Nonlinear responses study of two beams coupled by multiple nonlinear elements considered cubic stiffness

Abstract

Since the inception of nonlinear vibration theory, the majority of research has focused on elastic beams connected to a variety of nonlinear factors. Notwithstanding this, coupling beam systems with nonlinear coupling elements have been the subject of few investigations. In light of the fact that numerous coupling beam systems are typically connected via multiple couplers, this study develops a vibration model for two beams coupled by multiple nonlinear elements exhibiting cubic stiffness. The Lagrange method is utilized to compute the magnitude responses of the beam system. Once the accuracy and consistency of the magnitude responses associated with the beam system have been confirmed, a thorough investigation is conducted into the impact of nonlinear elements on the magnitude responses of two beams joined by multiple nonlinear elements exhibiting cubic stiffness. Nonlinear responses, such as peak jumping, intricate responses, and shifting resonance regions, are determined to be the result of nonlinear elements, according to simulation results. Modulating the parameters of nonlinear elements in a rational manner facilitates the regulation of vibrations across multiple resonance regions of the beam system. Parameter changes of nonlinear elements have a substantial impact on both the vibration states and peak values of magnitude responses for single-frequency vibration excitation in resonance regions. The incorporation of nonlinear components into the coupling beam system enables the regulation of both frequency and single-frequency responses. In the case of low damping, nonlinear vibration control for a system consisting of two beams through the use of multiple nonlinear elements with cubic stiffness is more effective.