Linearization of embedded patterns for optimization of structural natural frequencies

Abstract

The dynamic characteristics of structures (beams and plates) can be significantly changed by embossing small out-of-plane patterns in these structures. Recent results in literature show, both numerically and experimentally, that shaping a beam in the geometry of its first mode shape significantly increases the value of the first natural frequency of the beam. This phenomenon also occurs when the beam is shaped in the geometry of other mode shapes, and in the case of plates. This work presents new results (numerical and experimental) regarding the linearization of the forms to be imposed to the structure, focusing on shapes composed of straight regions, which would ease the design of stamping tools for example. The results show that the use of straight regions in the geometry of the beams (linear embossed pattern) has a similar effect to that obtained with curved shapes but requiring bigger distances to the baseline (higher shaping deformations). It is also shown that the linearized shapes can be used to optimize the shape of a beam for desired natural frequencies.