Dynamics of the Euler–Bernoully beam with distributed hysteresis properties

In this paper, we present a new mathematical approach to the analysis of a beam with distributed hysteresis properties. These hysteresis characteristics are described by two methods: phenomenological (Bouc–Wen model) and constructive (Prandtl–Ishlinskii model). The equations for beam are developed using the well-known Hamilton method. We investigate the dynamic response of a hysteresis beam under various external loads, including impulse, periodic and seismic loads. The results of numerical simulations show that the hysteresis beam exhibits differently to external influences as compared to the classical Euler-Bernoulli beam. In particular, under the same external loads, the vibration amplitude and energy characteristics of the hysteresis beam are lower than those of the classical one. These findings can be useful for buildings developers in the design of external load resistant buildings and structures