The electric admittance of a compound system composed of a thickness-shear mode (TSM) quartz crystal resonator (QCR) and an array of surface viscoelastic micro-beams (MBs) is studied. The governing equations of ...The electric admittance of a compound system composed of a thickness-shear mode (TSM) quartz crystal resonator (QCR) and an array of surface viscoelastic micro-beams (MBs) is studied. The governing equations of the MBs are derived from the Timoshenko-beam theory in consideration of shear deformation. The electrical admittance is described directly in terms of the physical properties of the surface epoxy resin (SU-8) MBs from an electrically forced vibration analysis. It is found that both the inertia effect and the constraint effect of the MBs produce competitive influence on the resonant frequency and admittance of the compound QCR system. By further comparing the numerical results calculated from the Timoshenko-beam model with those from the Euler-beam model, the shear deformation is found to lead to some deviation of an admittance spectrum. The deviations are revealed to be evident around the admittance peak(s) and reach the maximum when a natural frequency of the MBs is identical to the fundamental frequency of the QCR. Besides, a higher order vibration mode of the MBs corresponds to a larger deviation at the resonance.展开更多
Deformation of water drops in shock-induced high-speed flows is investigated with a focus to the influence of primitive flow parameters on the rear-surface deformation features. Two typical deformation patterns are di...Deformation of water drops in shock-induced high-speed flows is investigated with a focus to the influence of primitive flow parameters on the rear-surface deformation features. Two typical deformation patterns are discovered through high-speed photography. A simple equation to evaluate the radial acceleration of the drop surface is derived. The combined use of this equation and outer flow simulation makes it possible for us to reconstruct the profiles of the early deformed drops. The results agree well with the experiments. Further analysis shows that the duration of flow establishment with respect to the overall breakup time shapes the rear side profile of the drop. Thereby the ratio of the two times, expressed as the square root of the density ratio, appears to be an effective indicator of the deformation features.展开更多
Shear-mode piezoelectric materials have been widely used to shunt the damping of vibrations where utilizing surface or interface shear stresses. The thick-shear mode (TSM) elastic constant and the mechanical loss fa...Shear-mode piezoelectric materials have been widely used to shunt the damping of vibrations where utilizing surface or interface shear stresses. The thick-shear mode (TSM) elastic constant and the mechanical loss factor can change correspondingly when piezoelectric materials are shunted to different electrical circuits. This phenomenon makes it possible to control the performance of a shear-mode piezoelectric damping system through designing the shunt circuit. However, due to the difficulties in directly measuring the TSM elastic constant and the mechanical loss factor of piezoelectric materials, the relationships between those parameters and the shunt circuits have rarely been investigated. In this paper, a coupling TSM electro-mechanical resonant system is proposed to indirectly measure the variations of the TSM elastic constant and the mechanical loss factor of piezoelectric materials. The main idea is to transform the variations of the TSM elastic constant and the mechanical loss factor into the changes of the easily observed resonant frequency and electrical quality factor of the coupling electro-mechanical resonator. Based on this model, the formular relationships are set up theoretically with Mason equivalent circuit method and they are validated with finite element (FE) analyses. Finally, a prototype of the coupling electro-mechanical resonator is fabricated with two shear-mode PZT5A plates to investigate the TSM elastic constants and the mechanical loss factors of different circuit-shunted cases of the piezoelectric plate. Both the resonant frequency shifts and the bandwidth changes observed in experiments are in good consistence with the theoretical and FE analyses under the same shunt conditions. The proposed coupling resonator and the obtained relationships are validated with but not limited to PZT5A.展开更多
A shear mode piezoelectric energy harvester for harvesting energy from rotary motion is developed.The kinetic energy in the form of rotation is converted into electrical form of energy by piezoelectric principle with ...A shear mode piezoelectric energy harvester for harvesting energy from rotary motion is developed.The kinetic energy in the form of rotation is converted into electrical form of energy by piezoelectric principle with oscillation of piezoelectric patch through magnetic shear force.Efforts have been made to increase the output power using shear mode of operation.In order to estimate the induced voltage of piezoelectric patch,a mathematical model and an Finite Element(FE)model are developed.Considering various parameters,optimization of the harvester was made.Analytical and Finite Element Method(FEM)results are compared and good agreement has been found.The total average output power of 358.44 Wis generated when rotary speed of hub of about 600 RPM.展开更多
