RESUMO
A single-degree-of-freedom model is considered for flexible exercise bars based on the lumped-element approach. By considering the side segment of a flexible bar as a cantilever beam with an equivalent mass at the free end, its free-vibration response, as well as the forced response under the excitation of the grip, are expressed parametrically. Experiments are performed on a particular flexible bar (FLEXI_BAR) in order to obtain numerical values for quantifying the model's parameters. The model is also computationally simulated to study the response of the flexible bar to various excitations. The results are imported into a multi-segment musculoskeletal software (AnyBody), where the effect of different initial hand positions on the lumbar disc and back muscle forces is investigated (including Longissimus, Iliocostalis, and Transversus) during up-down exercises. The results show that all intervertebral discs and muscles forces are more sensitive to the horizontal position of the bar as compared to its vertical position.