aDepartment of Mechanics, Faculty of Technical Sciences, University of Novi Sad, 21121 Novi Sad, Serbia
bInstitute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, United Kingdom
Abstract:
An analytical approach to determine the steady-state response of a damped and undamped harmonically excited oscillator with no linear term and with cubic non-linearity is presented. The governing equation is transformed into a form suitable for the application of a classical series expansion technique. The Linstedt–Poincaré method and the method of multiple scales are then used to determine the amplitude-frequency response and approximate solution for the response at the excitation frequency. The results obtained are compared with numerical solutions and analytical solutions found in the literature for the case when there is strong non-linearity.