The time evolution of the resistances and inductances of thedischarges in a pulsed gas laser through its current waveforms

In the present work, the time-dependent resistances and inductances of the electric discharges in a pulsed gas laser are revealed through the current waveforms of the circuit. This can be achieved combining step-by-step the experimental current waveforms with the current differential equations of the system. Thus, digitizing the signal, the derivative is calculated through a computer. For a certain time instant, substituting the values of the current and its derivative into the integrodifferential equations describing the performance of the circuit loops, we form relationships which connect the values of the resistance and inductance for this particular time instant. Combining relationships originating from very close adjacent time instants, the values of the resistances and inductances can be found. Scanning the entire time region of the discharges, the time dependence of the resistances and inductances of the discharges are revealed. Their behavior shows an abrupt drop for the resistances and a sharp peak for the inductances, both during the “formation phase”. After that, the above characteristic quantities fluctuate slowly around constant values. The sharp drop of the resistances was expected, bearing in mind that the number of the charges increases dramatically through the electron avalanche multiplication during the first few nanoseconds, causing the abrupt reduction of the resistances. On the other hand, the sharp peak of the inductances was unexpected. A plausible explanation for this phenomenon is that the plasma undergoes a temporary constriction which is due to the predominant attractive magnetic forces during the “formation phase” of the discharge     

Preparation of a psammaplysene-based library

A 28-member focused library, based on the pseudosymmetric template of the marine alkaloids psammaplysenes, was prepared from combinations of components that were, in turn, derived from 4-iodophenol.     

Equations of motion of rotating composite beam with a nonconstant rotation speed and an arbitrary preset angle

In the presented paper the equations of motion of a rotating composite Timoshenko beam are derived by utilising the Hamilton principle. The non-classical effects like material anisotropy, transverse shear and both primary and secondary cross-section warpings are taken into account in the analysis. As an extension of the other papers known to the authors a nonconstant rotating speed and an arbitrary beam’s preset (pitch) angle are considered. It is shown that the resulting general equations of motion are coupled together and form a nonlinear system of PDEs. Two cases of an open and closed box-beam cross-section made of symmetric laminate are analysed in details. It is shown that considering different pitch angles there is a strong effect in coupling of flapwise bending with chordwise bending motions due to a centrifugal force. Moreover, a consequence of terms related to nonconstant rotating speed is presented. Therefore it is shown that both the variable rotating speed and nonzero pitch angle have significant impact on systems dynamics and need to be considered in modelling of rotating beams.     

Asymptotic homogenization modeling of smart composite generally orthotropic grid-reinforced shells: Part I – theory

We develop in this paper a comprehensive micromechanical model for the analysis of thin smart composite grid-reinforced shells with an embedded periodic grid of generally orthotropic cylindrical reinforcements that may also exhibit piezoelectric properties. The original boundary value problem which characterizes the thermopiezoelastic behavior of the smart shell is decoupled via the asymptotic homogenization technique into three simpler problems the solution of which permits the determination of the effective elastic, piezoelectric and thermal expansion coefficients. The general orthotropy of the constituent materials is very important from the practical viewpoint and it renders the resulting analysis a lot more complicated. In Part II of this work the model is applied to the analysis of several practically important examples including cylindrical reinforced smart composite shells and multi-layer smart shells.     

Total synthesis of psammaplysenes A and B, naturally occurring inhibitors of FOXO1a nuclear export

[reaction: see text] Two inhibitors of FOXO1a-mediated nuclear export, psammaplysenes A and B, have been synthesized by a flexible and efficient route. A common starting material, 4-iodophenol, was used to prepare both halves of these pseudosymmetric dibromotyrosine-derived metabolites.     

Broadband passive targeted energy pumping from a linear dispersive rod to a lightweight essentially non-linear end attachment

We examine non-linear resonant interactions between a damped and forced dispersive linear finite rod and a lightweight essentially non-linear end attachment. We show that these interactions may lead to passive, broadband and on-way targeted energy flow from the rod to the attachment, which acts, in essence, as non-linear energy sink (NES). The transient dynamics of this system subject to shock excitation is examined numerically using a finite element (FE) formulation. Parametric studies are performed to examine the regions in parameter space where optimal (maximal) efficiency of targeted energy pumping from the rod to the NES occurs. Signal processing of the transient time series is then performed, employing energy transfer and/or exchange measures, wavelet transforms, empirical mode decomposition and Hilbert transforms. By computing intrinsic mode functions (IMFs) of the transient responses of the NES and the edge of the rod, and examining resonance captures that occur between them, we are able to identify the non-linear resonance mechanisms that govern the (strong or weak) one-way energy transfers from the rod to the NES. The present study demonstrates the efficacy of using local lightweight non-linear attachments (NESs) as passive broadband energy absorbers of unwanted disturbances in continuous elastic structures, and investigates the dynamical mechanisms that govern the resonance interactions influencing this passive non-linear energy absorption.     

Nonlinear dynamics of a spinning shaft with non-constant rotating speed

Research on spinning shafts is mostly restricted to cases of constant rotating speed without examining the dynamics during their spin-up or spin-down operation. In this article, initially the equations of motion for a spinning shaft with non-constant speed are derived, then the system is discretised, and finally a nonlinear dynamic analysis is performed using multiple scales perturbation method. The system in first-order approximation takes the form of two coupled sets of paired equations. The first pair describes the torsional and the rigid body rotation, whilst the second consists of the equations describing the two lateral bending motions. Notably, equations of the lateral bending motions of first-order approximation coincide with the system in case of constant rotating speed, and considering the amplitude modulation equations, as it is shown, there are detuning frequencies from the Campbell diagram. The nonlinear normal modes of the system have been determined analytically up to the second-order approximation. The comparison of the analytical solutions with direct numerical simulations shows good agreement up to the validity of the performed analysis. Finally, it is shown that the Campbell diagram in the case of spin-up or spin-down operation cannot describe the critical situations of the shaft. This work paves the way, for new safe operational ‘modes’ of rotating structures bypassing critical situations, and also it is essential to identify the validity of the tools for defining critical situations in rotating structures with non-constant rotating speeds, which can be applied not only in spinning shafts but in all rotating structures.     

Asymptotic homogenization modeling of smart composite generally orthotropic grid-reinforced shells: Part II– Applications

A comprehensive micromechanical model for the analysis of thin smart composite grid-reinforced shells with an embedded periodic grid of generally orthotropic cylindrical reinforcements that may also exhibit piezoelectric properties is developed and applied to examples of practical importance. Details on derivation of a general homogenized smart shell model are provided in Part I of this work. The present paper solves the obtained unit cell problems and develops expressions for the effective elastic, piezoelectric and thermal expansion coefficients for the grid reinforced smart composite shell. Thus obtained effective coefficients are universal in nature and can be used to study a wide variety of boundary value problems. The applicability of the model is illustrated by means of several examples including cylindrical reinforced smart composite shells, and multi-layer smart shells. The derived expressions allow tailoring the effective properties of a smart grid-reinforced shell to meet the requirements of a particular application by changing certain geometric or physical parameters.     

Numerical analysis of the electrical and optical behaviour of a pulsed nitrogen laser through time-dependent resistances and inductances

Received: 28 September 1996