Presence of Resonance Frequencies in a Heavily Damped Two-Degree-of-Freedom System

It has been experimentally identified that a stationary crowd or an individual acts like a mass-spring-damper in structural vibration. However, experiments have shown that only one resonance frequency or damped natural frequency of human–structure systems are observed on structures, such as grandstands or floors with crowds. This paper studies the presence of the two resonance frequencies in a heavily damped, two-degree-of-freedom (TDOF) system in theory and in experiment. The invisibility, or nonpresence, of a resonance frequency is defined by investigating a heavily damped single-degree-of-freedom (SDOF) system subjected to a harmonic load. By using frequency response functions (FRFs) for acceleration, it is demonstrated that the observable presence of the two resonance frequencies of the TDOF system depends on the mass ratio and frequency ratio of the upper SDOF model to the lower SDOF model and the damping ratio of the upper SDOF model. The conditions for the presence of the two resonance frequencies are presented graphically based on a study of over 5,000 cases that covered reasonable ranges for these three parameters. Two sets of human–structure interaction experiments, whose design was based on the conditions for observing the resonance frequencies, demonstrated qualitatively the effect of the mass ratio of the system and damping ratio of the human body on the presence of the resonance frequencies, thus verifying the theoretical results. These limiting conditions are discussed and the observation of only one resonance frequency in experiments on some human–structure systems is explained.