finite element modelling and simulation of the hysteretic ‎behaviour of single- and bi-metal cantilever beams using a ‎modified non-linear beta-damping model

this paper explores a novel non-linear hysteresis model obtained from the modification of the conventional kelvin-voigt model, to produce a nonviscous hysteretic behaviour that is closer to metal damping. two case studies are carried out for a vibrating cantilever beam under tip loading (bending), the first considering a single uniform material and the second considering a bimetallic structure. the damping behaviour is studied in the frequency domain (constant damping ratio model vs. kelvin-voigt/ beta damping model) and timed-omain (proposed modified hysteresis model vs. kelvin-voigt/ beta damping model). in the frequency domain, it was found that the kelvinvoigt model essentially damps out the displacement response of the modes more than the constant damping ratio model does. in the transient analysis, the kelvin-voigt model likewise produced unnaturally rapid damping of the oscillations for both the single and bimetal beam, compared to the modified hysteretic damping model, which produced a damping behaviour closer to actual metal behaviour. this was consistent with results obtained in the frequency domain.