Exact Solution for Dynamic Response of Multi-Degree-of-Freedom Bilinear Hysteretic Systems

Abstract

An exact solution technique for the response of a bilinear hysteretic multi-degree-of-freedom system subjected to arbitrary dynamic loadings is proposed. Each function in the loading vector is represented by a piecewise interpolation polynomial. By using the modal superposition method and the Duhamel integral procedure on each branch of the force-displacement relationship and matching transitional conditions, one can obtain a closed-form solution. When the system is subjected to such piecewise polynomial loadings as an earthquake acceleration, which usually can be represented by a series of straight line segments, an exact result can be obtained. Thus the proposed method can provide much higher accuracy, and requires less computational effort than the traditional step-by-step integration solution technique. The reason for these advantages is discussed and the related formulas are provided.