Oriented “shish-kebab” structures could be obtained by shearing to enhance the mechanical properties of polymer samples markedly.However,the effect of shear mode on mechanical properties is still uncertain.The study...Oriented “shish-kebab” structures could be obtained by shearing to enhance the mechanical properties of polymer samples markedly.However,the effect of shear mode on mechanical properties is still uncertain.The study of stepped hoop shear field on the isotactic polypropylene(iPP)pipe was developed through applying a self-designed rotational shear system(RSS).The effect of stepped shear field on the microstructure and comprehensive properties of iPP pipe was investigated by the comparison with continuous shear.It could be found that the loosely-assembled shish-kebabs with the larger size were formed in the continuous shear pipes,but the smaller and tightly-stacked ones existed in the pipes with stepped shear.Surprisingly,due to differential morphologies under different shear modes,better comprehensive mechanical properties were obtained in the pipes with stepped shear.展开更多
In-plane shear crack sub-critical propagation of rock at high temperature was studied by finite element method and shear-box(i.e.compression-shear) test with newly designed electrically conductive adhesive method.Nume...In-plane shear crack sub-critical propagation of rock at high temperature was studied by finite element method and shear-box(i.e.compression-shear) test with newly designed electrically conductive adhesive method.Numerical and experimental results show that the normalized shear(Mode Ⅱ) stress intensity factors,K ⅡT/KT0 is decreased as the temperature increases because high temperature can improve stress distribution at crack tip and reduce the Mode Ⅱ stress intensity factor.Microscopic features of fractured surface are of little pits and secondary micro-cracks in the vicinity(1.5-4.0 mm) of the crack tip.The chevron-shape secondary cracks gradually merge in the length of about 4-5 mm and disappear along the direction of crack propagation.Stable shear crack propagation time is increased with the increasing temperature while the stable shear crack propagation rate is decreased with the increasing temperature,since high temperature can increase the shear(Mode Ⅱ) fracture toughness and prevent the crack growth.It is necessary to ensure the ligament of specimen long enough to measure the maximum unstable crack propagation rate of rock.展开更多
Shear-box(i.e.compression-shear) test and newly designed electrically conductive adhesive method were used to measure shear crack sub-critical propagation time and rate of sandstone specimen.Different cubic specimens ...Shear-box(i.e.compression-shear) test and newly designed electrically conductive adhesive method were used to measure shear crack sub-critical propagation time and rate of sandstone specimen.Different cubic specimens with and without holes were tested to study the effect of holes on the shear crack sub-critical propagation.Numerical and experimental results show that three independent variables of hole,the interval distance S,the distance between the center of hole and the crack tip L,and hole radius R,have different contribution to the ratio of stress intensity factor of the specimen with holes to that of the specimen without hole,KⅡ/KⅡ0.Increasing S and decreasing L and R will result in the decrease of KⅡ/KⅡ0 and help crack arrest.The weight relation of the independent variables for KⅡ/KⅡ0 is S>L>R.The specimen DH3 with the largest value of S and the smallest values of L and R has the longest sub-critical crack propagation time and the smallest sub-critical crack propagation rate.Adding two suitable holes symmetrically to the original crack plane in rock specimen is considered to be a potential method for crack arrest of rock.展开更多
The linear evolution of a resistive wall mode(RWM)with magnetic shears was analytically studied in a cylindrical geometry.The incompressible magnetohydrodynamic(MHD)equations were solved by the Fourier analysis method...The linear evolution of a resistive wall mode(RWM)with magnetic shears was analytically studied in a cylindrical geometry.The incompressible magnetohydrodynamic(MHD)equations were solved by the Fourier analysis method,and various equilibrium magnetic fields were considered.The shear in the magnetic field had an unstable effect on the linear evolution of the RWM.The linear growth rate increased obviously with increase of the magnetic shear rate for higher magnetic shears.Slow plasma rotation could stabilize the RWM with low magnetic shears,but the plasma rotation could not stabilize the RWM with high magnetic shears.The stabilizing effects of the wall conductivity on the RWM are more efficient for lager magnetic shear.展开更多
