Nonlinear vibrations of fractional nonlocal viscoelastic nanotube resting on a Kelvin-Voigt foundation

The nonlinear dynamic analysis of the fractional viscoelastic nanotube resting on a foundation, with simply-supported boundary conditions, is performed. The existence of a significant internal damping for the structure led to the choice of a fractional Zener model to obtain the governing equation. The solving of this is made with the help of a new variational iteration method, the Laplace transform, Bessel functions theory and binominal series. The effects of the nonlocal parameter, fractional order and viscoelastic foundation on the transverse displacements of the nanostructure are studied. Validation study was performed by comparing the results obtained for the model of the structure with the corresponding ones existing in the literature. The proposed algorithm for solving the integral-differential governing equation is useful in the engineering design of the biological nano-sensors and nanoscale devices resting on a viscoelastic foundation.

Automated summary

The nonlinear dynamic analysis of a fractional viscoelastic nanotube resting on a foundation with simply-supported boundary conditions was conducted using a fractional Zener model. Various methods such as a new variational iteration method, Laplace transform, Bessel functions theory, and binominal series were utilized to solve the governing equation. The study investigated the effects of nonlocal parameters, fractional order, and viscoelastic foundation on the transverse displacements of the nanostructure, with validation performed by comparing results with existing literature. The proposed algorithm for solving the integral-differential governing equation is beneficial for engineering design of biological nano-sensors and nanoscale devices on a viscoelastic foundation.