Steady-State Dynamic Response of Preisach Hysteretic Systems

The goal of this paper is to study the steady-state dynamic response of an oscillator involving a hysteretic component and exposed to harmonic excitation. This is accomplished by using the Preisach formalism in the description of the contribution of the hysteretic component. Two cases are considered. In the first one, the hysteretic component is modeled using a series of “Jenkin’s elements,” while in the second one the same component is modeled by a zero-memory plus a purely hysteretic term. The steady-state amplitude of the response is determined analytically by using the equivalent linearization technique which involves input-output relationships for the equivalent linear system, the stiffness and damping coefficients of which are response-amplitude dependent. The derived results are compared with pertinent numerical data obtained by integrating the nonlinear equation of motion of the oscillator. The analytical and the numerical results are found in excellent agreement and supplement the findings of certain previous studies.