ABSTRACT
In a previous work an elastic bar with a groove or notch that presents a doorway state was studied when the system was excited with 20 cycles of harmonic signals. The strength function had a Lorentzian width Γd = 1/πτd, where τd is the decay time of the prompt response. In the present paper, the doorway-state phenomenon is analyzed again for the same harmonic signals but for a very large number of cycles. The strength-function phenomenon is once more obtained, but now with a Lorentzian width Γ' which is larger than Γd. A qualitative and numerical explanation of this fact is given, leading therefore to further understanding of doorway states in elastic systems. The numerical results show a very good agreement with the values measured in the laboratory.
ABSTRACT
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.
ABSTRACT
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.
ABSTRACT
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. Timoshenko's 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.
