scholarly journals Wave propagation in micromorphic anisotropic continua with an application to tetragonal crystals

2020 ◽  
pp. 108128652097184
Author(s):  
Fabrizio Daví
Keyword(s):  
Wave Propagation ◽  
Point Group ◽  
Dispersion Relations ◽  
Exact Representation ◽  
Qualitative Information ◽  
Coupled Vibrations ◽  
Tetragonal Crystals ◽  
Lattice Wave

We study the coupled macroscopic and lattice wave propagation in anisotropic crystals seen as continua with affine microstructure (or micromorphic). In the general case, we obtain qualitative information on the frequencies and the dispersion relations. These results are then specialized to crystals of the tetragonal point group for various propagation directions: exact representation for the acoustic and optic frequencies and for the coupled vibrations modes are obtained for propagation directions along the tetragonal c-axis.

Refined Theories for the Dynamic Analysis of Sandwich Structures

2017 ◽  
Author(s):  
Serge Abrate
Keyword(s):  
Wave Propagation ◽  
Dynamic Analysis ◽  
Dynamic Loading ◽  
Sandwich Structures ◽  
Harmonic Wave ◽  
Dispersion Relations ◽  
Sandwich Beams ◽  
New Models ◽  
The Individual ◽  
Selection Of

The objective of this study is to give an overview of existing theories for analyzing the behavior of sandwich beams and plates and to develop an approach for evaluating their behavior under dynamic loading. The dispersion relations for harmonic wave propagation through sandwich structures are shown to be a sound basis for evaluating whether the individual layers are modeled properly. The results provide a guide in the selection of existing models or the development of new models.

scholarly journals Dynamics and Wave Propagation in Nonlinear Piezoelectric Metastructures

2021 ◽  
Author(s):  
Jaime Alberto Mosquera-Sánchez ◽  
Carlos De Marqui
Keyword(s):  
Wave Propagation ◽  
Vibration Control ◽  
Harmonic Balance ◽  
Electrical Circuit ◽  
Dispersion Relations ◽  
Dynamical Response ◽  
Negative Capacitance ◽  
Strongly Nonlinear ◽  
Time Domains ◽  
Nonlinear Regimes

Abstract This paper reports dynamical effects in onedimensional locally resonant piezoelectric metastructures that can be leveraged by nonlinear electrical attachments featuring either combined quadratic and quartic, or essentially quartic potentials. The nonlinear electromechanical unit cell is built upon a linear host oscillator coupled to a nonlinear electrical circuit via piezoelectricity. Its dynamical response to prescribed longitudinal harmonic displacements is approached in the frequency and time domains. Semi-analytical harmonic balance (HB)-based dispersion relations are derived to predict the location and edges of the nonlinear attenuation band. Numerical responses show that weakly and moderately nonlinear piezoelectric metastructures (NPMSs) promote a class of nonlinear attenuation band where a bandgap and a wave supratransmission band coexist, while also imparting nonlinear attenuation at the resonances around the underlying linear bandgap. Besides, strongly nonlinear regimes are shown to elicit broadband chaotic attenuation. Negative capacitance (NC)-based essentially cubic piezoelectric attachments are found to potentiate the aforementioned effects over a broader bandwidth. Excellent agreement is found between the predictions of the HB based dispersion relations and the nonlinear transmissibility functions of undamped and weakly damped NPMSs at weakly and moderately nonlinear regimes, even in the presence of NC circuits. This research is expected to pave the way towards fully tunable smart periodic metastructures for vibration control via nonlinear piezoelectric attachments.PACS 05.45.-a . 62.30.+d . 62.65.+kMathematics Subject Classification (2010) 37N15 . 74H45 . 74H65 . 74J30

WAVE PROPAGATION IN MAGNETOPLASMAS

1966 ◽  
Vol 44 (1) ◽  
pp. 255-264 ◽  
Author(s):  
S. R. Sharma
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Momentum Transfer ◽  
Transverse Wave ◽  
Energy Exchange ◽  
Dispersion Relations ◽  
Longitudinal Waves ◽  
Temperature Relaxation ◽  
The Magnetic Field

Wave propagation in a fully ionized unbounded magnetoplasma is considered taking into account the momentum transfer and energy exchange due to collisions. Dispersion relations are examined for wave propagation along and perpendicular to the magnetic field. It is found that there is no additional damping due to temperature relaxation for pure transverse wave propagation. For longitudinal waves dispersion relations are presented which include damping due to temperature relaxation and momentum transfer due to collisions.

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