Lucas and Fibonacci Effect in Bolted Metallic Dampers Arranged With Lucas Rectangle

ABSTRACT

Metallic dampers have become popular in recent years, particularly for structural reinforcement, because of their rapid response and interchangeability. This study aims to investigate the effects of the Fibonacci and Lucas number sequences on the structural performance of a bolted metallic damper arranged according to these sequences, using experimental and numerical (ANSYS) analyses. Four specimens were tested under a cyclic loading protocol in ± 2.5 kN increments: one standard, equally spaced specimen (Specimen 1) and three others based on the Fibonacci and Lucas sequences (Specimens 2, 3, and 4). Experimental results showed that the damper designed according to the Lucas sequence (Specimen 3) achieved the highest cumulative energy absorption capacity in the pull direction of 476.84 J and exhibited more stable behavior than the reference specimen. Specimen 4 (Fibonacci) achieved the highest displacement under push loading (10.06 mm), making it the most effective model at increasing the system's ductility. Numerical analyses conducted using ANSYS explain the fundamental reasons for these performance differences. von Mises, shear, and normal stress analyses confirmed that the Lucas arrangement distributes stress concentrations most homogeneously across the plate (optimizing stress flow) and prevents the plastic deformation of the end bolts observed in the conventional arrangement. Plastic strain maps show that mathematical arrangements use the yield capacity of the material more efficiently. In conclusion, it has been demonstrated that bolt arrangements based on the Lucas and Fibonacci sequences significantly improve both the energy absorption capacity and the ductility of metallic dampers compared with standard methods.