TY - JOUR
T1 - A Closed form Solution for Nonlinear Oscillators’ Frequencies Using Amplitude-Frequency Formulation
AU - Barari, Amin
AU - Kimiaeifar, Amin
AU - Nejad, M.G
AU - Motevalli, M
AU - Sfahani, G
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Amplitude Frequency Formulation (AFF)
KW - Nonlinear Oscillators
KW - Analytical Investigations
KW - Energy Balanced Method (EBM)
KW - Amplitude Frequency Formulation (AFF)
KW - Nonlinear Oscillators
KW - Analytical Investigations
KW - Energy Balanced Method (EBM)
UR - http://www.scopus.com/inward/record.url?scp=84872482751&partnerID=8YFLogxK
U2 - 10.3233/SAV-2012-0683
DO - 10.3233/SAV-2012-0683
M3 - Journal article
SN - 1070-9622
VL - 19
SP - 1415
EP - 1426
JO - Shock and Vibration
JF - Shock and Vibration
IS - 6
ER -