The energetic particle driven internal kink mode is investigated in this paper for q0〉 1 tokamak plasma with weak magnetic shear. With the effect of energetic particles, the m/n = 1/1 internal mode structure in tokam...The energetic particle driven internal kink mode is investigated in this paper for q0〉 1 tokamak plasma with weak magnetic shear. With the effect of energetic particles, the m/n = 1/1 internal mode structure in tokamak plasma does not appear as a rigid step-function when safety factor passes through q = 1 rational surface. It is found that even when the rational surface is removed, the mode may be still unstable under the low magnetic shear condition if the energetic particle drive is strong enough; with the low shear region of safety factor profile widening, the mode becomes more unstable with its growth-rate increasing. Furthermore, we find that the existence of the q = 1 rational surface does not have a significant effect on the stability of the plasma if energetic particles are present, which is very different from the scenarios of the ideal-MHD modes.展开更多
For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading lev...For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface crack- tip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.展开更多
A code named LARWM with non-ideal magnetohydrodynamic equations in cylindrical model is used to describe the instability in Tokamak plasma surrounded by a conducting wall with finite resistivity. We mainly take three ...A code named LARWM with non-ideal magnetohydrodynamic equations in cylindrical model is used to describe the instability in Tokamak plasma surrounded by a conducting wall with finite resistivity. We mainly take three factors related to the shear equilibrium plasma flow into consideration to study the stabilizing effect of the shear flow on the resistive wall modes (RWMs). The three factors are the velocity amplitude of flow, the shear rate of flow on plasma surface, and the inertial energy of equilibrium plasma flow. In addition, a local shear plasma flow is also calculated by the LARWM code. Consequently, it is found that the inertial energy of the shear equilibrium plasma flow has an important role in the stabilization of the RWMs.展开更多
The thickness-shear (TS) and thickness-twist (TT) vibrations of partially electroded AT-cut quartz plates for acoustic wave resonator and filter applications are theoretically studied. The plates have structural v...The thickness-shear (TS) and thickness-twist (TT) vibrations of partially electroded AT-cut quartz plates for acoustic wave resonator and filter applications are theoretically studied. The plates have structural variations in one of the two in-plane directions of the plates only. The scalar differential equations derived by Tiersten and Smythe for electroded and unelectroded AT-cut quartz plates are used, resulting in free vibration resonant frequencies and mode shapes for both fundamental and overtone fam- ilies of modes. The trapped modes with vibrations, mainly confined in the electroded areas, are found to exist in both the resonator and the filter structures. The numerical results for the trapped modes are presented for different aspect ratios of electrodes and material properties, providing a reference to the design and optimization of quartz acous- tic wave resonators and filters.展开更多
Previous researches on the mixed mode fracture initiation criteria were mostly focused on opening mode fracture. In this study, the authors proposed a new criterion for mixed mode sliding fracture initiation, which is...Previous researches on the mixed mode fracture initiation criteria were mostly focused on opening mode fracture. In this study, the authors proposed a new criterion for mixed mode sliding fracture initiation, which is the maximum twin shear stress factor criterion. The authors studied a finite width plate with central slant crack, subject to a far field uniform uniaxial tensile or compressive stress.展开更多
The linear analysis of the influence of diamagnetic effect and toroidal rotation at the edge of tokamak plasmas with BOUT++ is discussed in this paper. This analysis is done by solving the dispersion relation, which i...The linear analysis of the influence of diamagnetic effect and toroidal rotation at the edge of tokamak plasmas with BOUT++ is discussed in this paper. This analysis is done by solving the dispersion relation, which is calculated through the numerical integration of the terms with different physics. This method is able to reveal the contributions of the different terms to the total growth rate. The diamagnetic effect stabilizes the ideal ballooning modes through inhibiting the contribution of curvature. The toroidal rotation effect is also able to suppress the curvaturedriving term, and the stronger shearing rate leads to a stronger stabilization effect. In addition,through linear analysis using the energy form, the curvature-driving term provides the free energy absorbed by the line-bending term, diamagnetic term and convective term.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11272127 and51435006)the Research Fund for the Doctoral Program of Higher Education of China(No.20130142110022)
