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

Wang, Dongwei; Ji, Tianjian; Zhang, Qingwen; Duarte, Ernesto

doi:10.1061/(asce)em.1943-7889.0000668

Cited by 8 publications

(6 citation statements)

References 12 publications

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“…The equations of motion for the 2DOF model (Figure a) are given in time domain by Equation , where u s and u h are the displacement of the structure and the crowd, respectively; “

\overset{}{true}

” represents “time derivative”; m es , c es and k es are respectively the mass, damping constant and stiffness of the empty structure; m h , c h and k h are respectively the mass, damping constant, and stiffness of crowd and F s is an input force applied on the structure.

([], \begin{matrix} m_{es} & 0 \\ 0 & m_{h} \end{matrix}) ({}, \begin{matrix} {\ddot{u}}_{s} ((), t) \\ {\ddot{u}}_{h} ((), t) \end{matrix}) + ([], \begin{matrix} c_{es} + c_{h} & - c_{h} \\ - c_{h} & c_{h} \end{matrix}) ({}, \begin{matrix} {\dot{u}}_{s} ((), t) \\ {\dot{u}}_{h} ((), t) \end{matrix}) + ([], \begin{matrix} k_{es} + k_{h} & - k_{h} \\ - k_{h} & k_{h} \end{matrix}) ({}, \begin{matrix} u_{s} ((), t) \\ u_{h} ((), t) \end{matrix}) = ({}, \begin{matrix} F_{s} ((), t) \\ 0 \end{matrix})

…”

Section: Theoretical Background On Human‐structure Interactionmentioning

confidence: 99%

“…The frequency response function (FRF), H 2DOF (ω) , of the 2DOF system relating the acceleration of the structure (output) with the input force acting on the structure can be defined as

H_{2 italicDOF} ((), ω) = \frac{- ω^{2} ((), - m_{h} ω^{2} + i c_{h} ω + k_{h})}{([], - m_{es} ω^{2} + ((), k_{es} + k_{h}) + i ((), c_{es} + c_{h}) ω) ((), - m_{h} ω^{2} + i c_{h} ω + k_{h}) - {(k_{h} + i c_{h} ω)}^{2}} .

…”

Section: Theoretical Background On Human‐structure Interactionmentioning

confidence: 99%

“…This 2DOF model has been mainly used for passive persons and lately for walking people . In order to characterise the HSI, this model can be used to obtain, in a first step, the dynamic properties of the empty structure ( m es , c es and k es ) and, in a second step, to extract the biomechanical properties of the body ( m h , c h and k h ) based on the dynamic response of the occupied structure.…”

Section: Theoretical Background On Human‐structure Interactionmentioning

confidence: 99%

“…Similarly to the SDOF model 1, the model 2 (Figure b) represents the global assembly “structure plus person” that can be described by only one vibration mode, where m os , c os and k os are respectively the mass, damping constant, and stiffness of the occupied structure. As reported in the literature, model 2 is used before identifying the dynamic properties of the human body (see also Section ). The main assumption here is that the human body behaves, in most cases, as a highly damped mass absorber so that the FRF relating the structure acceleration with the applied force is described as

H_{SDOF} ((), ω) = \frac{- ω^{2}}{- m_{os} ω^{2} + i c_{os} ω + k_{os}} .

…”

Section: Theoretical Background On Human‐structure Interactionmentioning

confidence: 99%

“…In turn, the 2DOF model 3 (Figure c) incorporates the modal properties of the human body and is based on previous works, as explained in Section (see the 2DOF model in Figure a). On the other hand, the novelty of the proposed model 3 is that the experimental human‐induced force [ P' gnd (t) ] is summed to the shaker force and both act on the DOF of the structure.…”

Section: Theoretical Background On Human‐structure Interactionmentioning

confidence: 99%

See 4 more Smart Citations

Active human‐structure interaction during jumping on floors

Gaspar

Caetano

Moutinho

et al. 2019

Struct Control Health Monit

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The study of the human-structure interaction (HSI) using biodynamics models has gained attention lately. Several studies have demonstrated that the passive (standing still) and active (bobbing/bouncing or walking) persons can act for the benefit of the structural system by considering their body dynamic properties. Nevertheless, little concern has been addressed regarding the HSI during jumping loads on floors. This kind of human load is often considered as a "force-only" model by design guides, and the body dynamics is disregarded.Therefore, aiming at filling this gap, this work investigates experimental and numerically an individual jumping on a vibrating (flexible) floor mounted in the laboratory. The active HSI was evaluated considering both single and two degree of freedom models in time and frequency domains. Besides, the assessment of the human body dynamic parameters (spring, mass and damper) was carried out based on optimisation techniques. The results show the potential benefit of taking into account the active HSI in near-resonant cases to the detriment of a force-only model.

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“…The equations of motion for the 2DOF model (Figure a) are given in time domain by Equation , where u s and u h are the displacement of the structure and the crowd, respectively; “

\overset{}{true}

([], \begin{matrix} m_{es} & 0 \\ 0 & m_{h} \end{matrix}) ({}, \begin{matrix} {\ddot{u}}_{s} ((), t) \\ {\ddot{u}}_{h} ((), t) \end{matrix}) + ([], \begin{matrix} c_{es} + c_{h} & - c_{h} \\ - c_{h} & c_{h} \end{matrix}) ({}, \begin{matrix} {\dot{u}}_{s} ((), t) \\ {\dot{u}}_{h} ((), t) \end{matrix}) + ([], \begin{matrix} k_{es} + k_{h} & - k_{h} \\ - k_{h} & k_{h} \end{matrix}) ({}, \begin{matrix} u_{s} ((), t) \\ u_{h} ((), t) \end{matrix}) = ({}, \begin{matrix} F_{s} ((), t) \\ 0 \end{matrix})

…”

Section: Theoretical Background On Human‐structure Interactionmentioning

confidence: 99%

“…The frequency response function (FRF), H 2DOF (ω) , of the 2DOF system relating the acceleration of the structure (output) with the input force acting on the structure can be defined as