Second harmonic and ½ subharmonic excitations of machine-isolator-floor systems

The governing equations for the non-linear vibrations of machine- isolator-floor systems are derived from the principle of virtual work. The averaging technique and the method of multiple scales are used to solve the problem. The main purpose of the present paper is to deal with the second harmonic and the ½ subharmonic excitations. The Routh-Hurwitz criterion is used to check the stability of the i subharmonic excitations. It is found that there exists a threshold value of the dynamic loading beyond which the system becomes unstable. The numerical results show that the threshold values become larger for a stiff isolator or/and for a large supporting area of the machine, but become smaller for a heavy machine.