Hysteretic damping revisited

Abstract

An integral-differential equation (IDE) in the time domain has been proposed for the free vibration of a single-degree-of-freedom (SDOF) system with hysteretic damping which is different from the conventional complex stiffness model as employed in the frequency domain (Chen & You, Proposal NSC 85-2211-E-019-004, National Taiwan Ocean University, 1996; Proc. 3rd National Congress Structural Engineering, 1996; BETECH96 Conf., 1996).1–3 The integral of the Hilbert transform is embedded in the IDE and is calculated in the Cauchy principal value sense in Refs 1–3. In this paper, we extend the SDOF system to multi-degrees-of-freedom systems and continuous systems. Also, the ratio of dissipation energy vs time for SDOF systems is constructed for the free vibration and compared with viscous damping. Numerical examples for different loss factors have been presented and the lack of dependence of the exciting frequency on the dissipation energy has been confirmed when the maximum responses are the same.