MODE LOCALIZATION IN COUPLED CIRCULAR PLATES

When analyzing structures that are comprised of many similar pieces (p eriodic structures), it is common practice to assume perfect periodici ty. Such an assumption will lead to the existence of eigenmodes that a re global in character, i.e., the structural deflections will occur th roughout the system. However, research in structural mechanics has sho wn that, when only weak coupling is present between the individual pie ces of the system, small amounts of disorder can produce a qualitative change in the character Of the eigenmodes. A typical eigenmode of suc h a system will support motion only over a limited extend of the struc ture. Often only one or two of the smaller pieces that make up the str ucture show any motion, the rest remain quiescent. This phenomenon is known as ''mode localization,'' since the modes become localized at pa rticular locations on the overall structure. This paper will examine t he behavior of several circular plates that are coupled together throu gh springs, a system that models a multiple disk computer disk drive. These drives typically consist of several disks mounted on a single sp indle, coupled by read/write heads, which act as weak springs, thus le ading one to suspect the possibility of localization. Since such an ef fect would impact accurate read/write operations at small fly heights, the problem deserves attention. Although computer disk drives contain space fixed read/write heads, this paper will consider springs that a re fixed to the plates in order to understand the effect of localizati on on a set of infinite dimensional structures (the circular plates). Later work will extend the model to the case of space fixed springs an d the wave behavior and destabilizing effects that such a configuratio n will induce.