Transient processes in a gas/plate structure in the case of light loading

The problem of a pulse excitation in an acoustic half-space with a flexible wall described by a thin plate equation is studied. The solution is written as a double Fourier integral. A novel technique of estimation of this integral is developed. The surface of integration is deformed in such a way that the integrand is exponentially small everywhere except the neighbourhoods of several ‘special points’ that provide field components. Special attention is paid to the pulse associated with the coincidence point of the branches of the dispersion diagram of the acoustic medium and the plate. This pulse is shown to be a harmonic wave of a finite duration.

Ultra-wide bandgap in active metamaterial from feedback control

To widen the attenuation bandwidth in a mass-in-mass metamaterial chain, active feedback control is employed within the unit cell. The optimal control via Linear Quadratic Regulator is used to ensure the stability of the solution as well as adaptive tuning of the system. The key concept is to obtain a wider bandwidth by reducing the displacement amplitude of the outer mass of each unit of the metamaterial. Transmittance for finite number of units and dispersion diagram for infinitely long metamaterial chain are obtained using the backward-substitution method and Bloch–Floquet’s theorem, respectively. Results evidenced that an ultra-wide uninterrupted attenuation band starting from very low free wave frequency can be obtained. The dispersion diagram primarily depends on the frequency ratio of the resonating unit with the external main unit. The effect of the mass ratio is insignificant while active feedback control is implemented. This unique phenomenon implies that for a very low mass ratio also a wider bandwidth can be achieved. This enables to design a lightweight structure having wider bandwidth in low-frequency regime.

Dispersion Diagram of Trigonal Piezoelectric Phononic Structures with Langasite Inclusions

The dispersion relation of elastic Bloch waves in 1-3 piezoelectric phononic structures (PPnSs) with Langasite (La3Ga5SiO14) inclusions in a polymeric matrix is reported. Langasite presents promising material properties, for instance good temperature behaviour, high piezoelectric coupling, low acoustic loss and high quality factor. Furthermore, Langasite belongs to the point group 32 and has a trigonal structure. Thus, the 2-D bulk wave propagation in periodic systems with Langasite inclusions cannot be decoupled into XY and Z modes. The improved plane wave expansion (IPWE) is used to obtain the dispersion diagram of the bulk Bloch waves in 1-3 PPnSs considering the classical elasticity theory and D3 symmetry. Full band gaps are obtained for a broad range of frequency. The piezoelectricity enhances significantly the band gap widths and opens up a narrow band gap in lower frequencies for a filling fraction of 0.5. This study should be useful for surface acoustic wave (SAW) filter and 1-3 piezocomposite transducer design using PPnSs with Langasite.

The Dispersion Diagram for Magnetoacoustic Waves in Arbitrarily Structured Solar Waveguides

<p>The observation of large scale stable solar magnetic configurations, e.g. sunspots have been done over centuries. But only recently, thanks to modern high-resolution observations solar physicists were able to observe small scale solar features and associated plasma processes, i.e. magnetic bright points, spicules, plasma flows, structure of magnetic fields etc. in great detail. Therefore, advanced theoretical modelling becomes essential to explain observational results, allowing magneto-seismology to be conducted and provide more accurate information about MHD wave propagation and solar atmospheric plasma properties. In this work, we discuss a variety of theoretically constructed 2-3D MHD equilibria obtained by considering different magnetic field configurations and internal flow profiles. The dispersion diagrams and eigenfunctions were obtained numerically for the case where the equilibrium plasma density is modelled as a Gaussian profile with a varying inhomogeneous width and also as a sinc(x) function. The analytic dispersion relation is not required, making this numerical approach a very powerful tool. The proposed numerical approach allows the dispersion diagram and eigenfunctions to be obtained for any inhomogeneous magnetic hydrostatic equilibrium with or without plasma flow. To obtain the numerical solution, the shooting method has been used to match necessary boundary conditions on continuity of displacement and total pressure of the waveguide. The proposed methodology has been successfully tested against well-known analytical results obtained for uniform slab and uniform cylinder geometry. We have found that under coronal conditions, with increasing inhomogeneity in the equilibrium, an additional node appears in the resulting eigenfunctions for the slow body sausage mode, which could be misinterpreted by observers as the existence of an entirely different mode.</p>

High-frequency homogenization in periodic media with imperfect interfaces

In this work, the concept of high-frequency homogenization is extended to the case of one-dimensional periodic media with imperfect interfaces of the spring-mass type. In other words, when considering the propagation of elastic waves in such media, displacement and stress discontinuities are allowed across the borders of the periodic cell. As is customary in high-frequency homogenization, the homogenization is carried out about the periodic and antiperiodic solutions corresponding to the edges of the Brillouin zone. Asymptotic approximations are provided for both the higher branches of the dispersion diagram (second-order) and the resulting wave field (leading-order). The special case of two branches of the dispersion diagram intersecting with a non-zero slope at an edge of the Brillouin zone (occurrence of a so-called Dirac point) is also considered in detail, resulting in an approximation of the dispersion diagram (first-order) and the wave field (zeroth-order) near these points. Finally, a uniform approximation valid for both Dirac and non-Dirac points is provided. Numerical comparisons are made with the exact solutions obtained by the Bloch–Floquet approach for the particular examples of monolayered and bilayered materials. In these two cases, convergence measurements are carried out to validate the approach, and we show that the uniform approximation remains a very good approximation even far from the edges of the Brillouin zone.

A Fully-Printed CRLH Dual-Band Dipole Antenna Fed by a Compact CRLH Dual-Band Balun

In this paper, a new design method is proposed for a planar and compact dual-band dipole antenna. The dipole antenna has arms as a hybrid CRLH (Composite right- and left-handed) transmission-line comprising distributed and lumped elements for the dual-band function. The two arms are fed by the outputs of a compact and printed CRLH dual-band balun which consists of a CRLH hybrid coupler and an additional CRLH phase-shifter. Its operational frequencies are 2.4 and 5.2 GHz as popular mobile applications. Verifying the method, the circuit approach, EM (Electromagnetics) simulation and measurement are conducted and their results turn out to agree well with each other. Additionally, the CRLH property is shown with the dispersion diagram and the effective size-reduction is mentioned.

Bragg waveguide of rectangular cross-section

A method for calculating parameters of rectangular waveguides using separation of variables is presented. The method makes it possible to calculate multilayer Bragg waveguides with an arbitrary number of layers and an arbitrary composition as photonic crystal structures with defect. A result of the numerical calculation of the dispersion diagram of such a structure is given. This result is in good agreement with the earlier published data on the study of similar structures.

Modelling Propagating Bloch Waves in Magnetoelectroelastic Phononic Structures with Kagomé Lattice Using the Improved Plane Wave Expansion

We studied the dispersion diagram of a 2D magnetoelectroelastic phononic crystal (MPnC) with Kagomé lattice. The MPnC is composed of BaTiO3–CoFe2O4 circular scatterers embedded in a polymeric matrix. The improved plane wave expansion (IPWE) approach was used to calculate the dispersion diagram (only propagating modes) of the MPnC considering the classical elasticity theory, solid with transverse isotropy and wave propagation in the xy plane. Complete Bragg-type forbidden bands were observed for XY and Z modes. The piezoelectric and the piezomagnetic effects significantly influenced the forbidden band widths and localizations. This investigation can be valuable for elastic wave manipulation using smart phononic crystals with piezoelectric and piezomagnetic effects.