Based on the Maxwell equation and Kirchhoff assumption of thin plate, nonlinear magneto-elastic vibration equation, electrodynamics equation and electromagnetic force expressions of current-conducting thin plate were deduced. Furthermore, nonlinear super-harmonic resonance of thin beam-plate under lateral mechanical motive load in longitudinal magnetic field was studied. Considering the thin plate simply supported on two opposite sides, the magneto-elastic coupled vibration differential equations about function of displacement of vibration and electric field intensity were obtained by the method of Galerkin. Then, the amplitude-frequency response equation under super-harmonic resonance was derived by using method of Multiple scales. Correspondingly the stability of stable solution was analyzed. Through the numerical calculation, characteristic curves of amplitude changing with detuning parameter, the excitation amplitude and the magnetic intensity. At last, the influence of electric-magnetic and mechanic parameter on resonance phenomenon and stability of solution was analyzed.
The nonlinear superharmonic resonance phenomenon of damped circular sandwich plates under uniform load is investigated. From the movement equation of circular sandwich plate showed in displacement components, got the relevant nonlinear vibration equation by Galerkin method. Under the clamped BC. Using multi-scale method, the periodical solutions were obtained which was of nonlinear the third-order superharmonic resonance. The FRF equation of the superharmonic resonance is obtained, and the necessary and sufficient condition on stability of the vibration are obtained synchronously.The infection to the amplitude while the correlative physical and geometric parameters changing were discussed, Drew the trajectories in moving phase planes during the stabilization process, and the stabilities and singularities of the solutions are analyzed.
The nonlinear forced vibration of damped circular sandwich plates is studied. From the movement equations of circular sandwich plate expressed in displacement components, got the relevant nonlinear vibration equation by Galerkin method. The changing of initial deflection, stiffness and a harmonic force which can affect kinetic characteristic of configuration was researched. The FRF of primary resonance periodical solutions were obtained, synchronously modal analysis experiment for composite material plates were tested.
Molecular dynamics simulation is used to study the water flow in a charged nanotube. The simulation results show that the charge patterns on the nanotube have an important role in determining the flow behavior. In a nanotube charged with one pattern, the water flow rate decreases with increasing charge value, when the charge value increases from 0 to 0.8 e, the water flow rate decreases to 7%. While in the other one with a different charge pattern, the water flow rate is independent of charge value. By analyzing the morphology of water molecules, it is determined that this unexpected phenomenon is caused by the structure of water molecules near the nanotube wall. For the first charge pattern, the network of hydrogen bonds formed by water molecules near the wall had a hexagonal structure, similar to single layer ice, which changes the interactions between the wall and the water molecules. By contrast, the second pattern did not exhibit such an effect. This study provides a means to control the rate of water flow in nanotubes using an electric field. These results may provide new insights and lead to new methods for flow control in complex micro- or nanofluidic systems.
The nonlinear forced vibration of damped circular sandwich plates is studied. From the movement equations of circular sandwich plate expressed in displacement components, got the relevant nonlinear vibration equation by Galerkin method. The standard Duffing equation with square and cubic minor items was obtained by dimensionless processed. The quadratic analytical solution of the principal resonance was deduced by multi-scale method. The FRF of primary resonance periodical solutions were obtained, synchronously the necessary and sufficient condition on stability of the vibration are obtained. The infection to the amplitude when the correlative physical and geometric parameters changing was discussed. The trajectories in moving phase planes during the stabilization process, the stabilities and singularities of the solutions are analyzed.
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