G. Monsivais

Scattering of shear horizontal piezoelectric waves in piezocomposite media

The theory of shear horizontal wave scattering processes in layered piezoelectric composites is discussed in terms of a recursive system of equations involving the piezoelectric impedance. Piezoelectric materials of hexagonal 6 mm symmetry are considered. The behavior of an incident shear horizontal piezoelectric wave is analyzed as a function of the material properties, layer thicknesses, and frequency (ω). By an appropriate choice of the materials and layer thicknesses, frequencies at which almost all energy is transmitted can be found, optimizing the properties of the system for ultrasound transducers. This behavior is also dependent on the incident angle. Furthermore, most laminated materials are bonded using polymers. We show that adding these polymers hampers the response of the piezoelectric laminated system, localizing the transmission at particular incident angles. Thus, sharp spikes of ultrasonic pulses could be generated with these laminated structures.

Wannier-stark ladders in one-dimensional elastic systems.

The optical analogues of Bloch oscillations and their associated Wannier-Stark ladders have been recently analyzed. In this Letter we propose an elastic realization of these ladders, employing for this purpose the torsional vibrations of specially designed one-dimensional elastic systems. We have measured, for the first time, the ladder wave amplitudes, which are not directly accessible either in the quantum-mechanical or optical cases. The wave amplitudes are spatially localized and coincide rather well with theoretically predicted amplitudes. The rods we analyze can be used to localize different frequencies in different parts of the elastic systems and vice versa.

Interfacial waves between piezoelectric and piezomagnetic half-spaces with magneto-electro-mechanical imperfect interface

Abstract We study the propagation of shear horizontal waves between the interface of piezoelectric and piezomagnetic half-spaces with a magneto-electro-mechanical imperfect contact. Mechanical, electrical and magnetical imperfections are modelled by means of a spring, a capacitor and a inductor, respectively. A general expression for the dispersion relation not reported previously in literature is given in an explicit form, with the diverse limit cases analysed in detail. In some of these limit cases, new expressions are also obtained which predict the existence of interfacial waves. In the other cases, when already reported results exist, a comparison with them is done. Some physical interpretations are derived from the limit cases. The influence of mechanical, electrical and magnetical imperfect contacts are shown in some numerical examples.

Interfacial waves between two piezoelectric half-spaces with electro- mechanical imperfect interface

We study the propagation of shear horizontal waves between the interface of two piezoelectric materials with an electro-mechanical imperfect contact. Mechanical and electrical imperfections are modeled by means of a spring and a capacitor, respectively. The corresponding mathematical expressions for the imperfect contact are given in this article. The system of differential equations for the waves in the considered half-space is derived and the associate solutions are found. A general expression for the dispersion relation, not reported previously in the literature, is given in an explicit form, with the diverse limit cases analyzed in detail. In some of these limit cases, new expressions are also obtained, which predict the existence of interfacial waves. In the other cases, where already reported results exist, a comparison with them is done. Some physical interpretations are derived from the limit cases. The influence of mechanical and electrical imperfect contacts are shown in some numerical examples.

Dispersion curves of shear horizontal wave surface velocities in multilayer piezoelectric systems

A precise knowledge of the frequency responses, velocity dispersion, and distinct vibration modes in multilayer piezoelectric structures would permit the optimization of new designs for electromechanical sensor, actuator, and surface acoustic wave (SAW) filter devices under broad and narrow band conditions. In this paper, the singular-value decomposition technique, combined with the global matrix method and scaling procedure, are applied for studying the solutions of shear stationary waves in symmetric multilayer composite piezoelectric systems. This approach eliminates numerical instabilities sometimes appearing in the analysis of this type of piezoelectric systems, by using a multiple scaling strategy in the global matrix processing. The dispersion curves of the surface velocities, obtained by application of the proposed approach, have shown the presence of clearly separated odd and even bands in such a type of piezoelectric devices, which is explained by considering the eigenstates of the system. Detai...

Stark-ladder resonances in elastic waves

We discuss the existence of Stark-Ladder resonances for the propagation of elastic plane SH waves in a stratified elastic medium, with a finite number of layers, by calculating the displacement amplification for different angles of incidence. For the case of a periodic stratigraphy, we obtain a band structure and, when this periodicity is broken, by adding a linear term, the band structure is destroyed and Stark-Ladder resonances appear instead.

Presence of Stark ladders in scattering of shear horizontal piezoelectric waves

The global matrix techniques are used in the analysis of the Stark-Ladder resonances for transverse horizontal and surface waves in piezoelectric multilayers. Stark-Ladder resonances are observed when these waves propagate inside composites consisting of N piezoelectric layers whose piezoelectric properties obey a special linear relation. Each layer is made of materials with hexagonal 6 mm symmetry. The resonances are studied through the transmission coefficient. The transmission coefficient shows the well known band structure for a periodic piezocomposite, and when a linear term in the values of the piezoelectric parameters of the layers (which breaks the periodicity) is added, the band structure is destroyed and, in certain cases, resonances of the Stark-Ladder type are shown. The transmission coefficient is studied as a function of the properties of the materials and angle of incidence of the waves. Numerical results for two different configurations of piezocomposites are presented, one of them showing...

Interfacial waves between two magneto-electro-elastic half-spaces with magneto-electro-mechanical imperfect interface

The propagation of shear horizontal waves between the interface of two magneto-electro-elastic materials with an magneto-electro-mechanical imperfect contact has been studied. Mechanical, electrical and magnetical imperfections are modelled by means of a spring, a capacitor and an inductor, respectively. A general expression for the dispersion relation is given in an explicit form. Some limit cases are analysed in detail. The influence of imperfect contacts is shown in some numerical results.

Doorway states in quasi–one-dimensional elastic systems

The doorway state phenomenon has been recently analysed in many different systems, both quantum and classical. The systems range from nuclei to sedimentary valleys, therefore covering a range in size of 19 orders of magnitude. It also applies to systems with chaotic spectra as well as to integrable systems. In all these works, the doorway state has been discussed only in the energy or frequency domains. In this letter we present numerical and experimental results for a quasi–one-dimensional elastic system which presents a doorway state and, for the first time, the temporal evolution of the phenomenon is measured directly.

A simple way to understand the origin of the electron band structure

How the electron band structure appears in a one‐dimensional system using simple and intuitive arguments is discussed. The article presents both numerical and qualitative results.