A Theorem on the Exact Nonsimilar Steady-State Motions of a Nonlinear Oscillator

摘要: In this work the steady-state motions of a nonlinear, discrete, undamped oscillator are examined. This is achieved by using notion exact steady state, i.e., motion where all coordinates system oscillate equiperiodically, with period equal to that excitation. Special forcing functions periodic but not necessarily harmonic applied system, and its response approximately computed an asymptotic methodology. For cubic nonlinearity, general theorem given on necessary sufficient conditions excitation should satisfy in order lead motion. As result theorem, whole class admissible capable producing identified (in contrast linear case, only leading one). An analytic expression for modal curve describing configuration space derived numerical simulations strongly nonlinear excited two different presented.