General Form of Steady Response and Periodic Solution for an Impact Oscillator Having No Sticking

Abstract

In this paper, we propose a method for obtaining the strict solution of a steady response and the periodic solution by which only the impact time of the impact oscillator system was assumed to be a parameter for which no sticking occurred. First, the response conversion which is the derivation operation of a steady response is defined. Two methods are shown to exist for the deriving process of a steady response, depending on the order of application of the response conversion and the “reference value expansion”. By these methods, a general form of the periodic solution can be obtained from a steady response. In addition, the results obtained by these two methods show good agreement on the most fundamental periodic solution. Finally, the validity of the proposed method is confirmed using a numerical simulation example.