Apparent mass matrix of standing subjects exposed to multi-axial whole-body vibration

Abstract

This paper describes the experimental characterisation of the apparent mass matrix of eight male subjects in standing position and the identification of nonlinearities under both mono-axial and dual-axis whole-body vibration. The nonlinear behaviour of the response was studied using the conditioned response techniques considering models of increasing complexity. Results showed that the cross-axis terms are comparable to the diagonal terms. The contribution of the nonlinear effects are minor and can be endorsed to the change of modal parameters during the tests. The nonlinearity generated by the vibration magnitude is more evident in the subject response, since magnitude-dependent effects in the population are overlaid by the scatter in the subjects' biometric data. The biodynamic response is influenced by the addition of a secondary vibration axis and, in case of dual-axis vibrations, the overall magnitude has a marginal contribution. Practitioner Summary: We have measured both the diagonal and cross-axis elements of the apparent mass matrix. The effect of nonlinearities and the simultaneous presence of vibration along two axes are smaller than the inter-subject variability.

Vibration transmissibility and apparent mass changes from vertical whole-body vibration exposure during stationary and propelled walking

“…Continued study of the transmissibility of standing people has revealed that the body's response to WBV is heavily affected by postural differences (Harazin and Grzesik, 1998;Subashi et al, 2008;Tarabini et al, 2013). In addition to transmissibility, the apparent mass of humans exposed to WBV both while standing and seated has also been shown to change with frequency and posture, and is non-linear Griffin, 1989, 1990;Matsumoto and Griffin, 2003;Tarabini et al, 2014Tarabini et al, , 2016. Most of the studies (Nawayseh and Griffin, 2006;Tarabini et al, 2013Tarabini et al, , 2014Tarabini et al, , 2016 evidenced that the response of the standing human body depends on the knee joint angle.…”

“…In addition to transmissibility, the apparent mass of humans exposed to WBV both while standing and seated has also been shown to change with frequency and posture, and is non-linear Griffin, 1989, 1990;Matsumoto and Griffin, 2003;Tarabini et al, 2014Tarabini et al, , 2016. Most of the studies (Nawayseh and Griffin, 2006;Tarabini et al, 2013Tarabini et al, , 2014Tarabini et al, , 2016 evidenced that the response of the standing human body depends on the knee joint angle. Seeing that there were already evident differences in the human response to WBV with different standing postures, it was thought that there may be a need for the investigation of the human response to vibration while walking.…”

Design and Testing of a 3-DOF Robot for Studying the Human Response to Vibration

“…Experimental studies have been conducted in controlled and reproducible conditions, in order to observe the mechanical behavior of the human body under WBV conditions and to develop mathematical models representing specific aspects of the body's response [9][10][11][12][13][14][15][16][17][18]. Tarabini et al [12] investigated the effect of body posture on the apparent mass distribution of standing subjects, applying the vibration with an electrodynamic shaker.…”

“…The vibrating platform with a person on it should also be able to reach the acceleration of 5 m/s 2 along the three axes. Finally, the maximum weight carried by the shaker is defined as 200 kg, which corresponds to the apparent mass in the vertical direction of a standing subject weighing 100 kg subjected to vertical vibrations at the resonance frequency of 5-6 Hz [14].…”

Setup for the Measurement of Apparent Mass Matrix of Standing Subjects

“…The equivalent Von Mises stresses were computed by imposing on the upper disk the maximum displacement at the highest acceleration magnitude along the horizontal and vertical directions. As in the previous case, the standing subject was modeled with a vertical force of 2800 N; since the AM along the horizontal axis is much smaller than the one along the vertical axis [28] and given the limited force provided by the horizontal shaker, the horizontal forces were not included in the analysis. The stresses on the compliant elements of the dual-axis interface were not critical, given that the displacement along the compliant direction was driven by the lateral shaker, and the elements were sized to achieve low stiffness to avoid force loss.…”