In the past few decades the motion of multidegree of freedom (multi-DOF) oscillation systems has been widely considered. Moochhala and Raynor 1 proposed an approximate method for the motions of unequal masses connected by (n+1) nonlinear springs and anchored to rigid end walls. Huang 2 studied on the Harmonic oscillations of nonlinear two-degree-of-freedom systems. Gilchrist 3 analyzed the free oscillations of conservative quasilinear systems with two degrees of freedom. Efstathiades 4 developed the work on the existence and characteristic behaviour of combination tones in nonlinear systems with two degrees of freedom. Alexander and Richard 5 considered the resonant dynamics of a two-degree-of-freedom system composed of a linear oscillator weakly coupled to a strongly nonlinear one, with an essential (nonlinearizable) cubic stiffness nonlinearity. Chen 6 used generalized Galerkin's method to nonlinear oscillations of two-degree-of-freedom systems. Ladygina and Manevich 7 investigated the free oscillations of a conservative system with two degrees of freedom having cubic nonlinearities (of symmetric nature) and close natural frequencies by using multiscale method. Cveticanin 8, 9 used a combination of a Jacobi elliptic function and a trigonometric function to obtain an analytical solution for the motion of a two-mass system with two degrees of freedom in which the masses were connected with three springs.
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