RT journal article
T1 Convergence Analysis of the Straightforward Expansion Perturbation Method for Weakly Nonlinear Vibrations
A1 Moreno Pulido, Soledad
A1 García Pacheco, Francisco Javier
A1 Sánchez Alzola, Alberto
A1 Rincón Casado, Alejandro
A2 Estadística e Investigación Operativa
A2 Ingeniería Mecánica y Diseño Industrial
A2 Matemáticas
K1 numerical analysis
K1 approximation theory
K1 nonlinear vibration
K1 perturbation method
K1 Banach space
K1 unitary algebra
K1 sup norm
AB There are typically several perturbation methods for approaching the solution of weakly nonlinear vibrations (where the nonlinear terms are "small" compared to the linear ones): the Method of Strained Parameters, the Naive Singular Perturbation Method, the Method of Multiple Scales, the Method of Harmonic Balance and the Method of Averaging. The Straightforward Expansion Perturbation Method (SEPM) applied to weakly nonlinear vibrations does not usually yield to correct solutions. In this manuscript, we provide mathematical proof of the inaccuracy of the SEPM in general cases. Nevertheless, we also provide a sufficient condition for the SEPM to be successfully applied to weakly nonlinear vibrations. This mathematical formalism is written in the syntax of the first-order formal language of Set Theory under the methodology framework provided by the Category Theory.
PB MDPI
SN 2227-7390
YR 2021
FD 2021-05
LK http://hdl.handle.net/10498/24993
UL http://hdl.handle.net/10498/24993
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 08-nov-2026