Convergence of a variational iterative algorithm for nonlocal vibrations analysis of a nanotube conveying fluid

• Published in: Mathematical modelling and analysis Vol. 28; no. 3; pp. 360 - 373
• Main Author: Martin, Olga
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 04.09.2023
• Subjects: Algorithms; Boundary conditions; Convergence; Conveying; Dynamic response; Flow velocity; Forced vibration; Galerkin’s method; Iterative algorithms; Iterative methods; Laplace transform; Laplace transforms; nanobeam conveying fluid; Nanotubes; nonlocal calculus; variational iteration method; Viscoelasticity; nanobeam conveying fluid; nonlocal calculus; Laplace transform; Galerkin’s method; variational iteration method
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2023.16620

The amplitudes of the forced oscillations of a nano-structure conveying fluid are the solutions of an inhomogeneous integral-differential system. This is solved by an easily accessible scheme based on the variational iteration method (VIM), Galerkin’s method and the Laplace transform techniques. The presented method is accompanied by the study of the convergence of the iterative process and of the errors. In the literature, the dynamic response of a viscoelastic nanotube conveying fluid is frequently obtained by an iterative method. This leads to the double convolution products, whose presence will be avoided in the new method proposed in this paper. Thus, the numerical results will be obtained much faster and more accurately.