Exact Global Representation of Symmetric Periodic Solutions for Periodically Excited Lumped Mass Discontinuous System having no Stiffness

Extension to Derivation for All Symmetric Periodic Solutions by Cesàro's Summation Method

Abstract

A new calculation technique is proposed for getting symmetric periodic solutions of the lumped mass discontinuous system to periodic excitation. This system is adopted as a typical piecewise linear oscillator having no stiffness. First, it is pointed out that the feedback super-position method which was formerly proposed by authors can not be directly applied to this zero-stiffness oscillator. In order to overcome this difficulty, an improved calculation method using Cesaro's summation technique for getting the physically meaning value of divergent series appering in pseudo-feedback responses is newly proposed. According to this method, even unconverged series of the periodic pseudo-feedback response become to be evaluated by the Cesàro's (C. 2) summation to viscous damped system and those (C. 3) summation to undamped system, respectively.