20314 Riemannζ関数とダンピングファクターζの怪しい関係(OS6 非線形現象とその応用)

概要

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Global analytical method based on pesudo-feedback approach which was introduced by authors enable us to derive all periodic solutions appering in forced vibro-impact systems. According to this method, global function form of periodic solution for target system can be represented as sum of linear system periodic solution and finite number of periodic functions constructed from converted impulsive responses caused by impact nonlinearity. However, in zero-stiffness case, divergent series is appered in deriving process of periodic solution, evaluate method of this series is unknown. We showed this divergent series can be evaluated by Cesaro's summation tequnique in case of symmetric periodic solutions. However, this method can not adopt directly in damping free system, another difficulty is emerged. In this paper, we propose a new approach to deal with divergent series using Riemann ζ function. The key idea is to determine initial condition emerging from infinite past by means of Cesaro's summation method. Cesaro's mean can be converged by this new evaluation tequnique.
一般社団法人日本機械学会の論文
2005-03-17