A multiple times scale solution for non-linear vibration of mass grounded system

In this paper, the vibration of a mass grounded system which includes two linear and non-linear springs in series has been considered. Since this system, depending on its parameters can oscillate symmetrically and asymmetrically, both cases have been solved using multiple times scales (MTS) method and some analytical relations have been obtained for natural frequency of oscillations. The results have been compared with previous work and good agreement has been obtained. Also forced vibrations of system in primary and secondary resonances have been studied for the first time and the effects of different parameters on the frequency-response have been investigated.