Mean-Square Response of Hysteretic Oscillators Under Nonstationary Random Excitation

A method is introduced for the approximate analysis of the nonstationary random vibration of a broad class of multi-degree-of-freedom nonlinear systems, including (but not limited to) hysteretic systems. The approach uses a two-stage identification procedure to determine equivalent nonlinear memoryless (non-hysteretic) systems. For purposes of calibration with results obtained by other methods, applications in this paper are limited to the transient mean-square response statistics of a class of time-invariant bilinear hysteretic oscillators. However, the method is quite general and easily applied to systems incorporating dead-space, impact, frictional sliding, and general experimentally-determined nonlinearities.