Within the cytoplasm of a cell, there is a complex network of protein fibers that help maintain the cell’s shape, secure some cells in specific positions, and allow cytoplasm and vesicles to move within the cell. These protein fibers enable cells within multicellular organisms to move. Collectively, this skeleton-like complex network of protein fibers is known as the Cellular Cytoskeleton in biology. There are many structural model hypotheses that scholars have proposed. However, there were constrained to the efforts of abstraction and conception to identify the mechanical behavior of the Cytoskeleton structure. Understanding the mechanical behavior of the Cytoskeleton is highly important to learn the important function of biological processes in a cell to heal humans from diseases by developing the appropriate medicines to cure the broken/infected cell. Moreover, many viruses’ structures can be observed and identified from the cellular mechanical point of view. Sophisticated treatment methods to tame the viruses’ activities could be discovered in the near future.

There are three types of filamentous proteins: filamentous actin (F-actin), intermediate filaments, and microtubules. The dynamic mechanism of a cellular cytoskeleton is essential for its role as a cell, and its accurate characterization has been a long-standing problem for cell scientists. A cytoskeleton’s vibrations are highly influenced by interactions of filamentous proteins mediated by axial vibration of the stiff microtubules (compressive member) and lateral vibration of F-actin (tensile member). Among various structures in a cell, the cytoplasmic contractile bundles, Lamellipodia, and filipodia cells can be modeled by a symmetrical cylinder-shape self-equilibrium Tensegrity with different radii at the top and bottom of the cylinder. The truncated cone-like cylinder model is made to be small in height compared to the radii.

The tensegrity self-vibrational behavior of the Cytoskeleton is investigated to calculate the Cytoskeleton’s natural frequencies, which are composed of the individual vibration of microtubules and F-actins experimental data. The Spectral Element Method based on the Wittrick-Williams procedure is adopted to solve the vibrational of the cellular Cytoskeleton. Various n-polygon cylindrical truncated cone-shaped skeletons to mimic the cytoskeletons are presented to demonstrate the robustness of the present study.