A method for examining steady state solutions of forced discrete systems with strong non-linearities

An analytical method is presented for computing the exact steady state motions of forced, undamped, discrete systems with strong non-linearities. By expressing the forcing as a function of the steady state displacements, the forced problem is transformed to an equivalent free oscillation and subsequently a matching procedure is followed which results in the uncoupling of the differential equations of motion at the steady state. General conclusions are made concerning the topological portrait of the steady state response curves and applications of the method are given for systems with two degrees of freedom and cubic non-linearities.