Closed-Form Demonstration and Shake Table Verification of Damping Effect on the Seismic Energy

Abstract

This paper discusses closed-form demonstrations of the damping effect for a basic mass, spring, and damper (MSD) and a single degree of freedom (SDOF) system that are exposed to harmonic loading. Initially, the energy balance equations of the systems were solved in closed form by considering the damping ratio and loading frequency. Verification of the solutions obtained for SDOF systems is achieved by shake table tests. Based on the analytical and experimental results, it was found that the damping effect is highly related to the ratio of loading frequency to the natural vibrational frequency of the system. For the lower and higher values of the ratio, damping is found to be almost ineffective. However, the effect becomes substantial when the ratio reaches unity i.e. at the resonant frequency. Damping has a reverse relation with seismic energy at the dominant frequency. In contrast, the relation is proportional in the vicinity of resonance frequencies. Hence, considering the damping as a parameter for the energy-based design of structures is suggested.

Optimal selection and scaling of ground motion records compatible with input energy and acceleration spectra

“…In this context, a comparison was conducted between the responses of structures under dynamic and static loadings by solving both the equation of motion and the energy equilibrium equation. The dynamic amplification factors (dynamic response/static response) derived from the solutions of the equation of motion 48 and the energy equilibrium equation 49 for an SDoF system are presented in Figure 17. These figures illustrate that loading with very low and very high frequency ratios to the natural frequency leads to lower responses compared to those calculated by static procedures.…”

Empirical correlations of constant ductility seismic input and hysteretic energies with conventional intensity measures

“…Lin et al (2013) showed that an efficient and sufficient IM should consider both earthquake and structural characteristics. Further, Sandıkkaya and Akkar (2017) mentioned that ground motions can be characterized based on amplitude, duration, and frequency content which is also related to the imparted seismic energy, (Akiyama (1985); Güllü et al (2022b); Güllü et al (2023)).…”