文摘The electric admittance of a compound system composed of a thickness-shear mode (TSM) quartz crystal resonator (QCR) and an array of surface viscoelastic micro-beams (MBs) is studied. The governing equations of the MBs are derived from the Timoshenko-beam theory in consideration of shear deformation. The electrical admittance is described directly in terms of the physical properties of the surface epoxy resin (SU-8) MBs from an electrically forced vibration analysis. It is found that both the inertia effect and the constraint effect of the MBs produce competitive influence on the resonant frequency and admittance of the compound QCR system. By further comparing the numerical results calculated from the Timoshenko-beam model with those from the Euler-beam model, the shear deformation is found to lead to some deviation of an admittance spectrum. The deviations are revealed to be evident around the admittance peak(s) and reach the maximum when a natural frequency of the MBs is identical to the fundamental frequency of the QCR. Besides, a higher order vibration mode of the MBs corresponds to a larger deviation at the resonance.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11102204,11572313 and 11621202the Natural Science Foundation of Anhui Province under Grant No 1608085MA16
文摘Deformation of water drops in shock-induced high-speed flows is investigated with a focus to the influence of primitive flow parameters on the rear-surface deformation features. Two typical deformation patterns are discovered through high-speed photography. A simple equation to evaluate the radial acceleration of the drop surface is derived. The combined use of this equation and outer flow simulation makes it possible for us to reconstruct the profiles of the early deformed drops. The results agree well with the experiments. Further analysis shows that the duration of flow establishment with respect to the overall breakup time shapes the rear side profile of the drop. Thereby the ratio of the two times, expressed as the square root of the density ratio, appears to be an effective indicator of the deformation features.
基金Project supported by the National Defense Foundation of China(Grant No.9149A12050414JW02180)
文摘Shear-mode piezoelectric materials have been widely used to shunt the damping of vibrations where utilizing surface or interface shear stresses. The thick-shear mode (TSM) elastic constant and the mechanical loss factor can change correspondingly when piezoelectric materials are shunted to different electrical circuits. This phenomenon makes it possible to control the performance of a shear-mode piezoelectric damping system through designing the shunt circuit. However, due to the difficulties in directly measuring the TSM elastic constant and the mechanical loss factor of piezoelectric materials, the relationships between those parameters and the shunt circuits have rarely been investigated. In this paper, a coupling TSM electro-mechanical resonant system is proposed to indirectly measure the variations of the TSM elastic constant and the mechanical loss factor of piezoelectric materials. The main idea is to transform the variations of the TSM elastic constant and the mechanical loss factor into the changes of the easily observed resonant frequency and electrical quality factor of the coupling electro-mechanical resonator. Based on this model, the formular relationships are set up theoretically with Mason equivalent circuit method and they are validated with finite element (FE) analyses. Finally, a prototype of the coupling electro-mechanical resonator is fabricated with two shear-mode PZT5A plates to investigate the TSM elastic constants and the mechanical loss factors of different circuit-shunted cases of the piezoelectric plate. Both the resonant frequency shifts and the bandwidth changes observed in experiments are in good consistence with the theoretical and FE analyses under the same shunt conditions. The proposed coupling resonator and the obtained relationships are validated with but not limited to PZT5A.
文摘A shear mode piezoelectric energy harvester for harvesting energy from rotary motion is developed.The kinetic energy in the form of rotation is converted into electrical form of energy by piezoelectric principle with oscillation of piezoelectric patch through magnetic shear force.Efforts have been made to increase the output power using shear mode of operation.In order to estimate the induced voltage of piezoelectric patch,a mathematical model and an Finite Element(FE)model are developed.Considering various parameters,optimization of the harvester was made.Analytical and Finite Element Method(FEM)results are compared and good agreement has been found.The total average output power of 358.44 Wis generated when rotary speed of hub of about 600 RPM.
基金supported by the National Natural Science Foundation of China(No.21627804).
