The classical small deflection theory of elastic plates id based on the Kirchhoff-Lore assumptions￣[1,2].Ther are used on the basis of the thinness of plate and the smallness of deflection.In terms of Cartesian tens...The classical small deflection theory of elastic plates id based on the Kirchhoff-Lore assumptions￣[1,2].Ther are used on the basis of the thinness of plate and the smallness of deflection.In terms of Cartesian tensor coordinates x_i(i=0, 12)these basic assumptions are:(1)the transversal normal strain may be neglected i.e._(00)=0;(2)the transversal shear strain may be neglected i.e.e_(0α)=0(α= 1, 2)(3)the transversal normal stress may be neglected i.e.. σ_(00)=0 .In classical theory of elastic plates,the strain-displacement relations and the corresponding stress-displacement relations are established on the basis of these assumptions. And the equations of the classical theory for a set of undetermined quantities defined on the middle surface are established through integrating the three dimensional equations of equilibrium of stress over the thickness.In the previous papers￣[3,4,5],an approximation theory is given on the basis of Ihree dimensional theory of elastic plates without using Kirchhoff-Love assumptions。However,no uniqueness study is given,and also the boundary conditions have never been studied. In this paper.the same problems are studied on the basis of generalizedvariational principle of the three dimensional theory of elastic bodies￣[6].The stationary conditions of variation give an unique and complete set of field equations and the related boundary conditions for the approximation theory.In this paper,the first order approximation theory is studied in detail.展开更多
Multipactor and low-pressure gas discharges have a negative impact on the performance and security of microwave components in space.In this manuscript,a 2-dimensional parallel flat plate structural model was designed ...Multipactor and low-pressure gas discharges have a negative impact on the performance and security of microwave components in space.In this manuscript,a 2-dimensional parallel flat plate structural model was designed to simulate the breakdown of multipactor to low-pressure gas discharges.The breakdown levels in the pressure range of 0.1 to 100 torr were verified under the conditions of the Ag material,4-mm gap,2.6-GHz frequency,and air as the background gas.Random secondary electron emission and gas molecule collision processes are incorporated,and the effect of their transition section is studied using trajectory tracking and Monte Carlo methods.A comparison of the model to the available experimental data demonstrates the model’s accuracy.On this basis,the variation of gas adsorption in relation to the surface secondary electron yields was considered,and the effect of the gas adsorption issues on breakdown level was calculated by means of numerical simulations based on some assumptions.The calculation reveals that in a finite volume of space,smaller desorption volumes cause negligible pressure changes,but the secondary electron emission capacity of the material decreases,which,in turn,leads to a flat or rising breakdown level.On the contrary,the larger the desorption volume,the more the gas is collisionally ionized and the breakdown level decreases.展开更多
文摘The classical small deflection theory of elastic plates id based on the Kirchhoff-Lore assumptions￣[1,2].Ther are used on the basis of the thinness of plate and the smallness of deflection.In terms of Cartesian tensor coordinates x_i(i=0, 12)these basic assumptions are:(1)the transversal normal strain may be neglected i.e._(00)=0;(2)the transversal shear strain may be neglected i.e.e_(0α)=0(α= 1, 2)(3)the transversal normal stress may be neglected i.e.. σ_(00)=0 .In classical theory of elastic plates,the strain-displacement relations and the corresponding stress-displacement relations are established on the basis of these assumptions. And the equations of the classical theory for a set of undetermined quantities defined on the middle surface are established through integrating the three dimensional equations of equilibrium of stress over the thickness.In the previous papers￣[3,4,5],an approximation theory is given on the basis of Ihree dimensional theory of elastic plates without using Kirchhoff-Love assumptions。However,no uniqueness study is given,and also the boundary conditions have never been studied. In this paper.the same problems are studied on the basis of generalizedvariational principle of the three dimensional theory of elastic bodies￣[6].The stationary conditions of variation give an unique and complete set of field equations and the related boundary conditions for the approximation theory.In this paper,the first order approximation theory is studied in detail.
基金substantially supported by the National Natural Science Foundation of China(grant nos.61901361 and 51827809).
文摘Multipactor and low-pressure gas discharges have a negative impact on the performance and security of microwave components in space.In this manuscript,a 2-dimensional parallel flat plate structural model was designed to simulate the breakdown of multipactor to low-pressure gas discharges.The breakdown levels in the pressure range of 0.1 to 100 torr were verified under the conditions of the Ag material,4-mm gap,2.6-GHz frequency,and air as the background gas.Random secondary electron emission and gas molecule collision processes are incorporated,and the effect of their transition section is studied using trajectory tracking and Monte Carlo methods.A comparison of the model to the available experimental data demonstrates the model’s accuracy.On this basis,the variation of gas adsorption in relation to the surface secondary electron yields was considered,and the effect of the gas adsorption issues on breakdown level was calculated by means of numerical simulations based on some assumptions.The calculation reveals that in a finite volume of space,smaller desorption volumes cause negligible pressure changes,but the secondary electron emission capacity of the material decreases,which,in turn,leads to a flat or rising breakdown level.On the contrary,the larger the desorption volume,the more the gas is collisionally ionized and the breakdown level decreases.
