Plastic input motion: Transformation for the response of yielding oscillators

A transformation method is presented for the response of yielding oscillators to dynamic loading. The method employs a translation in the ordinates and the abscissa of the excitation function by means of a pair of parameters uniquely dependent on the yielding resistance and the vibrational characteristics of the system. By this approach: (1) the differential operator becomes linearlike, with the nonlinearity transferred to the right-hand side; (2) the initial conditions are simplified; and (3) the modified forcing term becomes uniquely associated with the development of plastic deformation. The theory is applied to various yielding oscillators subjected to idealized earthquake pulses, with the modified excitation function termed plastic input motion (PIM). A procedure for applying the method to general waveforms is provided. The coordinates of PIM may be discontinuous and significantly smaller than those of the original excitation function, as a considerable amount of ground acceleration is devoted to overcoming the elastic resistance of the system. The theory can be useful in earthquake engineering by offering a replacement to physical ground motions with system-dependent PIMs for establishing demand indices.