Transient energy exchange between a primary structure and a set of oscillators: return time and apparent damping

In this paper we examine the conditions that influence the return time, the time it takes before energy returns from a set of satellite oscillators attached to a primary structure. Two methods are presented to estimate the return time. One estimate is based on an analysis of the reaction force on a rigid base by a finite number of oscillators as compared with an infinite number of continuously distributed oscillators. The result gives a lower-bound estimate for the return time. A more accurate estimation results from considering the dynamic behavior of a set of oscillators as waves in a waveguide. Such an analogy explains energy flow between a primary structure and the oscillators in terms of pseudowaves and shows that a nonlinear frequency distribution of the oscillators leads to pseudodispersive waves. The resulting approximate expressions show the influence of the natural frequency distribution within the set of oscillators, and of their number, on the return time as compared with the asymptotic case of a continuous set with infinite oscillators. In the paper we also introduce a new method based on a Hilbert envelope to estimate the apparent damping loss factor of the primary structure during the return time considering transient energy flow from the primary structure before any energy reflects back from the attached oscillators. The expressions developed for return time and damping factor show close agreement with direct numerical simulations. The paper concludes with a discussion of the return time and its relation to apparent damping and optimum frequency distribution within a set of oscillators that maximize these quantities.     

Dependence on average atomic number of coherent/incoherent scattering intensity ratios in compounds

We have investigated the dependence on average atomic number of coherent/incoherent scattering intensity ratios in molecules. A Am-241 source is used to provide γ-rays. Several compounds having different average atomic numbers were used as scatterers. Scattering γ-rays were counted by a Si(Li) detector (FWHM at ). We observed an increase in the coherent/incoherent scattering intensity ratios with increasing average atomic number.     

Transient thermo-elastic waves in a half-space with thermal relaxation

We use the Cagniard-De Hoop method to develop the displacement and temperature fields in a half-space subjected on its free surface to an instantaneously applied heat source. We include in our analysis the thermal relaxation time of heat conduction, which insures that the termal waves propagate with a finite signal speed. We express our solution in terms of a small thermo-elastic coupling coefficient, and obtain explicit expressions for the wave-speeds and wave-amplitudes. Due to the existence of the thermal damping, we give only the short-time solution. We then present numerical results for the dilatation and the temperature so as to illustrate the salient features of the problem.

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Zusammenfassung Die Autoren benutzen die Methode von Cagniard-De Hoop zur Ermittlung des Verschiebungs-und des Temperaturfeldes in einem elastischen Halbraum unter dem Einfluß einer an der freien Oberfläche plötzlich angebrachten Wärmequelle. Sie berücksichtigen dabei die Relaxationszeit der Wärmeleitung, welche eine endliche Fortpflanzungsgeschwindigkeit der Wärmewellen garantiert. Die Lösung wird in einem kleinen thermoelastischen Koppelungskoeffizienten ausgedrückt, und es werden explizite Ausdrücke für die Fortpflanzungsgeschwindigkeiten und Wellenamplituden gegeben. Mit Rücksicht auf die thermische Dämpfung werden nur kurzfristige Lösungen betrachtet. Schließlich werden numerische Resultate für die Dilatation und die Temperatur angegeben, um die wesentlichen Eigenschaften des Problems zu illustrieren.

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This work was in part (A.H.N.) supported by the National Science Foundation under Grant GK-277 at the University of California, San Diego.     

Über faktorisierbare nichtauflösbare Gruppen

Ohne ZusammenfassungDiese Arbeit entstand, während der Verfasser als Stipendiat der Alexander von Humboldt-Stiftung an der Universität Freiburg weilte.Ich möchte mich an dieser Stelle für das Interesse an dieser Arbeit und die wertvollen Anregungen bei den Herren Dr. Peter Hauck und Prof. Dr. Otto H. Kegel bedanken.     

