Doorway states in flexural oscillations

Torres-Guzmán, José C.; Díaz‐de‐Anda, A.; Flores, J.; Monsiváis, G.; Gutiérrez, L.; Morales, A.

doi:10.1209/0295-5075/114/54001

Cited by 5 publications

(4 citation statements)

References 32 publications

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“…However, this 0th state, ξ * 0 , resurfaces in every beam in the second band, in agreement with ref. [39], where the same function ξ * 0 is reported to revive to act as a Doorway state at low frequencies, almost independent of the length , as observed in this case.…”

supporting

confidence: 78%

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Wannier-Stark ladders in free oscillations of Timoshenko-Ehrenfest beams

Rodríguez-Cruz¹,

Torres-Guzmán²,

Díaz‐de‐Anda³

2021

EPL

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We report on the observation of Wannier-Stark ladders in the bending vibrations of elastic beams. By introducing a gradient in the length distribution of N weakly coupled beams, the elastic equivalent of the Wannier-Stark ladder is obtained in a system governed by two coupled second-degree differential equations, instead of the common wave equation, and whose oscillations are also dispersive and, above a certain critical frequency, occur with two wavelengths. We have measured for the first time, not only the spectrum of the ladders, but the wave amplitudes in this type of system, which are not directly accessible in quantum-mechanical systems, and we have found that the wavelengths are spatially localized and in good agreement with the theoretically predicted amplitudes. Due to the combination of differential equations and the boundary conditions imposed on the system, the Wannier-Stark ladder phenomenon occurs from the third band of states onwards, unlike other classical systems.

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supporting

confidence: 78%

“…1 for free-ends boundary conditions have been calculated using the transfer matrix method as in refs. [38,39]. Both frequencies and wave amplitudes were measured using the experimental setup described in fig.…”

mentioning

confidence: 99%

Wannier-Stark ladders in free oscillations of Timoshenko-Ehrenfest beams

Rodríguez-Cruz¹,

Torres-Guzmán²,

Díaz‐de‐Anda³

2021

EPL

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“…For flexural vibrations and at low frequencies, the Bernoulli-Euler formula holds and a resonant frequency f i of the i -th independent beam is inversely proportional to the square of its length d i . As the frequency increases, the dependence on d i becomes more complex, however, it is still well described on the average, by the inverse of the square of the length d i of the beam 30,34 .…”

Section: Resultsmentioning

confidence: 99%

“…(10), which allows the coefficients A j +1 , B j +1 , C j +1 and D j +1 to be expressed in terms of A j , B j , C j and D j as follows,where T means the transpose and M j → j +1 is a 4 × 4 diagonal matrix calculated as in ref. 34 . Applying successively M j → j +1 we obtain…”

Section: Methodsmentioning

confidence: 99%

Anderson localization of flexural waves in disordered elastic beams

Ángel

Torres-Guzmán

Anda

2019

Sci Rep

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We study, both experimentally and numerically, the Anderson localization phenomenon in flexural waves of a disordered elastic beam, which consists of a beam with randomly spaced notches. We found that the effect of the disorder on the system is stronger above a crossover frequency f c than below it. For a chosen value of disorder, we show that above f c the normal-mode wave functions are localized as occurs in disordered solids, while below f c the wave functions are partially and fully extended, but their dependence on the frequency is not governed by a monotonous relationship, as occurs in other classical and quantum systems. These findings were corroborated with the calculation of the participation ratio, the localization length and a level statistics. In particular, the nearest spacing distribution is obtained and analyzed with a suitable phenomenological expression, related to the level repulsion.

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