The human response to vibration is typically studied using linear estimators of the frequency response function, although different literature works evidenced the presence of non-linear effects in whole-body vibration response. This paper analyses the apparent mass of standing subjects using the conditioned response techniques in order to understand the causes of the non-linear behaviour. The conditioned apparent masses were derived considering models of increasing complexity. The multiple coherence function was used as a figure of merit for the comparison between the linear and the non-linear models. The apparent mass of eight male subjects was studied in six configurations (combinations of three vibration magnitudes and two postures). The contribution of the non-linear terms was negligible and was endorsed to the change of modal parameters during the test. Since the effect of the inter-subject variability was larger than that due to the increase in vibration magnitude, the biodynamic response should be more meaningfully modelled using a linear estimator with uncertainty rather than looking for a non-linear modelling.

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.

This paper describes a system for the measurement of the apparent mass (AM) matrix of standing subjects. The system uses two electrodynamic shakers to generate vibrations along two mutually perpendicular axes (vertical and horizontal) and allows the identification of the full AM matrix with two tests, in which the standing subject is exposed to vertical excitation combined in turn with fore-and-aft and lateral vibration. A 3-D force platform measures the forces and the torques transmitted from the vibrating platform to the feet. The force platform, set up with piezoelectric load cells, has been designed in order to obtain a measurement bandwidth of 20 Hz. The supports of different load cells are meant to minimize bending moments on the sensors and to minimize the axes crosstalk. The force platform has been calibrated with a least-squares approach, using reference masses and a dynamometric hammer. The AM uncertainty, evaluated through the experiments' repeatability and reproducibility, is lower than 3.4% along the three axes (confidence level 68%). The measurement bandwidth is 20 Hz (±2%) and the crosstalk between orthogonal axes is lower than 5%, in accordance with the design requirements