On the spectrum of periodic signals

In theory, there are many methods for the representation of signals. In practice, however, Fourier analysis involving the resolution of signals into sinusoidal components is used widely. There are several methods for Fourier analysis available for representation of signals. If the signal is periodic, then the Fourier series is used to represent the signal in terms of a set of harmonically related sinewaves. In this article new formulae for evaluating the trigonometric Fourier series coefficients when the signal under consideration is polynomial are developed by changing the integration to a derivation form. The solution presented here is an extension of the formulae proposed by Al-Smadi and Wilkes to the trigonometric Fourier series. The proposed technique is a powerful tool that can be used for solving practical science and engineering problems without excessive tedium.     

Comparison of a modified vibro-impact nonlinear energy sink with other kinds of NESs

Meccanica - Vibration mitigation is essential to many dynamical and engineering structures that are subjected to destructive vibration amplitudes induced by impulsive loading, seismic excitation,...     

Structural and luminescence studies of trivalent europium complexes with pentaethylene glycol and 18-crown-6 ligands in the presence of picrate anion

Two new isostructural complexes of europium picrate (Eu-Pic) with pentaethylene glycol (EO5) and 18-crown-6 (18C6) ligands formed complexes of molecular formula [Eu(Pic)₂(18C6)]⁺(Pic)⁻I and [Eu(Pic)₂(EO5)]⁺(Pic)⁻II have been isolated and characterised. Compound I showed 10-coordination number through six oxygen atoms from the 18C6 ligand and two bidentate picrate anions. Meanwhile, compound II exhibited 9-coordination number via six oxygen atoms from EO5 ligand, two oxygen atoms from a bidentate and one oxygen atom from monodentate picrate anions. Photoluminescence (PL) spectra of the solid-state europium complexes display sharp lines which are assigned to ⁵D₀→⁷F_0-4 and ⁵D₁→⁷F_1,2,4 transitions. No emission of polyether ligands is observed, indicating that the energy transfer from the polyether ligands to the Eu³⁺ ion is quite efficient. The PL spectra of [Eu(Pic)₂(OH₂)₆]⁺(Pic)⁻·6H₂O III, [Eu(NO₃)₃(OH₂)₃]·(18C6) IV, [Eu(NO₃)₃·6H₂O] V and Eu₂O₃VI are also observed. Compounds I-IV exhibited high Ω₂ intensity parameter values, namely 16.93, 10.23, 17.10 and 12.35 (in units of 10⁻²⁰ cm²), respectively. These relatively high values reflect the hypersensitive behaviour of the ⁵D₀→⁷F₂ transition and indicate that the Eu³⁺ ion is located in a highly polarisable chemical environment.     

Assessment of adsorption properties of inorganic–organic hybrid cyclomatrix type polyphosphazene microspheres for the removal of Pb(II) ions from aqueous solutions

Abstract

Inorganic–organic hybrid cyclomatrix type polyphosphazene microspheres (poly[cyclotriphosphazene-co-(4,4′-diaminodiphenylmethane)]) (HDMS) and poly[cyclotetraphosphazene-co-4,4′-diaminodiphenylmethane)] (ODMS) were prepared to investigate their possible use as alternative adsorbents for the comparative study on Pb(II) ions removal from aqueous solutions. The structures of the microspheres were elucidated by Fourier Transform Infrared (FTIR) spectroscopy and Dynamic Light Scattering (DLS) measurements, and the surface morphologies were also observed by Scanning Electron Microscopy (SEM). The adsorption of Pb(II) ions onto HDMS and ODMS from aqueous solutions was examined by means of pH, temperature, contact time and concentration. Furthermore, adsorption kinetics and isotherm models were applied and the experimental data fitted well with Langmuir isotherm and pseudo-second-order kinetic models. The maximum adsorption capacities of HDMS and ODMS for Pb(II) ions were obtained as 157.8 and 308.0?mg g^?1 at 20?°C and pH 5.5, respectively.