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

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.