This work dealt with the damping performance and its underlying mechanism in SiC nanoparticles reinforced AZ91D composite(SiC_(np)/AZ91D)processed by cyclic extrusion and compression(CEC).It was found that the CEC pro...This work dealt with the damping performance and its underlying mechanism in SiC nanoparticles reinforced AZ91D composite(SiC_(np)/AZ91D)processed by cyclic extrusion and compression(CEC).It was found that the CEC process significantly affects the damping performance of the composite due to alterations in the density of dislocations and grain boundaries in the matrix alloy.Although there would be dynamic precipitation of the Mg17Al12 phase during processing which increases the phase interface and limits the mobility of dislocations and grain boundaries.The results also showed that the damping capacity of 1%SiC_(np)/AZ91D composite continuously decreases with adding CEC pass number and it consistently increases with rising the applied temperature.Considering the first derivative of the tanδ-T curve,the dominant damping mechanism based on test temperature can be divided into three regions.These three regions are as follows(i)dislocation vibration of the weak pinning points(≤T_(cr)),(ii)dislocation vibration of the strong pinning points(T_(cr)∼T_(V)),and(iii)grain boundary/interface sliding(≥T_(V))展开更多
The focus of this paper is on a linearized backward differential formula(BDF)scheme with Galerkin FEM for the nonlinear Klein-Gordon-Schrödinger equations(KGSEs)with damping mechanism.Optimal error estimates and ...The focus of this paper is on a linearized backward differential formula(BDF)scheme with Galerkin FEM for the nonlinear Klein-Gordon-Schrödinger equations(KGSEs)with damping mechanism.Optimal error estimates and superconvergence results are proved without any time-step restriction condition for the proposed scheme.The proof consists of three ingredients.First,a temporal-spatial error splitting argument is employed to bound the numerical solution in certain strong norms.Second,optimal error estimates are derived through a novel splitting technique to deal with the time derivative and some sharp estimates to cope with the nonlinear terms.Third,by virtue of the relationship between the Ritz projection and the interpolation,as well as a so-called"lifting"technique,the superconvergence behavior of order O(h^(2)+τ^(2))in H^(1)-norm for the original variables are deduced.Finally,a numerical experiment is conducted to confirm our theoretical analysis.Here,h is the spatial subdivision parameter,andτis the time step.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant Numbers of U1902220,51674166,51374145,51074106,50674067)the National Key Research and Development Program of China(Grant Number 2016YFB0301001).
文摘This work dealt with the damping performance and its underlying mechanism in SiC nanoparticles reinforced AZ91D composite(SiC_(np)/AZ91D)processed by cyclic extrusion and compression(CEC).It was found that the CEC process significantly affects the damping performance of the composite due to alterations in the density of dislocations and grain boundaries in the matrix alloy.Although there would be dynamic precipitation of the Mg17Al12 phase during processing which increases the phase interface and limits the mobility of dislocations and grain boundaries.The results also showed that the damping capacity of 1%SiC_(np)/AZ91D composite continuously decreases with adding CEC pass number and it consistently increases with rising the applied temperature.Considering the first derivative of the tanδ-T curve,the dominant damping mechanism based on test temperature can be divided into three regions.These three regions are as follows(i)dislocation vibration of the weak pinning points(≤T_(cr)),(ii)dislocation vibration of the strong pinning points(T_(cr)∼T_(V)),and(iii)grain boundary/interface sliding(≥T_(V))
基金supported by the National Natural Science Foundation of China(No.11671369,No.12071443)Key Scientific Research Project of Colleges and Universities in Henan Province(No.20B110013).
文摘The focus of this paper is on a linearized backward differential formula(BDF)scheme with Galerkin FEM for the nonlinear Klein-Gordon-Schrödinger equations(KGSEs)with damping mechanism.Optimal error estimates and superconvergence results are proved without any time-step restriction condition for the proposed scheme.The proof consists of three ingredients.First,a temporal-spatial error splitting argument is employed to bound the numerical solution in certain strong norms.Second,optimal error estimates are derived through a novel splitting technique to deal with the time derivative and some sharp estimates to cope with the nonlinear terms.Third,by virtue of the relationship between the Ritz projection and the interpolation,as well as a so-called"lifting"technique,the superconvergence behavior of order O(h^(2)+τ^(2))in H^(1)-norm for the original variables are deduced.Finally,a numerical experiment is conducted to confirm our theoretical analysis.Here,h is the spatial subdivision parameter,andτis the time step.
