We present a class of preconditioners for the linear systems resulting from a finite element or discontinuous Galerkin discretizations of advection-dominated problems.These preconditioners are designed to treat the ca...We present a class of preconditioners for the linear systems resulting from a finite element or discontinuous Galerkin discretizations of advection-dominated problems.These preconditioners are designed to treat the case of geometrically localized stiffness,where the convergence rates of iterative methods are degraded in a localized subregion of the mesh.Slower convergence may be caused by a number of factors,including the mesh size,anisotropy,highly variable coefficients,and more challenging physics.The approach taken in this work is to correct well-known preconditioners such as the block Jacobi and the block incomplete LU(ILU)with an adaptive inner subregion iteration.The goal of these preconditioners is to reduce the number of costly global iterations by accelerating the convergence in the stiff region by iterating on the less expensive reduced problem.The tolerance for the inner iteration is adaptively chosen to minimize subregion-local work while guaranteeing global convergence rates.We present analysis showing that the convergence of these preconditioners,even when combined with an adaptively selected tolerance,is independent of discretization parameters(e.g.,the mesh size and diffusion coefficient)in the subregion.We demonstrate significant performance improvements over black-box preconditioners when applied to several model convection-diffusion problems.Finally,we present performance results of several variations of iterative subregion correction preconditioners applied to the Reynolds number 2.25×10^(6)fluid flow over the NACA 0012 airfoil,as well as massively separated flow at 30°angle of attack.展开更多
In order to describe the performance of thin wall bearing on rotor system more accurate,the simplified model of bearing local stiffness was proposed. The load distribution and local contact deformation in angular cont...In order to describe the performance of thin wall bearing on rotor system more accurate,the simplified model of bearing local stiffness was proposed. The load distribution and local contact deformation in angular contact ball bearings were calculated using quasi dynamic calculation method. Based on the relationship of local load to contact deformation,the calculation model of local bearing stiffness was subsequently built to get radial and axial components of local stiffness. Effects of external loads on the local bearing stiffness were analyzed. The results showed that local stiffness in bearings is symmetric to the axis of radial load,and its value has a maximum on the symmetry axis along the radial load direction. External radial and axial load have different effects on local bearing stiffness.展开更多
Traditional technique such nanoindenter（NI） can＇t measure the local elastic modulus at nano-scale（lateral）. Atomic force acoustic microscopy （AFAM） is a dynamic method, which can quantitatively determine indent...Traditional technique such nanoindenter（NI） can＇t measure the local elastic modulus at nano-scale（lateral）. Atomic force acoustic microscopy （AFAM） is a dynamic method, which can quantitatively determine indentation modulus by measuring the contact resonance spectra for high order modes of the cantilever. But there are few reports on the effect of experimental factors, such length of cantilever, contact stiffness on measured value. For three different samples, including copper（Cu） film with 110 nm thickness, zinc（Zn） film of 90 nm thickness and glass slides, are prepared and tested, using referencing approach in which measurements are performed on the test and reference samples （it＇s elastic modulus is known）, and their contact resonance spectra are measured used the AFAM system experimentally. According to the vibration theory, from the lowest two contact resonance frequencies, the tip-sample contact stiffness is calculated, and then the values for the elastic properties of test sample, such as the indentation modulus, are determined. Using AFAM system, the measured indentation modulus of copper nano-film, zinc nano-film and glass slides are 113.53 GPa, 87.92 GPa and 57.04 GPa, which are agreement with literature values Mcu--105-130 GPa, Mzn = 88.44 GPa and Molass = 50-90 GPa. Furthermore, the sensitivity of contact resonance frequency to contact stiffness is analyzed theoretically. The results show that for the cantilevers with the length 160 pm, 225 μm and 520 μm respectively, when contact stiffness increases from 400 N/m to 600 N/m, the increments of first contact resonance frequency are 126 kHz, 93 kHz and 0.6 kHz, which show that the sensitivity of the contact resonance frequency to the contact stiffness reduces with the length of cantilever increasing. The novel method presented can characterize elastic modulus of near surface for nano-film and bulk material, and local elasticity of near surface can be evaluated by optimizing the experimental parameters using the AFAM system.展开更多
