Abstract
This paper presents, for the first time, an analytical formulation to determine the transient response of an elastic beam possessing distributed inertia and connected to a coupling inertial resonator, represented by a gyroscopic spinner. The latter couples the transverse displacement components of the beam in the two perpendicular directions, thus producing roto-flexural vibrations. A detailed parametric study is presented that illustrates the effects of the beam’s distributed inertia and of the resonator’s characteristics. The limit case of massless beam is examined and it is shown that in some situations the distributed inertia in the beam should not be neglected. Analytical results are also validated by finite element computations. An illustration is also presented that demonstrates the effectiveness of using the considered inertial devices to mitigate hazardous vibrations in structural systems. It is envisaged that this paper may be useful in the analysis of flexural waveguides and metamaterials consisting of inertial elastic beam elements.
Highlights
In recent years, there has been an increasing interest in the study of engineering elements that produce inertial coupling effects
We present an analytical formulation that provides a method to determine the response of an inertial beam in the transient regime
We have presented an approach for analysing the transient response of an inertial beam, clamped at one end and attached to a gyro-hinge at the other end
Summary
There has been an increasing interest in the study of engineering elements that produce inertial coupling effects. This has been partially motivated by the need to better characterise the tools embedded in preexisting technologies, for instance, rotor systems used in aircraft and drive shafts employed in a variety of land and sea vehicles. Rotating elements play a crucial role in the stabilisation of light, flexible and large spacecraft, and this has motivated research in this direction concerning mechanical elements with embedded gyroscopic effects in the last 40 years. This research has been reinvigorated through the development of devices used to design structured systems or metamaterials possessing rotating inertial elements for the purposes of controlling wave. Electronic Supplementary material The online version contains supplementary material available at https://doi.org/10.1007/ s10665-021-10110-w
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