Akademik Veri Yönetim Sistemi
The 8th Mediterranean International Conference of Pure & Applied Mathematics and Related Areas (MICOPAM 2025), Osijek, Hırvatistan, 8 - 12 Eylül 2025, ss.1, (Tam Metin Bildiri)
In the current work, a modal analysis on an Atomic Force Microscopy (AFM) micro-cantilever is conducted using a finite element approach for the first six eigenmodes. Analytical expressions, Timoshenko, Euler-Bernoulli, and solid models are utilized to obtain eigenfrequencies at different vibrational modes. Changes in the fundamental and higher eigenmode frequencies are noted as the geometrical parameters of the rectangular silicon micro-cantilever such as the length (100 - 300 micrometer), the width (20 - 50 micrometer), and the thickness (0.8 - 7 micrometer) change. Mode shapes of the AFM micro-cantilever are also demonstrated and evaluated for the first and higher vibration modes. The simulation results indicate that the results of the solid model obtained in the COMSOL software environment agree well with the analytical ones. Based on micro-cantilever models, eigenfrequencies have distinct tendencies to variations in values of geometrical parameters. For instance, the eigenfrequency at the sixth eigenmode varies by around 0.56 % in the width range of 20-40 micrometer based on the solid model. On the other hand, it changes by approximately 323 % in the thickness range of 0.8-6 micrometer. Therefore, the theoretical results reveal that the solid model can be robustly utilized to obtain more accurate eigenfrequencies at higher eigenmodes, compared with other cantilever beam models. Using solid models brings great opportunities to explore the observable responses of the AFM micro-cantilevers to external forces such as tip-sample interaction forces, and acoustic forces for nanometrology applications.