Apparent mass of small children: Modelling

Mass-spring-damper models are widely available for quantifying the whole-body vibration characteristics of primates, human adolescents and human adults, but no models have previously been developed for small children. In this study a single degree of freedom, linear, mass-spring-damper with base support model was determined from the seated vertical apparent mass modulus function of each of eight small children of less than 18 kg in mass. A differential evolution optimisation algorithm was used in conjunction with a mean squared error measure and penalty functions to identify the optimal child model parameter values. The eight child models were characterised by a mean moving mass m1 of 8.5 kg, a mean body stiffness k1 of 21,131 N/m and a mean damping coefficient c1 of 329 Ns/m. Comparison to the parameter values of similar models reported in the literature for Rhesus monkeys, Baboons, large children and adults suggests that the values obtained in the current study for small children are intermediate between the smaller primates and the larger humans. A regression analysis of the model parameters was performed as a function of subject mass for a data set consisting of the eight child models, 12 similar models for primates, and 60 similar models for large children and adults. The moving mass m1 of the group of models grew with a power exponent of approximately unity, the body stiffness k1 grew with a power exponent of approximately +1/2, the damping coefficient c1 grew with a power exponent of approximately +3/4 and the dimensionless damping ratio was independent of subject mass. The natural frequency of the models grew with a power exponent of approximately −1/4.