Loaded Euler-Bernoulli beam with the distributed hysteresis properties

Abstract

In this article, we propose a new perspective mathematical model of the beam with the distributed hysteresis properties. Hysteresis properties are formalized within two approaches: phenomenological (Bouc-Wen model) and design (Prandtl-Ishlinskii model). The equations for the beam vibrations are obtained using the well-known Hamilton approach. The dynamical response of the beam with distributed hysteresis is considered under various types of external load, such as impulse, periodic, and a seismic load. Numerical simulations show that the hysteresis beam is more “resistant” to external loads than the classical Euler-Bernoulli beam. Particularly, with the same types of the external load, the amplitude of oscillations of the hysteresis beam as well as its energy characteristics are lower than those of the classical one. These results may find some applications in the field of the design of earthquake-resistant constructions and buildings.