A gradient metamaterial with varying-stiffness local resonators is proposed to open the multiple bandgaps and further form a broad fusion bandgap.First,three local resonators with linearly increasing stiffness are per...A gradient metamaterial with varying-stiffness local resonators is proposed to open the multiple bandgaps and further form a broad fusion bandgap.First,three local resonators with linearly increasing stiffness are periodically attached to the spring-mass chain to construct the gradient metamaterial.The dispersion relation is then derived based on Bloch's theorem to reveal the fusion bandgap theoretically.The dynamic characteristic of the finite spring-mass chain is investigated to validate the fusion of multiple bandgaps.Finally,the effects of the design parameters on multiple bandgaps are discussed.The results show that the metamaterial with a non-uniform stiffness gradient pattern is capable of opening a broad fusion bandgap and effectively attenuating the longitudinal waves within a broad frequency region.展开更多
Broadband acoustic transmission enhancement(ATE)is realized for a periodically structured stiff plate without any opening that is conventionally thought to be only capable of supporting narrowband ATE,by introducing l...Broadband acoustic transmission enhancement(ATE)is realized for a periodically structured stiff plate without any opening that is conventionally thought to be only capable of supporting narrowband ATE,by introducing locally resonant(LR)elements.This exotic phenomenon is interpreted by analyzing the vibration pattern of the structure-induced LR modes,and is well modeled by a simple"spring-mass"system which reveals the contribution of the LR effect to the important broadband performance.Our findings should help to better understand the physical mechanism of ATE and may have potential impact on ultrasonic applications such as broadband acoustic filters or compact acoustic devices in subwavelength scale.展开更多
Multi-seam mining often leads to the retention of a significant number of coal pillars for purposes such as protection,safety,or water isolation.However,stress concentration beneath these residual coal pillars can sig...Multi-seam mining often leads to the retention of a significant number of coal pillars for purposes such as protection,safety,or water isolation.However,stress concentration beneath these residual coal pillars can significantly impact their strength and stability when mining below them,potentially leading to hydraulic support failure,surface subsidence,and rock bursting.To address this issue,the linkage between the failure and instability of residual coal pillars and rock strata during multi-seam mining is examined in this study.Key controls include residual pillar spalling,safety factor(f.),local mine stiffness(LMS),and the post-peak stiffness(k)of the residual coal pillar.Limits separating the two forms of failure,progressive versus dynamic,are defined.Progressive failure results at lower stresses when the coal pillar transitions from indefinitely stable(f,>1.5)to failing(f,<1.5)when the coal pillar can no longer remain stable for an extended duration,whereas sud-den(unstable)failure results when the strength of the pillar is further degraded and fails.The transition in mode of failure is defined by the LMS/k ratio.Failure transitions from quiescent to dynamic as LMS/k.<1,which can cause chain pillar instability propagating throughout the mine.This study provides theoretical guidance to define this limit to instability of residual coal pillars for multi-seam mining in similar mines.展开更多
文摘We present a class of preconditioners for the linear systems resulting from a finite element or discontinuous Galerkin discretizations of advection-dominated problems.These preconditioners are designed to treat the case of geometrically localized stiffness,where the convergence rates of iterative methods are degraded in a localized subregion of the mesh.Slower convergence may be caused by a number of factors,including the mesh size,anisotropy,highly variable coefficients,and more challenging physics.The approach taken in this work is to correct well-known preconditioners such as the block Jacobi and the block incomplete LU(ILU)with an adaptive inner subregion iteration.The goal of these preconditioners is to reduce the number of costly global iterations by accelerating the convergence in the stiff region by iterating on the less expensive reduced problem.The tolerance for the inner iteration is adaptively chosen to minimize subregion-local work while guaranteeing global convergence rates.We present analysis showing that the convergence of these preconditioners,even when combined with an adaptively selected tolerance,is independent of discretization parameters(e.g.,the mesh size and diffusion coefficient)in the subregion.We demonstrate significant performance improvements over black-box preconditioners when applied to several model convection-diffusion problems.Finally,we present performance results of several variations of iterative subregion correction preconditioners applied to the Reynolds number 2.25×10^(6)fluid flow over the NACA 0012 airfoil,as well as massively separated flow at 30°angle of attack.
