Magneto-elastic dynamics and bifurcation of rotating annular plate ^*

Abstract

In this paper, magneto-elastic dynamic behavior, bifurcation, and chaos of a rotating annular thin plate with various boundary conditions are investigated. Based on the thin plate theory and the Maxwell equations, the magneto-elastic dynamic equations of rotating annular plate are derived by means of Hamilton's principle. Bessel function as a mode shape function and the Galerkin method are used to achieve the transverse vibration differential equation of the rotating annular plate with different boundary conditions. By numerical analysis, the bifurcation diagrams with magnetic induction, amplitude and frequency of transverse excitation force as the control parameters are respectively plotted under different boundary conditions such as clamped supported sides, simply supported sides, and clamped-one-side combined with simply-anotherside. Poincaré maps, time history charts, power spectrum charts, and phase diagrams are obtained under certain conditions, and the influence of the bifurcation parameters on the bifurcation and chaos of the system is discussed. The results show that the motion of the system is a complicated and repeated process from multi-periodic motion to quasi-period motion to chaotic motion, which is accompanied by intermittent chaos, when the bifurcation parameters change. If the amplitude of transverse excitation force is bigger or magnetic induction intensity is smaller or boundary constraints level is lower, the system can be more prone to chaos.

Couple stress and Darcy Forchheimer hybrid nanofluid flow on a vertical plate by means of double diffusion Cattaneo–Christov analysis

“…The researchers used several numerical and computational methods [42][43][44][45][46][47][48][49][50]53] to find the solution to different models. Our work also depends on the computational analysis PCM.…”

Thermoelastic strongly nonlinear vibration of rotating functionally graded ring plate

“…A lot of research has been done on dynamic problems of functionally graded structures (FGS). Hu et al (2017) used the Bessel function as a mode function to study bifurcation and chaos of a rotating annular thin plate with different boundary conditions in a magnetic field. In addition, bending and vibration problems of FGM ring plates and shells in thermal environment were studied.…”

Characteristic signal extracted from a continuous time signal on the aspect of frequency domain*

“…In order to analyze or apply the dynamic characteristics of a system, the traditional analytical methods have been applied to many research fields. For instance, the Lyapunov exponent is used to detect weak signals [1] and prove the intra-layer synchronization of the duplex network; [2] the numerical simulation method is used to study the magnetoelastic dynamic behavior of a rotating annular thin [3] and the Hopf bifurcation control of a modified Pan-like chaotic system; [4] the bifurcation is used to study the nonlinear dynamic behavior of the PMSG [5] and external-cavity multi-quantum-well laser; [6] the Poincaré section is used to analyze the limit cycle oscillation flutter and chaotic motion of a two degree-of-freedom aeroelastic airfoil [7] and the chaos properties of the time-dependent driven Dicke model. [8] All these methods may help people predict the behavior of these systems or avoid their negative effects.…”