TY - JOUR

T1 - Presence of Resonance Frequencies in a Heavily Damped Two-Degree-of-Freedom System

AU - Wang, Dongwei

AU - Ji, Tianjian

AU - Zhang, Qingwen

AU - Duarte, Ernesto

N1 - The work reported in this paper has been supported by the Leverhulme Trust for the Human-Structure Interaction—Applying Body Biodynamics into Structural Dynamics project, which is gratefully acknowledged.

PY - 2014/2

Y1 - 2014/2

N2 - 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.

AB - 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.

KW - Natural frequency; Resonance frequency; Highly damped two-degree-of-freedom (TDOF) system; Human–structure interaction; Experiment.

U2 - 10.1061/(ASCE)EM.1943-7889.0000668

DO - 10.1061/(ASCE)EM.1943-7889.0000668

M3 - Article

VL - 140

SP - 406

EP - 415

JO - Journal of Engineering Mechanics

JF - Journal of Engineering Mechanics

SN - 0733-9399

IS - 2

ER -