Interaction of the elements characterizing the quadratic nonlinearity and forced excitation with the other excitations

In nonlinear systems, the first order of smallness terms of quadratic nonlinearity and the forced excitation with nonresonance frequency and the second order of smallness terms of linear friction, cubic nonlinearity, forced and parametric excitation with resonance frequencies have no effect on the oscillation in the first approximation. However, they do· interact one with another in the second approximation a.nd new nonlinear phenomena occur. The study of these phenomena, using the asymptotic method of nonlinear mechanics [1] with a digital computer, is our aim.