Non-linear free and forced vibration of bi-directional functionally graded truncated conical tube based on the nonlocal gradient strain theory

• Published in: Waves in random and complex media 2024-07, Vol.34 (4), p.2366-2393
• Main Authors: Zhang, Fusheng, Lu, Wei
• Format: Article
• Language: English
• Subjects: Beam theory (structures); bi-directional FG; Boundary conditions; Cross-sections; Differential equations; Forced vibration; functionally graded tube; Functionally gradient materials; Generalized differential quadrature method; Hamilton's principle; Iterative methods; Nanotubes; non-uniform tube; Nonlinear response; Nonlinear vibration; nonlocal gradient strain theory; Parameters; Quadratures; Strain analysis; Thickness; truncated conical tube; Two dimensional analysis
• ISSN: 1745-5030; 1745-5049
• DOI: 10.1080/17455030.2021.1956016

This paper deals with the free and forced, linear and nonlinear vibration of functionally graded (along with thickness) nanotube, considering the non-uniform cross-section that made a two-dimensional functionally graded (2D-FG) structure. The bi-dimensional nanostructure-dependent governing equation is modeled based on the classic beam theory (Euler-Bernoulli), and they are derived by Hamilton's principle based on nonlocal gradient strain theory considering the von-Kármán nonlinear strain and the external harmonic load. To solve the general equations and calculate the results, the generalized differential quadrature method (GDQM) was used coupled with the numerical iteration method for the nonlinear response. The results are discussed for the different simply-supported and clamped boundary conditions. The 2D-FG nanotube's behavior is analyzed for different nonlinear amplitudes, nonlocal strain gradient parameters and nonlocal parameters, different rates of cross-sections, and different material distributions.