Investigation of wave propagation in architected uniform triangle mass center fractal nano-bio-filters based on microtubules

Microtubules, polymer tubes stretched from the cell nucleus to the cell membrane, are the major parts of the cytoskeleton that provide the mechanical rigidity, organization, and shape retention for the cytoplasm of eukaryotic cells. These structures play a key role in some cellular processes such as cell division, intracellular transport, and the internal organization of cells. In all the above applications, the network structure of microtubules is the main reason for the importance of in-depth studies of their mechanical properties. In this paper, the propagation of elastic waves in periodic networks based on two-dimensional fractal microtubules of fixed mass-center triangles is analyzed. This study begins with the selection of a suitable beam model for a microtubule and examines the dynamic behavior of microtubules by creating periodic structures. To obtain dispersion curves, finite element models of microtubules and their networks are developed, and the bandgap equations are calculated based on Bloch's theory. The results show that depending on the topology of the selected unit cells as well as the considered periods, it is possible to design a frequency gap in specific ranges for the application of low and high-frequency bio-filters. This study helps researchers control or absorb some unwanted vibrations using periodic structures, and thanks to their better biocompatibility, these networks can be used in next-generation nanomechanical devices such as implantable biosensors.