文摘Oriented “shish-kebab” structures could be obtained by shearing to enhance the mechanical properties of polymer samples markedly.However,the effect of shear mode on mechanical properties is still uncertain.The study of stepped hoop shear field on the isotactic polypropylene(iPP)pipe was developed through applying a self-designed rotational shear system(RSS).The effect of stepped shear field on the microstructure and comprehensive properties of iPP pipe was investigated by the comparison with continuous shear.It could be found that the loosely-assembled shish-kebabs with the larger size were formed in the continuous shear pipes,but the smaller and tightly-stacked ones existed in the pipes with stepped shear.Surprisingly,due to differential morphologies under different shear modes,better comprehensive mechanical properties were obtained in the pipes with stepped shear.
基金Project(50374073) supported by the National Natural Science Foundation of ChinaProject(1343-77239) supported by the Graduate Education Innovation Project of Central South University,China
文摘In-plane shear crack sub-critical propagation of rock at high temperature was studied by finite element method and shear-box(i.e.compression-shear) test with newly designed electrically conductive adhesive method.Numerical and experimental results show that the normalized shear(Mode Ⅱ) stress intensity factors,K ⅡT/KT0 is decreased as the temperature increases because high temperature can improve stress distribution at crack tip and reduce the Mode Ⅱ stress intensity factor.Microscopic features of fractured surface are of little pits and secondary micro-cracks in the vicinity(1.5-4.0 mm) of the crack tip.The chevron-shape secondary cracks gradually merge in the length of about 4-5 mm and disappear along the direction of crack propagation.Stable shear crack propagation time is increased with the increasing temperature while the stable shear crack propagation rate is decreased with the increasing temperature,since high temperature can increase the shear(Mode Ⅱ) fracture toughness and prevent the crack growth.It is necessary to ensure the ligament of specimen long enough to measure the maximum unstable crack propagation rate of rock.
基金Project(50374073) supported by the National Natural Science Foundation of ChinaProject(1343-77239) supported by the Graduate Education Innovation Project of Central South University,China
文摘Shear-box(i.e.compression-shear) test and newly designed electrically conductive adhesive method were used to measure shear crack sub-critical propagation time and rate of sandstone specimen.Different cubic specimens with and without holes were tested to study the effect of holes on the shear crack sub-critical propagation.Numerical and experimental results show that three independent variables of hole,the interval distance S,the distance between the center of hole and the crack tip L,and hole radius R,have different contribution to the ratio of stress intensity factor of the specimen with holes to that of the specimen without hole,KⅡ/KⅡ0.Increasing S and decreasing L and R will result in the decrease of KⅡ/KⅡ0 and help crack arrest.The weight relation of the independent variables for KⅡ/KⅡ0 is S>L>R.The specimen DH3 with the largest value of S and the smallest values of L and R has the longest sub-critical crack propagation time and the smallest sub-critical crack propagation rate.Adding two suitable holes symmetrically to the original crack plane in rock specimen is considered to be a potential method for crack arrest of rock.
基金National Science Foundation of Shangong Province of China(No.ZR2016AM30)National Natural Science Foundation of China(No.11875290)Foundation of Shandong Province Higher Educational Science and Technology Program,China(No.J15LN15)
文摘The linear evolution of a resistive wall mode(RWM)with magnetic shears was analytically studied in a cylindrical geometry.The incompressible magnetohydrodynamic(MHD)equations were solved by the Fourier analysis method,and various equilibrium magnetic fields were considered.The shear in the magnetic field had an unstable effect on the linear evolution of the RWM.The linear growth rate increased obviously with increase of the magnetic shear rate for higher magnetic shears.Slow plasma rotation could stabilize the RWM with low magnetic shears,but the plasma rotation could not stabilize the RWM with high magnetic shears.The stabilizing effects of the wall conductivity on the RWM are more efficient for lager magnetic shear.
