Resonance is the phenomenon in which a structure experiences amplified response when the frequency of the applied dynamic load matches one of its natural frequencies. In earthquake engineering, resonance is a primary cause of disproportionate damage and a critical consideration in structural design.
Resonance is the phenomenon by which a dynamic system responds with unusually large amplitude when subjected to excitation at or near one of its natural frequencies. In a linear undamped system, resonance produces theoretically infinite response; in real structures, damping limits the amplitude, but the amplification can still be dramatic β a factor of 10 to 50 for structures with typical 2β5% damping ratios. The physical mechanism is the constructive interference of energy input: when the excitation frequency matches the natural frequency, each cycle of loading adds energy to the system in phase with its motion, building up amplitude over time. When the excitation frequency differs from the natural frequency, energy inputs and outputs alternate, preventing accumulation.
In earthquake engineering, resonance is a central concern because earthquake ground motions contain a broad range of frequencies, and any structure will have its natural frequencies somewhere within this spectrum. The critical question is whether the dominant frequencies of the ground motion coincide with the structure's natural frequencies. The 1985 Mexico City earthquake β with dominant periods around 2 seconds β caused disproportionate collapse of mid-rise buildings whose natural periods matched the ground motion, while taller and shorter buildings survived. The 2011 Christchurch earthquake destroyed buildings in a narrow period range that resonated with the high-frequency ground motion, while adjacent buildings with different periods were spared. Site effects amplify this risk: soft soil sites amplify ground motions at specific periods (typically 0.5β3 seconds), so structures with natural periods in this range on soft soil are especially vulnerable.
Design against resonance involves multiple strategies. One approach is to stiffen or soften the structure to shift its natural frequencies away from the dominant frequencies of expected ground motion β but this is often impractical because ground motions have broad frequency content. A more robust approach is to increase damping, either through the inherent damping of the structural system (higher for reinforced concrete than for steel) or through supplemental damping devices (viscous dampers, viscoelastic dampers, friction dampers, hysteretic dampers). Base isolation takes a different approach: it shifts the structure's fundamental period to a long value (typically 2β4 seconds) where the earthquake's energy content is lower, effectively moving the structure out of the resonance range for most ground motions. Modern performance-based design explicitly checks for resonance by comparing structural periods to site-specific response spectra and considering both the fundamental mode and higher modes. Tall buildings, in particular, require careful assessment of higher-mode resonance, since their natural periods span a wide range that may include multiple peaks in the ground motion spectrum.