Abstract

This study examines the impact of damping and frequency on seismic resonance in structures, a crucial aspect of earthquake engineering. Using the second-order differential equation of motion, m(d²x/dt²) + c(dx/dt) + kx = F(t), we model a damped harmonic oscillator subjected to external forces. Key parameters-mass (m), damping coefficient (c), stiffness (k), and external force (F(t))—are analyzed to determine how different damping ratios (0.03 to 0.1) influence structural oscillations. By integrating real-world seismic data, including frequency response and peak ground accelerations, we highlight the critical role of damping in reducing vibration amplitudes, particularly in high-frequency seismic waves. Advanced damping mechanisms such as tuned mass dampers and viscous dampers are explored for their effectiveness in enhancing building resilience (TMDs). A detailed literature review provides insights into structural resonance, damping strategies, and seismic modeling. The findings emphasize that proper damping significantly mitigates seismic damage, aiding engineers and architects in designing earthquake-resistant structures. Graphs and experimental data illustrate the influence of damping ratios on structural response, contributing to the ongoing discourse on effective seismic mitigation. This study underscores the necessity of advanced damping solutions in earthquake-prone regions to improve infrastructure resilience.

Keywords: Seismic resonance, Structural damping, Vibration control, TMDs, Seismic mitigation