Periodic Solution for Zero Stiffness Impact Oscillator (Derivation of Symmetric Fundamental Periodic Solution by Initial Value Corrective Extension Method)

Abstract

A new analytical method to find the exact solution to nonlinear impact oscillator system having no spring stiffness is proposed. In this study, we apply the pseudo feedback superposition method in order to derive the fundamental form of unconverged periodic fundamental series which inevitably appear through the analysis. First, for this stiffness-free impact oscillator we assume the solution facing towards the future. Under this assumption, we have to evaluate unfavorable two terms ; “trend” term and “offset” term which lead to failure of periodicity and symmetricity among the solution. Second, we propose an alternative method to derive corrected terms based on the evaluation of only finite terms summation. Solution calculated through the approach can be indentical to that through Cesàro's summation approach reported in the previous paper. According to the proposed solving procedure, it is also found that the derivation of the periodic solution calculated through the conventional patching method assures the approval condition to the periodic solution.