Analytical treatment of the transient motion of inertial beams attached to coupling inertial resonators

Abstract This paper presents, for the first time, an analytical formulation to determine transient response of elastic beam possessing distributed inertia and connected a coupling inertial resonator, represented by gyroscopic spinner. The latter couples transverse displacement components in two perpendicular directions, thus producing roto-flexural vibrations. A detailed parametric study is presented that illustrates effects beam’s resonator’s characteristics. limit case massless examined it shown some situations should not be neglected. Analytical results are also validated finite element computations. An illustration demonstrates effectiveness using considered devices mitigate hazardous vibrations structural systems. It envisaged this may useful analysis flexural waveguides metamaterials consisting elements.