Shape adaptation of beams (1D) and plates (2D) to maximise eigenfrequencies

Abstract

Finding the optimal structural design to avoid resonance has been a goal for decades. While recent applied methods often result in using additional active systems or higher mass, structural adaptation enables to shift eigenfrequencies without adding weight. The aim of this study is to investigate the influence of the structural adaptation of a beam and a plate on its eigenfrequency change, while varying the height of the structural pre-deformation according to its mode shapes. Besides the maximisation of single eigenfrequencies, also the simultaneous increase of multiple eigenfrequencies is analysed. It is possible to almost exclusively raise the frequency of the targeted [Formula: see text]-th mode shape ([Formula: see text] = 1–5) of a beam, while the increase of the [Formula: see text]-th plate mode shape frequency ([Formula: see text] = 1–4) simultaneously alters other eigenfrequencies. Both the eigenfrequencies and specific mode shape frequencies are able to be significantly increased. In conclusion, the investigated, easy applicable method allows a strong eigenfrequency raise of axially constrained 1D and 2D structures by performing only small structural deformations without adding additional weight.