Shape Adaptation of 1D, 2D, and 3D Structuresto increase Eigenfrequencies
Finding the optimal structural design to avoid resonance by shifting eigenfrequencies out of the range of external frequencies has been a goal for decades. Biological structures, such as diatom shells, obtain an overall shape adaptation similar to their mode shapes, which might lead to improved vibration characteristics. The aim of this study was to investigate the eigenfrequency increases of a 1D Bernoulli beam, a 2D Kirchhoff plate and a 3D Timoshenko beam by pre-deforming the structures according to the corresponding mode shapes. Besides the maximisation of single eigenfrequencies, also the simultaneous increase of other eigenfrequencies were analysed. The results showed that the eigenfrequencies can be strongly increased by shaping the structures according to the corresponding mode shapes. Small pre-deformations led already to high eigenfrequency increases. In conclusion, the investigated, easy applicable method allowed a strong eigenfrequency increase by performing only small structural deformations without additional weight increase.