The natural frequency is the rate at which a structure oscillates in free vibration, measured in cycles per second (Hz). It is the inverse of the natural period and determines how the structure interacts with the frequency content of earthquake ground motion.
The natural frequency (f) of a structure is the number of complete oscillations it undergoes per unit time when vibrating freely, expressed in Hertz (Hz), where 1 Hz = 1 cycle per second. It is the inverse of the natural period: f = 1/T. For an SDOF system, the natural frequency is given by f = (1/2Ο)β(k/m), where k is the stiffness and m is the mass. Angular natural frequency (Ο = 2Οf), expressed in radians per second, is often used in analytical formulations. Together, period and frequency describe the same physical property β how quickly the structure oscillates β and the choice between them is largely a matter of convention.
In earthquake engineering, natural frequency is the bridge between ground motion and structural response. Earthquakes produce ground motions with a broad range of frequencies, typically from 0.1 Hz to 20 Hz. Structures with natural frequencies in the range of strong ground motion energy will experience amplified response, while those outside this range will respond more gently. Short, stiff structures typically have high natural frequencies (2β10 Hz); tall, flexible structures have low natural frequencies (0.1β1 Hz); and mid-rise structures fall in between (1β3 Hz). This distribution explains many observed damage patterns: the 1985 Mexico City earthquake, with dominant periods around 2 seconds, caused disproportionate damage to mid-rise buildings whose natural periods matched the ground motion. Similarly, the 1994 Northridge earthquake caused severe damage to parking structures with high natural frequencies, which resonated with the high-frequency content of the near-source motion.
Natural frequency is measured and monitored using the same techniques as natural period β ambient vibration testing, forced vibration testing, and modal analysis. In structural health monitoring, changes in natural frequency are among the most reliable indicators of damage, since damage typically reduces stiffness and thus lowers frequency. However, natural frequency is also sensitive to environmental factors such as temperature, humidity, and occupancy, which can cause shifts of several percent even without damage. Distinguishing damage-induced frequency shifts from environmental effects is a major challenge in SHM. In design, engineers use natural frequency to select appropriate ground motions, to avoid resonance with expected loading frequencies (such as wind-induced vortex shedding or machine vibrations), and to ensure that the structure's dynamic response falls within the range assumed by code-based design procedures.