Affiliations: Department of Civil Engineering, Aalborg University,
Aalborg, Denmark | Department of Mechanical Engineering, Aalborg
University, Aalborg East, Denmark | Department of Civil and Mechanical Engineering, Babol
University of Technology, Babol, Iran | Department of Civil Engineering, Azad University,
Central Tehran Branch, Tehran, Iran
Note: [] Corresponding author: A. Kimiaeifar, Department of Mechanical
Engineering, Aalborg University, Fibigerstraede 16, DK-9220 Aalborg East,
Denmark. E-mail: [email protected]
Abstract: Many nonlinear systems in industry including oscillators can be
simulated as a mass-spring system. In reality, all kinds of oscillators are
nonlinear due to the nonlinear nature of springs. Due to this nonlinearity,
most of the studies on oscillation systems are numerically carried out while an
analytical approach with a closed form expression for system response would be
very useful in different applications. Some analytical techniques have been
presented in the literature for the solution of strong nonlinear oscillators as
well as approximate and numerical solutions. In this paper, Amplitude-Frequency
Formulation (AFF) approach is applied to analyze some periodic problems arising
in classical dynamics. Results are compared with another approximate analytical
technique called Energy Balance Method developed by the authors (EBM) and also
numerical solutions. Close agreement of the obtained results reveal the
accuracy of the employed method for several practical problems in
engineering.
Keywords: Amplitude Frequency Formulation (AFF), nonlinear oscillators, analytical investigations, Energy Balanced Method (EBM)
