ON THE PRIMARY FREQUENCY-RESPONSE OF STRONGLY NONLINEAR OSCILLATORS - A LINEARIZATION APPROACH

The problem considered is the primary frequency response of the class of strongly non-linear forced oscillators u ̈ + 2η u ̇ + mu + εg(u) = P cos (Ωt), whee g(u) is an odd non-linear function of the displacement u(t), ε may be arbitrarily large, and m = -1, 0 or +1. A simple approximation to the fundamental harmonic of the response is obtained by first linearizing the static terms using the frequency relations developed in reference [1] for the autonomous conservative oscillator and then using the averaging method to solve the linearized forced problem. A comparison with the numerical and other approximate analytic methods results is made, which shows the advantages of the present technique in terms of computational effort and accuracy. © 1990.