Plate In Transverse Magnetic Field Research Articles

Principal and internal resonance of rectangular conductive thin plate in transverse magnetic field

ABSTRACT The principle and 1:3 internal resonance of a rectangular thin plate in a transverse magnetic field is investigated. Based on the magneto-elastic vibration equation and electromagnetic force expressions of the thin plates, the nonlinear magneto-elastic vibration differential equations of rectangular plates under external excitation in a transverse magnetic field are derived. For a rectangular plate with one side fixed and three other sides simply supported, the two-degree-of-freedom nonlinear Duffing vibration differen-tial equations are proposed by the method of Galerkin. The method of multiple scales is adopted to solve the model equations and obtain four first-order ordinary differential equations governing modulation of the amplitudes and phase angles involved via the first-order or the second-order primary-internal reso-nances. With a numerical example, the amplitude frequency response curves, time history responses, phase portraits and Poincare maps of the first two order vibration modes via principle-internal resonance are respectively captured. And the effects of external excitation amplitudes, magnetic field intensities and thicknesses on the vibration of system are discussed. The results show that the response is dominated by the low mode when principle-internal resonance occurs. The internal resonance provides a mechanism for transferring energy from a high mode to a low mode.

The Magneto-Elastic Internal Resonances of Rectangular Conductive Thin Plate With Different Size Ratios

AbstractBased on the basic equations of electromagnetic elastic motion and the expression of electromagnetic force, the electromagnetic vibration equation of the rectangular thin plate in transverse magnetic field is obtained. For a rectangular plate with one side fixed and three other sides simply supported, its time variable and space variable are separated by the method of Galerkin, and the two-degree-of-freedom nonlinear Duffing vibration differential equations are proposed. The method of multiple scales is adopted to solve the model equations and obtain four first-order ordinary differential equations governing modulation of the amplitudes and phase angles involved via 1:1 or 1:3 internal resonances with different size ratios. With a numerical example, the time history response diagrams, phase portraits and 3-dimension responses of two order modal amplitudes are respectively captured. And the effects of initial values, thickness and magnetic field intensities on internal resonance characteristics are discussed respectively. The results also present obvious characteristics of typical nonlinear internal resonance in this paper.

Strongly Nonlinear Subharmonic Resonance and Chaotic Motion of Axially Moving Thin Plate in Magnetic Field

In this paper, the nonlinear vibration and chaotic motion of the axially moving current-conducting thin plate under external harmonic force in magnetic field is studied. Improved multiple-scale method is employed to derive the strongly nonlinear subharmonic resonance bifurcation-response equation of the strip thin plate in transverse magnetic field. By using the singularity theory, the corresponding transition variety and bifurcation, which contain two parameters of the universal unfolding for this nonlinear system, are obtained. Numerical simulations are carried out to plot the bifurcation diagrams, corresponding maximum Lyapunov exponent diagrams, and dynamical response diagrams with respect to the bifurcation parameters such as magnetic induction intensity, axial tension, external load, external excited frequency, and axial speed. The influences of different bifurcation parameters on period motion, period times motion, and chaotic motion behaviors of subharmonic resonance system are analyzed. The results show that the complex dynamic behaviors of resonance system can be controlled by changing the corresponding parameters.

FREE CONVECTION OF HEAT TRANSFER IN FLOW PAST A SEMI-INFINITE FLAT PLATE IN TRANSVERSE MAGNETIC FIELD WITH HEAT FLUX

A steady two-dimensional MHD free convection of heat transfer in flow past a semi-infinite flat plate in transverse magnetic field with heat flux has been examined. The governing partial differential equation are non-dimensionalised and transformed into a system of nonlinear ordinary differential similarity equations, in a single independent variable η and using Runge-Kutta Gill method with shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction coefficient and the Nusselt number are derived, discussed numerically and their numerical values for various values of physical parameter are presented through tabular form. The effects of magnetic parameter, permeability parameter and Prandtl number on the velocity and temperature profiles were displayed graphically for different values of parameters entering into the problem. Significant changes were obtained in heat transfer coefficient due to the parameters. In addition, the skin friction coefficient and Nusselt number were shown in tabular form.

Buckling analysis of thin circular FG plates made of saturated porous-soft ferromagnetic materials in transverse magnetic field

This study presents the buckling analysis of soft ferromagnetic FG circular plates made of poro material. Equilibrium and stability equations of a poro circular plate in transverse magnetic field are derived. This study analyzes the poroelastic instability of clamped edge ferromagnetic plates subjected to magnetic loadings. The geometrical nonlinearities are considered in the Love–Kirchhoff hypothesis sense. In this paper the effect of pore pressure on critical magnetic field of plate and the effect of important parameters of poroelastic material on buckling capacity are investigated. Also the compressibility of fluid and porosity on the buckling strength are being investigated.

Analysis of Magneto-elastic Principal Resonance of Axially Moving Current-conducting Plate in Magnetic Field

Based on the expressions of kinetic energy, strain energy and virtual work done by electromagnetic forces, the nonlinear magneto-elastic vibration equations of an axially moving strip thin plate in transverse magnetic field are deduced by using Hamilton principle. Based on displacement mode hypothesis, by using Galerkin method, vibration differential equations in the form of three orders displacement mode of axially moving thin plate with two simply supported are obtained. Principal resonance problem solved by using multiple scales method and amplitude-frequency response functions of steady solution in three different frequency relationships are obtained. Based on Liaypunov theory, stability of solution is analyzed and the critical condition of stability is determined. By the numerical examples, variation of amplitude curves in the cases of different axially moving velocity, magnetic induction intensity and thick of thin plate are obtained. The influence of different parameters on resonance amplitude and nonlinear characteristics are analyzed and different frequency relationship is compared.

Heat transfer in flow past a continuously moving semi-infinite flat plate in transverse magnetic field with heat flux

Thermal boundary layer on a continuously moving semi-infinite flat plate in the presence of transverse magnetic field with heat flux has been examined. Similarity solutions have been derived and the resulting equations are integrated numerically. This investigation has indicated a fall in the temperature of the thermal boundary layer with increase in magnetic field parameter.

Flow past a continuously moving flat plate in transverse magnetic field

The analysis of flow past a continuously moving semi-infinite flat plate in the presence of transverse magnetic field has been presented. Model solutions have been derived and the resulting equations are integrated numerically. Velocity profiles are displayed graphically and the numerical values of the transverse velocity skin friction are given in the form of tables. It has been observed that an increase inM (magnetic field parameter) leads to a decrease in velocity.