ON THE DYNAMICS OF OSCILLATORS WITH BILINEAR DAMPING AND STIFFNESS

The long time response of a class of harmonically excited, single degree-of-freedom, strongly non-linear oscillators is analysed. The non-linearity appears in both the damping and restoring forces, which are bi-linear functions of the system velocity and displacement, respectively, The existence and stability of single-crossing, periodic solutions is analysed, using a formulation which is appropriate for general piecewise linear systems. The oscillator examined is found to exhibit a regular behavior for some combinations of its parameters. However, there are sets of parameters for which the system undergoes bifurcations which may lead to loss of stability of periodic solutions and the appearance of chaotic response. Results obtained by the present methodology are compared with findings of previous studies on similar systems. Phenomena characterizing the response of the system are investigated in detail. © 1990.