FREE WAVES IN PERIODICALLY DISORDERED SYSTEMS: NATURAL AND BOUNDING FREQUENCIES OF UNSYMMETRIC SYSTEMS AND NORMAL MODE LOCALIZATION
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文摘
A general method has been developed and applied to study the effect of different amounts of disorders on free flexural wave motion in undamped beam-type systems consisting of finite multi-span repeating units that are disordered identically due to (i) unequal support spacings and (ii) the presence of point masses and point springs at some of the supports. The frequency primary propagation zones (pass bands) of periodic systems are, in general, divided into as many intermediate propagation zones as the number of beam elements of the disordered repeating units. In the case of systems with symmetrically disordered repeating units, the frequency propagation zones are always bound by the frequencies that are identified with natural frequencies of the repeating unit with the extreme ends simply supported or clamped. This is not the case when the repeating units are disordered unsymmetrically. Natural frequencies of unsymmetric multi-span beams normally lie inside the attenuation zones (stop bands) and the conditions under which they can lie at the bounds and even inside the propagation zones have been identified. The presence of disorders normally interferes with free wave motion and narrows down the effective frequency bands of free wave propagation, but this is not always true. Conditions have been identified under which some specific beam length disorders do not interfere with the free wave propagation in certain frequency bands and can even broaden such bands. It is also explained how the transmission of waves (and vibrations) can be controlled by introducing appropriate disorders. Confinement of free waves corresponding to normal modes of disordered systems has been discussed in terms of the attenuation constant of free wave motion. It is argued on the basis of present and earlier studies on periodically disordered systems, that the normal modes only of the unsymmetrically disordered systems that lie in attenuation zones can become localized (even when the system elements are not weakly coupled). The influence of variation of coupling, disorder, damping and that of the frequency on wave confinement is discussed and interpreted qualitatively in terms of the attenuation (decay) constant of periodically disordered systems. The effect of these parameters is found to compare well in general with their well-known effects on normal mode localization in beam-type structures.