Analysis Of Magnetoelastic Stability Of Current-carrying Nano-plates

Magneto-elastic problems widely exist in high-tech devices made of ferromagnetic,piezoelectric,conductor and other materials.At present,micro-electro-mechanical systems are the focus of high-tech research.Studying the magneto-elastic problems of basic components of micro-electro-mechanical systems is of great significance for preventing component failure and optimizing its structure and working efficiency.After years of development,magnetoelastic theory and microstructure mesoscopic theory have been gradually applied to engineering practice,providing a perfect theoretical basis and a broad application prospect for the research of this topic.Based on the theory of non-local elasticity and the theory of magnetoelastic mechanics of plates and shells,the magnetoelastic stability of current-carrying nano-plates is studied in this paper.The main research contents of this paper are as follows:Based on the governing equations of macro plates,the magnetoelastic dynamic stability equations of current-carrying nano plates are derived by combining the non-local elasticity theory with the magnetoelastic theory of plates and shells.Then,taking a simply supported nano-plate on four sides as an example,Galerkin principle is applied to simplify the equation into the standard form of the Mathieu equation,and the relation between the critical current density of instability of the simply supported nano-plate on four sides and magnetic induction intensity,plate length,plate thickness,mechanical load and small-scale parameters is analyzed by using the eigenvalue relation of the coefficient of the Mathieu equation.The numerical simulation results show that the critical current density decreases with the increase of magnetic induction intensity,plate length and small-scale parameters.With the increase of plate thickness and mechanical load,it increases,and there is a sensitive interval between the plate length and the plate thickness of the nano-plate.In this interval,the magnetic induction intensity,plate length and plate thickness have great influence on the stability of the nano-plate.By analyzing the influence of different boundary conditions on the stability of nano-plates,the variation of magneto-elastic stability of nano-plates with three sidessimply supported,one side free;two sides simply supported,two sides fixed;four sides fixed and four sides simply supported with various parameters is compared.The results show that the fixed edge has a great influence on the stability of the nano-plate,and the more the number of fixed edges,the better the stability of the nano-plate.On the basis of magnetic field and mechanical load,the relationship between the stability of current-carrying nano-plates and various parameters under the action of temperature field and the influence of different temperatures on the stability of nano-plates are considered.The results show that the critical current density of nano-plate instability will be significantly increased when considering the temperature field,and the degree of influence of temperature field on the stability of nano-plate will change with the changes of other parameters.The research in this paper extends the problem of magnetoelasticity from macroscopic components to nano-plates,and conducts a series of researches on its stability,which has certain reference significance for practical application,and also provides some ideas for the research of magnetoelasticity of micro-nano components.