Dynamic behavior analysis of systems with friction and hysteretic effects

Abstract

This paper investigates the steady-state response of a nonlinear system that incorporates both a hysteretic element and frictional contact under harmonic excitation. While previous studies have separately explored hysteretic oscillators and frictional systems, the simultaneous consideration of both elements has received limited attention. In this study, an analytical solution for the steady-state response is proposed, employing the equivalent linearization approach. This method enables the determination of equivalent stiffness and equivalent damping coefficients for the linearized system, which are directly linked to the amplitude of the steady-state response. To validate the derived analytical solution, a numerical model is utilized, demonstrating the agreement between the analytical and numerical results. Moreover, this paper identifies noteworthy dynamic characteristics of the designed system, notably the occurrence of peak amplitude at excitation frequencies lower than the pre-yield natural frequency. Furthermore, the apex point can be adjusted by manipulating the nonlinear parameters. Building upon these observations, a new mounting system is examined, revealing distinctive behavior.