On harmonic plane wave propagation under fractional order thermoelasticity: an analysis of fractional order heat conduction equation

In the present paper, we investigate the propagation of an harmonic plane wave propagating with assigned frequency by implementing the thermoelasticity theory based on a fractional order heat conduction law where the fractional order parameter [Formula: see text] satisfies [Formula: see text]. After formulating the problem, the exact dispersion relation solutions for the plane wave are determined analytically and asymptotic expressions of different characterization of the wave are analyzed in two special cases, namely for a high-frequency field and low-frequency field. We consider the case of longitudinal wave which is coupled with the thermal field and we ignore the transverse wave as it is observed to be independent to the thermal field. Two different modes: predominantly thermal and predominantly elastic mode longitudinal waves are found. Finally we compute wave characterizations for the intermediate values of frequency and verify our analytical results for the limiting cases of wave frequency. A detailed analysis is presented to highlight the effects of the fractional order parameter, [Formula: see text], on the wave fields. Several important points are highlighted and the most important point which we have found is that [Formula: see text] plays a very important role in the behavior of the wave. As [Formula: see text], the thermal mode wave behaves similarly as in the case of a classical thermoelastic model and the nature of the wave changes significantly as [Formula: see text] gets nearer to the value 1, behaving more similarly to the case of a generalized thermoelastic model (Lord–Shulman model).

Band-Gap of a Soft Magnetorheological Phononic Crystal

This paper presents the wave propagation in a tunable phononic crystal consisting of a porous hyperelastic magnetorheological elastomer (MRE) subjected to an external magnetic field. Finite deformations and magnetic induction influence phononic characteristics of the periodic structure through altering the geometry and material properties of the unit cell. The governing equations for incremental time-harmonic plane wave motions superimposed on a static predeformed media are derived. Analytical and finite element (FE) methods are used to investigate dispersion relation and band structure of the phononic crystal for different levels of deformation and applied magnetic induction. It is demonstrated that large deformations and magnetic induction could transform the location and width of band-gaps.

Electromagnetic field distribution of a nearby lightning discharge inside an overground wire conductive structure

Lightning is a major natural source of electromagnetic (EM) radiation and the most impressive one, but only from a secure distance. Its most dangerous effects happen in the case of a direct strike, but it can also make damages to electronic systems and equipment from the distances of up to 1.5km from the direct strike, i.e. in the case of a nearby discharge. Lightning EM field can be analyzed using Fast Fourier Transform (FFT). One simple approximation [3] for external pulse field is used and parameters are calculated for the standard pulse function 1.2/50. EM field of a lightning discharge induces currents along conductive structures and resulting field can be obtained using program SPAN. Computer package SPAN for analysis of conductive structures, consisting of linear cylindrical segments, in external EM field of time harmonic plane wave of arbitrary direction and frequency, was made by the author [1,2]. Time response is obtained performing Inverse Fast Fourier Transform (IFFT) to the results of program SPAN in frequency domain. The results for EM field inside the structure and in the near field out of some cage structures on the ground in the case of a nearby lightning discharge are presented in the paper.

Relativistic self-focusing of laser beams in time-harmonic plane waves: arbitrary intensity

This paper presents a paraxial theory of relativistic self-focusing of a Gaussian laser beam in plasma for a time-harmonic plane wave at arbitrary beam intensity. Since the relativistic mechanism is instantaneous, the theory is also applicable to self-focusing of laser pulses. The analysis leads to two values for the critical beam power for self-focusing, Pcr1 and Pcr2. When P < Pcr1 < Pcr2, the beam diverges. When Pcr1 <P <pcr2, it first converges, then diverges, and so on. When P > Pcr2 it first diverges, then converges, and so on.