With increasing mu, the perturbations increase, until the coupled wavenumbers are better identified as perturbations to the pressure-release wavenumbers. The systematic derivation for the separate cases of small and large mu gives more insight into the physics and helps to continuously track the wavenumber solutions as the fluid-loading parameter is varied from small to large values. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. This method of asymptotics is simple to implement using a symbolic computation package (like Maple). (C) 2008 Elsevier Ltd. All rights reserved.

Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam

We explore an isoparametric interpolation of total quaternion for geometrically consistent, strain-objective and path-independent finite element solutions of the geometrically exact beam. This interpolation is a variant of the broader class known as slerp. The equivalence between the proposed interpolation and that of relative rotation is shown without any recourse to local bijection between quaternions and rotations. We show that, for a two-noded beam element, the use of relative rotation is not mandatory for attaining consistency cum objectivity and an appropriate interpolation of total rotation variables is sufficient. The interpolation of total quaternion, which is computationally more efficient than the one based on local rotations, converts nodal rotation vectors to quaternions and interpolates them in a manner consistent with the character of the rotation manifold. This interpolation, unlike the additive interpolation of total rotation, corresponds to a geodesic on the rotation manifold. For beam elements with more than two nodes, however, a consistent extension of the proposed quaternion interpolation is difficult. Alternatively, a quaternion-based procedure involving interpolation of relative rotations is proposed for such higher order elements. We also briefly discuss a strategy for the removal of possible singularity in the interpolation of quaternions, proposed in [I. Romero, The interpolation of rotations and its application to finite element models of geometrically exact rods, Comput. Mech. 34 (2004) 121–133]. The strain-objectivity and path-independence of solutions are justified theoretically and then demonstrated through numerical experiments. This study, being focused only on the interpolation of rotations, uses a standard finite element discretization, as adopted by Simo and Vu-Quoc [J.C. Simo, L. Vu-Quoc, A three-dimensional finite rod model part II: computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79–116]. The rotation update is achieved via quaternion multiplication followed by the extraction of the rotation vector. Nodal rotations are stored in terms of rotation vectors and no secondary storages are required.

Dynamics and control of buckling type devices using SMA wire integrated beam

An analysis and design study using Shape Memory Alloy (SMA) wire integrated beam and its buckling shape control are reported. The dynamical system performance is analyzed with a mathematical set-up involving nonlocal and rate sensitive kinetics of phase transformation in the SMA wire. A standard phenomenological constitutive model reported by Brinson (1993) is modified by considering certain consistency conditions in the material property tensors and by eliminating spurious singularity. Considering the inhomogeneity effects, a finite element model of the SMA wire is developed. Simulations are carried out to study the buckling shape control of a beam integrated with SMA wire.

Testing and Modeling of MR Damper and Its Application to SDOF Systems Using Integral Backstepping Technique

Magnetorheological dampers are intrinsically nonlinear devices, which make the modeling and design of a suitable control algorithm an interesting and challenging task. To evaluate the potential of magnetorheological (MR) dampers in control applications and to take full advantages of its unique features, a mathematical model to accurately reproduce its dynamic behavior has to be developed and then a proper control strategy has to be taken that is implementable and can fully utilize their capabilities as a semi-active control device. The present paper focuses on both the aspects. First, the paper reports the testing of a magnetorheological damper with an universal testing machine, for a set of frequency, amplitude, and current. A modified Bouc-Wen model considering the amplitude and input current dependence of the damper parameters has been proposed. It has been shown that the damper response can be satisfactorily predicted with this model. Second, a backstepping based nonlinear current monitoring of magnetorheological dampers for semi-active control of structures under earthquakes has been developed. It provides a stable nonlinear magnetorheological damper current monitoring directly based on system feedback such that current change in magnetorheological damper is gradual. Unlike other MR damper control techniques available in literature, the main advantage of the proposed technique lies in its current input prediction directly based on system feedback and smooth update of input current. Furthermore, while developing the proposed semi-active algorithm, the dynamics of the supplied and commanded current to the damper has been considered. The efficiency of the proposed technique has been shown taking a base isolated three story building under a set of seismic excitation. Comparison with widely used clipped-optimal strategy has also been shown.