Energy flux and dissipation of inhomogeneous plane waves in hereditary viscoelasticity

Inhomogeneous small-amplitude plane waves of (complex) frequency ω are propagated through a linear dissipative material which displays hereditary viscoelasticity. The energy density, energy flux and dissipation are quadratic in the small quantities, namely, the displacement gradient, velocity and velocity gradient, each harmonic with frequency ω , and so give rise to attenuated constant terms as well as to inhomogeneous plane waves of frequency 2 ω . The quadratic terms are usually removed by time averaging but we retain them here as they are of comparable magnitude with the time-averaged quantities of frequency ω . A new relationship is derived in hereditary viscoelasticity that connects the amplitudes of the terms of the energy density, energy flux and dissipation that have frequency 2 ω . It is shown that the complex group velocity is related to the amplitudes of the terms with frequency 2 ω rather than to the attenuated constant terms as it is for homogeneous waves in conservative materials.

An Analytical Study of Electromagnetic Deep Penetration Conditions and Implications in Lossy Media through Inhomogeneous Waves

This paper illustrates how the penetration of electromagnetic waves in lossy media strongly depends on the waveform and not only on the media involved. In particular, the so-called inhomogeneous plane waves are compared against homogeneous plane waves illustrating how the first ones can generate deep penetration effects. Moreover, the paper provides examples showing how such waves may be practically generated. The approach taken here is analytical and it concentrates on the deep penetration conditions obtained by means of incident inhomogeneous plane waves incoming from a lossless medium and impinging on a lossy medium. Both conditions and constraints that the waveforms need to possess to achieve deep penetration are analysed. Some results are finally validated through numerical computations. The theory presented here is of interest in view of a practical implementation of the deep penetration effect.

New capabilities of Chetaev´s model

This paper considers anomalies in the magnetotelluric field in the Pc3 range of geomagnetic pulsations. We report experimental data on Pc3 field recordings which show negative (from Earth’s surface to air) energy fluxes Sz<0 and reflection coefficients |Q|>1. Using the model of inhomogeneous plane wave (Chetaev’s model), we try to analytically interpret anomalies of energy fluxes. We present two three-layer models with both electric and magnetic modes satisfying the condition |Qh|>1. Here we discuss a possibility of explaining observable effects by the resonance interaction between inhomogeneous plane waves and layered media.

Propagation of inhomogeneous plane waves in isotropic solid crystals

In this paper we study the impact of initial mechanical deformation and electric fields applied to linear elastic isotropic solid, on the propagation of inhomogeneous plane waves in such media. We derive the decomposition of the propagation condition for particular isotropic directional bivectors and we show that the specific coefficients are similar to the case of guided waves propagation in isotropic solids subject to a bias.