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.

本文首次提出了一种解析公式，用于确定具有分布惯性并连接到以陀螺旋转器为代表的耦合惯性谐振器的弹性梁的瞬态响应。后者在两个垂直方向上耦合梁的横向位移分量，从而产生旋转挠曲振动。进行了详细的参数研究，该研究说明了光束的分布惯性和谐振器特性的影响。研究了无质量梁的极限情况，结果表明，在某些情况下，不应忽略梁中的分布惯性。分析结果也通过有限元计算得到验证。还提供了一个说明，说明了使用所考虑的惯性装置来减轻结构系统中的有害振动的有效性。可以设想，本文可能对弯曲波导和由惯性弹性梁单元组成的超材料的分析有用。