Nonlinear Dynamics and Phenomena in Oscillators with Hysteresis

Many mechanical systems are characterized by hysteretic behaviors with a restoring force dependent on their deformation history. Several materials and elements base their capacity to dissipate vibratory energy on hysteresis. Hysteresis can be classified among material nonlinearities and is recognized as a strong nonlinearity due to the high variation of stiffness and damping with deformation. This chapter illustrates the main characteristics of the dynamic response by means of frequency response curves of a hysteretic oscillator, highlighting the dependence of the response on the oscillation amplitude. It considers the response of a two degree-of-freedom system (2DOF) chain system with one hysteretic element to harmonic excitation. A 2DOF chain system is suitable to study the features of the main nonlinear coupling phenomena in a multi-degree-of-freedom system. The chapter also considers two different configurations: base-hysteresis configuration with the hysteretic element at the base and top-hysteresis configuration with the hysteretic element at the top, between the two masses.