Equivalence of Bilinear Hysteresis and Viscous Damping Energy Dissipation

Abstract

Abstract To evaluate the energy dissipation differences between metal dampers and viscous dampers and to gauge the degree of equivalence between bilinear hysteresis and viscous damping, we studied the equivalence of bilinear hysteresis and viscous damping. Using a MATLAB program and the principle of equal energy dissipation, the energy dissipation effect of bilinear hysteresis was equated based on the effect of viscous damping. Under a state of sinusoidal excitation, the displacement response of the numerical method, which strictly considers the bilinear hysteresis, was compared with the displacement response of the equivalent viscous damping calculation method. The results show that the oscillation periods for the two models demonstrate high consistency, with the displacement curves in the steady-state response stage nearly identical. Because of the lag in hysteresis energy dissipation, the bilinear hysteresis system always reaches the steady-state stage slower than the equivalent viscous damping system, implying that the metal damper responds more slowly to transient energy. In the free vibration stage, the bilinear hysteresis system cannot return to the initial position, while the displacement of the equivalent viscous damping system approaches zero, suggesting that the self-resetting effect of the viscous damper is better.