Two degree-of-freedom oscillator coupled to a non-ideal source

In the paper the one-mass two degree-of-freedom system with non-ideal excitation is considered. The resonance motion of the system is investigated. The mathematical model of the system contains three coupled second order differential equations. In the paper an analytical solving procedure is developed. The steady-state motion and the criteria for stability of solutions are developed. Two special cases of motion depending on the frequency properties of the system are studied. When the frequency properties in both orthogonal direction are equal there is only one resonance. If the frequency in one direction is two times higher than in other two different resonances occur: one in x and the other in y direction. The conditions for jump phenomena and for Sommerfeld effect are presented. The analytically obtained solutions are compared with numerical ones. They show good agreement.