Steady-state dynamic response of preisach hysteretic systems

The goal of this paper is to study the steady-state dynamic response of an oscillator with a hysteretic component to harmonic excitations. This is accomplished by using the Preisach formalism in the description of the contribution of the hysteretic part. Two cases are considered. In the first the hysteretic component is modeled using a series of Jenkin's elements, while in the second 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 numerical results are found in excellent agreement, and supplement the analytical findings of certain previous studies.