Stiffness and Damping Response Associated with Shock Attenuation in Downhill Running

2004 ◽  
Vol 20 (3) ◽  
pp. 291-308 ◽  
Author(s):  
Jeffrey J. Chu ◽  
Graham E. Caldwell

Studies on shock attenuation during running have induced alterations in impact loading by imposing kinematic constraints, e.g., stride length changes. The role of shock attenuation mechanisms has been shown using mass-spring-damper (MSD) models, with spring stiffness related to impact shock dissipation. The present study altered the magnitude of impact loading by changing downhill surface grade, thus allowing runners to choose their own preferred kinematic patterns. We hypothesized that increasing downhill grade would cause concomitant increases in both impact shock and shock attenuation, and that MSD model stiffness values would reflect these increases. Ten experienced runners ran at 4.17 m/s on a treadmill at surface grades of 0% (level) to 12% downhill. Accelerometers were placed on the tibia and head, and reflective markers were used to register segmental kinematics. An MSD model was used in conjunction with head and tibial accelerations to determine head/arm/trunk center of mass (HATCOM) stiffness (K1), and lower extremity (LEGCOM) stiffness (K2) and damping (C). Participants responded to increases in downhill grade in one of two ways. Group LowSAhad lower peak tibial accelerations but greater peak head accelerations than Group HighSA, and thus had lower shock attenuation. LowSAalso showed greater joint extension at heelstrike, higher HATCOMheelstrike velocity, reduced K1stiffness, and decreased damping than HighSA. The differences between groups were exaggerated at the steeper downhill grades. The separate responses may be due to conflicts between the requirements of controlling HATCOMkinematics and shock attenuation. LowSAneeded greater joint extension to resist their higher HATCOMheelstrike velocities, but a consequence of this strategy was the reduced ability to attenuate shock with the lower extremity joints during early stance. With lower HATCOMimpact velocities, the HighSArunners were able to adopt a strategy that gave more control of shock attenuation, especially at the steepest grades.

2019 ◽  
Vol 64 (7) ◽  
pp. 583 ◽  
Author(s):  
S. Harabasz

Collisions of heavy nuclei at (ultra-)relativistic energies provide a fascinating opportunity to re-create various forms of matter in the laboratory. For a short extent of time (10-22 s), matter under extreme conditions of temperature and density can exist. In dedicated experiments, one explores the microscopic structure of strongly interacting matter and its phase diagram. In heavy-ion reactions at SIS18 collision energies, matter is substantially compressed (2–3 times ground-state density), while moderate temperatures are reached (T < 70 MeV). The conditions closely resemble those that prevail, e.g., in neutron star mergers. Matter under such conditions is currently being studied at the High Acceptance DiElecton Spectrometer (HADES). Important topics of the research program are the mechanisms of strangeness production, the emissivity of matter, and the role of baryonic resonances herein. In this contribution, we will focus on the important experimental results obtained by HADES in Au+Au collisions at 2.4 GeV center-of-mass energy. We will also present perspectives for future experiments with HADES and CBM at SIS100, where higher beam energies and intensities will allow for the studies of the first-order deconfinement phase transition and its critical endpoint.


2021 ◽  
Vol 11 (14) ◽  
pp. 6407
Author(s):  
Huiqi Liang ◽  
Wenbo Xie ◽  
Peizi Wei ◽  
Dehao Ai ◽  
Zhiqiang Zhang

As human occupancy has an enormous effect on the dynamics of light, flexible, large-span, low-damping structures, which are sensitive to human-induced vibrations, it is essential to investigate the effects of pedestrian–structure interaction. The single-degree-of-freedom (SDOF) mass–spring–damping (MSD) model, the simplest dynamical model that considers how pedestrian mass, stiffness and damping impact the dynamic properties of structures, is widely used in civil engineering. With field testing methods and the SDOF MSD model, this study obtained pedestrian dynamics parameters from measured data of the properties of both empty structures and structures with pedestrian occupancy. The parameters identification procedure involved individuals at four walking frequencies. Body frequency is positively correlated to the walking frequency, while a negative correlation is observed between the body damping ratio and the walking frequency. The test results further show a negative correlation between the pedestrian’s frequency and his/her weight, but no significant correlation exists between one’s damping ratio and weight. The findings provide a reference for structural vibration serviceability assessments that would consider pedestrian–structure interaction effects.


1996 ◽  
Vol 29 (12) ◽  
pp. 1523-1529 ◽  
Author(s):  
Mario A. Lafortune ◽  
Ewald M. Hennig ◽  
Mark J. Lake

Author(s):  
Jang-Der Jeng ◽  
Yuan Kang ◽  
Yeon-Pun Chang ◽  
Shyh-Shyong Shyr

The Duffing oscillator is well-known models of nonlinear system, with applications in many fields of applied sciences and engineering. In this paper, a response integration algorithm is proposed to analyze high-order harmonic and chaotic motions in this oscillator for modeling rotor excitations. This method numerically integrates the distance between state trajectory and the origin in the phase plane during a specific period and predicted intervals with excitation periods. It provides a quantitative characterization of system responses and can replace the role of the traditional stroboscopic technique (Poincare´ section method) to observe bifurcations and chaos of the nonlinear oscillators. Due to the signal response contamination of system, thus it is difficult to identify the high-order responses of the subharmonic motion because of the sampling points on Poincare´ map too near each other. Even the system responses will be made misjudgments. Combining the capability of precisely identifying period and constructing bifurcation diagrams, the advantages of the proposed response integration method are shown by case studies. Applying this method, the effects of the change in the stiffness and the damping coefficients on the vibration features of a Duffing oscillator are investigated in this paper. From simulation results, it is concluded that the stiffness and damping of the system can effectively suppress chaotic vibration and reduce vibration amplitude.


1999 ◽  
Vol 82 (3) ◽  
pp. 1622-1626 ◽  
Author(s):  
Pietro G. Morasso ◽  
Marco Schieppati

A stiffness control model for the stabilization of sway has been proposed recently. This paper discusses two inadequacies of the model: modeling and empiric consistency. First, we show that the in-phase relation between the trajectories of the center of pressure and the center of mass is determined by physics, not by control patterns. Second, we show that physiological values of stiffness of the ankle muscles are insufficient to stabilize the body “inverted pendulum.” The evidence of active mechanisms of sway stabilization is reviewed, pointing out the potentially crucial role of foot skin and muscle receptors.


2008 ◽  
Vol 1 (3) ◽  
pp. 311
Author(s):  
S. Hotz-Boendermaker ◽  
J. Petersen ◽  
M. Laubacher ◽  
M.-C. Hepp-Reymond ◽  
M. Schubert

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