New Research


Understanding and prediction of localization in periodic structures

— For application of nonlinear mechanics to engineering —

Professor Nobumasa Sugimoto, Associate Professor Takao Yoshinaga, Assistant Professors Yoko Hase & Y

Nonlinear mechanics often reveals that a phenomenon which looks complex at first sight or appears independently can be explained well by a simple model or by a common mechanism.
Nonlinearity manifests itself in a rich variety of phenomena. As far as oscillations and waves in mechanical systems are concerned, for example, it leads to emergence of self-excited oscillations or chaotic oscillations, propagation of solitons (solitary waves) or shocks, formation of patterns, and so on.
But it is quite a recent matter that the importance of nonlinearity has been widely recognized and accepted in various fields and become popular even in social science. Now Nonlinear Science is indispensable to describe the phenomena more accurately and to grasp the essence behind it.
Our group is studying nonlinear oscillations and waves in fluids or fluid-structure systems in terms of fluid mechanics and nonlinear mechanics for understanding the essence of phenomena. This aims at solving real problems by new findings as well as at creating novel machines or mechanisms.
One of our recent researches is on “localization and delocalization of waves” in a spatially periodic structure.
Suppose an impact is applied locally to a continuous structure. Its effect usually spreads over the whole structure and decays out eventually. But if the magnitude of the impact were too strong to ignore nonlinearity, it may happen that its effect remains to be localized around the impact point. Please note, however, that localization may occur even in linear systems due to inhomogeneity. But the localization attracting much attention recently is so-called “intrinsic localized mode” (ILM simply). This is temporally periodic oscillations localized spatially. When the ILM occurs, it traps energy of oscillations locally.
Recently we have clarified theoretically that the ILM may occur commonly in a spatially periodic and articulated structure. This models a large-scaled structure such as a periodically ribbed solar panel, a periodic truss of long bridges with supports, a Mega-Float build up of many pontoons, a long pipeline with periodic supports, a train, and so on. In addition, we have shown that the movable ILM may occur and that they may be trapped near the boundary of the structure, exhibiting a very peculiar and intriguing behavior.
While the localization appears to have a merit of trapping energy, it may bring about unexpectedly persistent oscillations to yield nuisance and even damages.
On the basis of these new findings, we are now looking at fluid-structure interactions which occur in the cases of the Mega-float and a train traveling in a tunnel at high speed to clarify possibility of the ILM.
For further details and other research activities, please visit our website:

Sugimoto laboratory web page
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