Compressional and torsional wave amplitudes in rods with periodic structures

Morales, A.; Flores, J.; Gutiérrez, L.; Méndez‐Sánchez, R. A.

doi:10.1121/1.1509431

Cited by 58 publications

(71 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…When the parameter γ is equal to zero, a locally periodic beam is formed. This kind of locally periodic beams shows a discrete band spectrum [Morales et al 2002]. If we break the periodicity by setting γ = 0, a completely different spectrum occurs.…”

Section: The Physical Systemmentioning

confidence: 99%

Elastic Wannier–Stark ladders in torsional waves

Monsiváis

Méndez‐Sánchez

Anda

et al. 2007

JOMMS

View full text Add to dashboard Cite

We study the normal modes of torsional waves in an elastic beam consisting of a set of N cuboids of varying heights. We present experimental, theoretical, and numerical results. We show that some analogies to the Wannier-Stark ladders resonances, originally introduced by Wannier in 1962, are exhibited by this classical system. The original ladders studied by Wannier consist of a series of equidistant energy levels for the electrons in a crystal in the presence of a static external electric field with the nearestneighbor level spacing proportional to the intensity of the external field. For the case of torsional waves in the beam we have observed a similar behavior, namely, the vibrations of the beam show resonances of equidistant frequencies with the nearest-neighbor spacing proportional to parameter γ associated with the geometry of the beam analogously to the electric field. However, this analogy is not perfect; we address the origin of the differences.

show abstract

Section: The Physical Systemmentioning

confidence: 99%

Elastic Wannier–Stark ladders in torsional waves

Monsiváis

Méndez‐Sánchez

Anda

et al. 2007

JOMMS

View full text Add to dashboard Cite

show abstract

“…When the arbitrary parameter γ is set equal to zero, a locally periodic rod is formed. This locally periodic rod shows a band spectrum [20].…”

mentioning

confidence: 99%

“…1 (a) and (b) with freeend boundary conditions using the transfer matrix method for torsional waves discussed in Ref. [20]. The normal mode frequencies and amplitudes were measured using the experimental set up described in Fig.…”

mentioning

confidence: 99%

Wannier-Stark Ladders in One-Dimensional Elastic Systems

et al. 2006

Self Cite

View full text Add to dashboard Cite

The optical analogues of Bloch oscillations and their associated Wannier-Stark ladders have been recently analyzed. In this paper 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 viceversa. PACS numbers: 43.35.+d,63.20.Pw,43.40.Cw Recently, undulatory systems showing analogues of Bloch oscillations and Wannier-Stark ladders (WSL) attracted increasing attention in several fields of physics [1,2,3,4,5]. As shown by Bloch, electrons in a periodic potential have extended solutions. The same is true for the behavior of an electron under the action of a static electric field. In contrast, and opposite to intuition, when both the periodic potential and the electric field are present, the solutions are localized; this is only true when band to band Zener tunneling is negligible or the system is short enough. The spectrum then shows equally spaced resonances known as Wannier-Stark ladders, the nearest-neighbor level spacing being proportional to the intensity of the external field [6]. In the time domain, the Wannier-Stark ladders yield the so called Bloch oscillations which consist in a counterintuitive effect where the electrons show an * Permanent address:

show abstract

“…When N is large enough the spectrum consists of allowed and forbidden bands, each consisting of N levels. The wave amplitudes are also obtained and compared with the ones obtained numerically using the transfer matrix method [7]. The waves are extended along the rod.…”

Section: Building Translation Symmetrymentioning

confidence: 99%

“…Among them, mechanical [1], microwave [2], optical [3,4,5,6], and elastic systems [7] have been studied along these lines. This approach is sometimes, jokingly speaking, referred to as megascopic physics.…”

Section: Introductionmentioning

confidence: 99%

Building and destroying symmetry in 1-D elastic systems

Flores¹,

Monsiváis²,

Mora³

et al. 2010

AIP Conference Proceedings

Self Cite

View full text Add to dashboard Cite

Abstract. Locally periodic rods, which show approximate invariance with respect to translations, are constructed by joining N unit cells. The spectrum then shows a band spectrum. We then break the local periodicity by including one or more defects in the system. When the defects follow a certain definite prescription, an analog of the Wannier-Stark ladders is gotten; when the defects are random, an elastic rod showing Anderson localization is obtained. In all cases experimental values match the theoretical predictions.

show abstract

Compressional and torsional wave amplitudes in rods with periodic structures

Cited by 58 publications

References 23 publications

Elastic Wannier–Stark ladders in torsional waves

Elastic Wannier–Stark ladders in torsional waves

Wannier-Stark Ladders in One-Dimensional Elastic Systems

Building and destroying symmetry in 1-D elastic systems

Contact Info

Product

Resources

About