Deterministic and random analysis of systems with hysteresis using the Preisach formalism

The hysteretic behavior of single-degree-of-freedom systems subjected to external loads is examined using the classical Preisach model. Two cases are considered. First, the response of an oscillator having a non-linear component described by a series of Jenkin's elements and subjected to monochromatic and white noise excitation is computed. The steady-state amplitude of the response to the deterministic loading is derived analytically using the equivalent linearization method and is compared with the numerical results obtained by direct integration of the equation of motion. For the stochastic excitation, an analytical approximation for the probability density function of the response envelope is obtained by implementing the stochastic averaging method and is compared with the numerical results derived by a pertinent Monte Carlo study. The second case involves a similar oscillator with a shape memory alloy device under harmonic excitation. The steady-state amplitude of the response is computed analytically and numerically using the Preisach formalism for a range of excitation frequencies.