Innovative zigzag hollow symmetrically composite tube: Examination through stress strain gradient elasticity theory

In recent decades, there has been an increase in research focused on nanotechnology, examining its remarkable properties and investigating its applications across various domains, including microelectronics, energy, mechanics, and biology. This paper examines the vibration of zigzag single-walled carbon nanotubes utilizing stress-strain gradient theory. The governing equations, along with boundary conditions, are employed to understand the influence of Young's modulus on the vibrations of a zigzag construction. Consequently, the Young's modulus of the tube is elevated for the impact of shape change through simulation on the structural flexibility of zigzag single-walled carbon nanotubes. Different graphs are developed to measure tube Young's modulus and vibration frequencies. The frequencies lie in the terahertz spectrum to investigate the smallest influences on the vibrations of zigzag single-walled carbon nanotubes. The zigzag index ranges as (6, 0), (9, 0), and (14, 0). When vibration happens in a zigzag tube with the designated indices, one can observe the complete mechanism of frequencies. Under both boundary conditions, Young's modulus increases the frequency surges at stiffness values of 1.0 and 1.5. As the frequency rises, the stuff gets stiff. Computational methods are used to evaluate the present findings for validity and correctness.