Wave transmission through one-dimensional near periodic structures: Optimum and random disorder

A general analysis is presented of wave transmission through a one-dimensional near periodic structure which is embedded in an otherwise uniform system. The occurrence of frequencies of perfect transmission is discussed, and the inverse problem of design for minimum transmission is addressed. This part of the work is aimed at providing design techniques for structural filters which might either block or allow wave transmission depending upon the intended application. Attention is then turned to the case of wave transmission through a randomly disordered system, and a simple and exact method for the calculation of the expected value of the inverse squared transmission coefficient is presented. The localization measure which may be deduced from this result is compared with the conventional definition of the localization factor, and it is found that quantitative results for the latter may be computed by using the present approach. The effects of damping are included, and the interaction of disorder and damping is investigated. This part of the work is aimed at providing a simple technique for the assessment of vibration localization effects in structures of this type. (C) 1995 Academic Press Limited