ELSEVIER Wave Motion 23 (1996) 67-82 Vibration localization in multi-coupled and multi-dimensional near-periodic structures Dong Li, Haym Benaroya * Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854, USA Received 30 January 1995 Abstract The vibration localization of multi-coupled 2-D and 3-D lattices are parametrically investigated. The lattices are made of slightly randomly disordered masses embedded in an elastic medium, the nearest-neighbor interaction potential of the lattices gives rise to the weak central and angular coupling forces within neighboring masses of each mass. It is observed that the first normal mode of a 2-D lattice has a strong tendency to localize. Both free and forced vibration localization due to random mass disorder exist, but are otherwise abated with the increase of the dimension of the lattices. Disorder also tends to increase energy leakage from one degree-of-freedom to another degree-of-freedom at the vibration localization sites. 1. Introduction Periodic and near-periodic structures have received significant attention in recent years. In particular, the study of the dynamics of periodic and near-periodic mono-coupled structures have been extensively investigated and valuable results are obtained in understanding the vibration localization phenomenon in structures. The simplicity of one-dimension periodic structures permits both an efficient analytic approach to the problem, i.e., the transfer matrix method, and physical insight into the essence of localization both in discrete and continuous systems [ l-31. Comprehensive reviews on dynamics of 1-D periodic and near-periodic structures may be found in [4,5]. Mead [ 61 presented a detailed study on wave propagation and normal modes in perfect multi-coupled periodic structures. There seems to be very little work done on localization in multi-coupled and multi-dimensional structures, perhaps because of the increased complexity involved with the use of the transfer matrix method in higher-dimensional structures [7]. Kissel [8] proposed a general theory for localization in multi-coupled disordered periodic systems. Most recently, Chen, Bouzit and Pierre [9,10] examined the complex dynamics and wave conversion mechanisms in multi-coupled disordered beams. They found that if a wave of a given type is incident to a chain of random bays, it will produce transmitted and reflected components of waves of both its * Corresponding author. E-mail benaroya@zodiac.rutgers.edu. 0165-2125/96/$15.00 @ 1996 Elsevier Science B.V. All rights reserved SSDIO165-2125(95)00045-3