Nonlinear magnetic-induced vibration behavior of axially moving nanoplate

The semi-analytical method will examine the vibration behavior of axially moving nanoplates exposed to a magnetic field. Using von Karman nonlinear strain-displacement relations, the influence of large deformations is taken into account in the formulation of governing equations of motion. Novel equations have been suggested to investigate the nonlinear magnetic-induced dynamic behavior of the system in light of more realistic hypotheses. By discretizing the nonlinear equations by the Galerkin technique, the time response is numerically determined. In this study, the influence of the mean velocity, velocity fluctuations, and magnetic field intensity on the nonlinear dynamic response, including time response, phase paths, and Poincare maps, will be examined. Based on the results, it appears that magnetic fields enhance the natural frequencies of a system and may also cause it to behave chaotically. The frequency of axial velocity fluctuations also has a significant impact on the characteristics of nonlinear dynamic response and can lead to a quasi-oscillating or chaotic response. In addition, it is observed that by considering vx = 1 m/s and vx = 4 m/s, magnetic fields of 2.7 T and 3.23 T can be achieved, respectively. Due to the complexity of such systems, it is indispensable to analyze how they behave in order to understand their behavior.