基金Project supported by the National Natural Science Foundation of China(Grant No.11261140326)
文摘The energetic particle driven internal kink mode is investigated in this paper for q0〉 1 tokamak plasma with weak magnetic shear. With the effect of energetic particles, the m/n = 1/1 internal mode structure in tokamak plasma does not appear as a rigid step-function when safety factor passes through q = 1 rational surface. It is found that even when the rational surface is removed, the mode may be still unstable under the low magnetic shear condition if the energetic particle drive is strong enough; with the low shear region of safety factor profile widening, the mode becomes more unstable with its growth-rate increasing. Furthermore, we find that the existence of the q = 1 rational surface does not have a significant effect on the stability of the plasma if energetic particles are present, which is very different from the scenarios of the ideal-MHD modes.
基金Project supported by the National Natural Science Foundation of China(No.11302054)the Fundamental Research Funds for the Central Universities(No.HEUCF130216)
文摘For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface crack- tip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.
基金the National Natural Science Foundation of China(Grant Nos.11105065 and 11275041)the National Basic Research Program of China(Grant Nos.2008CB717801,2008CB787103,2009GB105004,and 2010GB106002)
文摘A code named LARWM with non-ideal magnetohydrodynamic equations in cylindrical model is used to describe the instability in Tokamak plasma surrounded by a conducting wall with finite resistivity. We mainly take three factors related to the shear equilibrium plasma flow into consideration to study the stabilizing effect of the shear flow on the resistive wall modes (RWMs). The three factors are the velocity amplitude of flow, the shear rate of flow on plasma surface, and the inertial energy of equilibrium plasma flow. In addition, a local shear plasma flow is also calculated by the LARWM code. Consequently, it is found that the inertial energy of the shear equilibrium plasma flow has an important role in the stabilization of the RWMs.
基金supported by the Program for New Century Excellent Talents in Universities of the Ministry of Education of China(No.NCET-12-0625)the National Natural Science Foundation of China(Nos.11232007 and 11502108)+2 种基金the Science Foundation for Distinguished Young Scholars of Jiangsu Province(No.SBK2014010134)the Fundamental Research Funds for the Central Universities(Nos.NE2013101 and NZ2013307)funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
文摘The thickness-shear (TS) and thickness-twist (TT) vibrations of partially electroded AT-cut quartz plates for acoustic wave resonator and filter applications are theoretically studied. The plates have structural variations in one of the two in-plane directions of the plates only. The scalar differential equations derived by Tiersten and Smythe for electroded and unelectroded AT-cut quartz plates are used, resulting in free vibration resonant frequencies and mode shapes for both fundamental and overtone fam- ilies of modes. The trapped modes with vibrations, mainly confined in the electroded areas, are found to exist in both the resonator and the filter structures. The numerical results for the trapped modes are presented for different aspect ratios of electrodes and material properties, providing a reference to the design and optimization of quartz acous- tic wave resonators and filters.
文摘Previous researches on the mixed mode fracture initiation criteria were mostly focused on opening mode fracture. In this study, the authors proposed a new criterion for mixed mode sliding fracture initiation, which is the maximum twin shear stress factor criterion. The authors studied a finite width plate with central slant crack, subject to a far field uniform uniaxial tensile or compressive stress.
基金supported by program of Fusion Reactor Physics and Digital Tokamak with the CAS ‘OneThree-Five’ Strategic Planningthe JSPS-NRF-NSFC A3 Foresight Program in the field of Plasma Physics (NSFC: No. 11261140328 and NRF: No. z012K2A2A6000443)+1 种基金supported by National Natural Science Foundation of China under Contract Nos. 11405215, 11505236 and 11675217the National Magnetic Confinement Fusion Science Program of China under Contract Nos. 2015GB101003, 2014GB106001 and 2013GB111002
文摘The linear analysis of the influence of diamagnetic effect and toroidal rotation at the edge of tokamak plasmas with BOUT++ is discussed in this paper. This analysis is done by solving the dispersion relation, which is calculated through the numerical integration of the terms with different physics. This method is able to reveal the contributions of the different terms to the total growth rate. The diamagnetic effect stabilizes the ideal ballooning modes through inhibiting the contribution of curvature. The toroidal rotation effect is also able to suppress the curvaturedriving term, and the stronger shearing rate leads to a stronger stabilization effect. In addition,through linear analysis using the energy form, the curvature-driving term provides the free energy absorbed by the line-bending term, diamagnetic term and convective term.