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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 FROM AUTHOR]

Three classical systems formed by the pairs of coupled resonators are analyzed, including a system of elastically coupled masses, a system of rigid rods separated by a notch, and an optical system made by a pair of dielectric films separated by a thin metallic layer. We show numerically that these systems are analogous to each other. For the latter two systems, the theoretical results are confirmed experimentally. This study allows us to discuss in classical systems properties that typically are only described quantum mechanically, such as the avoided crossing theorem, the strength function phenomenon, and the effect of the coupling element. [ABSTRACT FROM AUTHOR]

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 FROM AUTHOR]

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.