J. Flores

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.

Locally periodic Timoshenko rod: experiment and theory.

The flexural vibrations of a locally periodic rod, which consists of N unit cells, are discussed both from the experimental and theoretical points of view. Timoshenkos beam theory and the transfer matrix method are used to calculate the normal-mode frequencies and amplitudes. The theoretical values are then compared with the experimental ones, which are obtained using an electromagnetic acoustic transducer (EMAT). Good agreement between the numerical results and the experimental measurements is obtained. It is shown that as N grows, a band spectrum emerges.

Compressional and torsional wave amplitudes in rods with periodic structures

To measure and detect elastic waves in metallic rods a low-frequency electromagnetic-acoustic transducer has been developed. Frequencies range from a few hertz up to hundreds of kilohertz. With appropriate configuration of the transducer, compressional or torsional waves can be selectively excited or detected. Although the transducer can be used in many different situations, it has been tested and applied to a locally periodic rod, which consists of a finite number of unit cells. The measured wave amplitudes are compared with theoretical ones, obtained with the one-dimensional transfer matrix method, and excellent agreement is obtained.

Generation of inhomogeneous P waves in a layered medium

Abstract The generation of inhomogeneous, horizontally propagating P waves in a stratified elastic medium were analyzed for incident SV waves beyond the critical angle. Using realistic values of S and P wave velocities and considering both clay and alluvial sedimentary layers overlying a bedrock half-space, we obtained enormous amplifications for the horizontal displacements at the free surface. These amplifications are of the order of several thousands for the fundamental mode of the system, which systematically dominates all other frequencies.

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.

Novel doorways and resonances in large-scale classical systems

We show how the concept of doorway states carries beyond its typical applications and usual concepts. The scale on which it may occur is increased to large classical wave systems. Specifically we analyze the seismic response of sedimentary basins covered by water-logged clays, a rather common situation for urban sites. A model is introduced in which the doorway state is a plane wave propagating in the interface between the sediments and the clay. This wave is produced by the coupling of a Rayleigh and an evanescent SP-wave. This in turn leads to a strong resonant response in the soft clays near the surface of the basin. Our model calculations are compared with measurements during Mexico City earthquakes, showing quite good agreement. This not only provides a transparent explanation of catastrophic resonant seismic response in certain basins but at the same time constitutes up to this date the largest-scale example of the doorway state mechanism in wave scattering. Furthermore the doorway state itself has interesting and rather unusual characteristics. open access Copyright c EPLA, 2011

Anderson localization in finite disordered vibrating rods

We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are exponentially localized as occurs in disordered solids. The localization length, measured using these wave amplitudes, decreases as a function of frequency. The normal-mode spectrum is also measured as well as computed, so its level statistics can be analyzed. From the spectrum, the nearest-neighbor spacing distribution can be obtained. This distribution can be described by a phenomenological expression that depends on a parameter α, related to the level repulsion, which is also a function of the frequency. Therefore, the localization length can be expressed in terms of the parameter α. There exists a range in which the localization length grows linearly with α. However, at low values of this parameter the linear dependence does not hold.

Doorway states in flexural oscillations

The doorway-state phenomenon has been observed in many quantum and classical undulatory systems when two oscillating systems are coupled, one that has a high level density and the other one a very low density. Up to now the systems analysed have in common that they are governed by second-order differential equations. In the present work it is shown that the doorway state mechanism also appears when dealing with flexural vibrations of elastic systems, which are governed by fourth-order differential equations. It should be mentioned that this phenomenon also emerges from the two coupled second-order differential Navier equations.

Emergence of acoustic and optical bands in elastic systems

Two elastic systems are considered in this work: A special linear chain of harmonic oscillators and a quasi one-dimensional vibrating rod. Starting in both cases with a locally periodic system formed by unit cells with a single element, these cells are converted into binary cells. The acoustic and optical bands then appear. For the vibrating rod experimental values are compared with theoretical results; in particular, the normal-mode amplitudes are obtained and the agreement is excellent.

Topological defects in 1D elastic waves

Abstract It has been recently shown theoretically that a topological defect in a 1D periodic potential may give rise to two localized states within the energy gaps. In this work we present an experimental realization of this effect for the case of torsional waves in elastic rods. We also show numerically that three, or even more, localized states can be present if the parameters characterizing the topological defect are suitably varied.