基金Sponsored by the National Basic Research Program of China (Grant No. 2013CB632305)the National Natural Science Foundation of China (GrantNo. 51275125)
文摘In order to describe the performance of thin wall bearing on rotor system more accurate,the simplified model of bearing local stiffness was proposed. The load distribution and local contact deformation in angular contact ball bearings were calculated using quasi dynamic calculation method. Based on the relationship of local load to contact deformation,the calculation model of local bearing stiffness was subsequently built to get radial and axial components of local stiffness. Effects of external loads on the local bearing stiffness were analyzed. The results showed that local stiffness in bearings is symmetric to the axis of radial load,and its value has a maximum on the symmetry axis along the radial load direction. External radial and axial load have different effects on local bearing stiffness.
基金supported by National Natural Science Foundation of China(Grant No. 50775005)General Program of Science and Technology Development Project of Beijing Municipal Education Commission(Grant No. KM201110015009)
文摘Traditional technique such nanoindenter（NI） can＇t measure the local elastic modulus at nano-scale（lateral）. Atomic force acoustic microscopy （AFAM） is a dynamic method, which can quantitatively determine indentation modulus by measuring the contact resonance spectra for high order modes of the cantilever. But there are few reports on the effect of experimental factors, such length of cantilever, contact stiffness on measured value. For three different samples, including copper（Cu） film with 110 nm thickness, zinc（Zn） film of 90 nm thickness and glass slides, are prepared and tested, using referencing approach in which measurements are performed on the test and reference samples （it＇s elastic modulus is known）, and their contact resonance spectra are measured used the AFAM system experimentally. According to the vibration theory, from the lowest two contact resonance frequencies, the tip-sample contact stiffness is calculated, and then the values for the elastic properties of test sample, such as the indentation modulus, are determined. Using AFAM system, the measured indentation modulus of copper nano-film, zinc nano-film and glass slides are 113.53 GPa, 87.92 GPa and 57.04 GPa, which are agreement with literature values Mcu--105-130 GPa, Mzn = 88.44 GPa and Molass = 50-90 GPa. Furthermore, the sensitivity of contact resonance frequency to contact stiffness is analyzed theoretically. The results show that for the cantilevers with the length 160 pm, 225 μm and 520 μm respectively, when contact stiffness increases from 400 N/m to 600 N/m, the increments of first contact resonance frequency are 126 kHz, 93 kHz and 0.6 kHz, which show that the sensitivity of the contact resonance frequency to the contact stiffness reduces with the length of cantilever increasing. The novel method presented can characterize elastic modulus of near surface for nano-film and bulk material, and local elasticity of near surface can be evaluated by optimizing the experimental parameters using the AFAM system.
基金supported by the National Natural Science Foundation of China(Nos.12122206,52175125,12272129,12304309,and 12302039)the Zhejiang Provincial Natural Science Foundation of China(No.LQ24A020006)+1 种基金the Hong Kong Scholars Program of China(No.XJ2022012)the Natural Science Foundation of Hunan Province of China(No.2024JJ4004)。
文摘A gradient metamaterial with varying-stiffness local resonators is proposed to open the multiple bandgaps and further form a broad fusion bandgap.First,three local resonators with linearly increasing stiffness are periodically attached to the spring-mass chain to construct the gradient metamaterial.The dispersion relation is then derived based on Bloch's theorem to reveal the fusion bandgap theoretically.The dynamic characteristic of the finite spring-mass chain is investigated to validate the fusion of multiple bandgaps.Finally,the effects of the design parameters on multiple bandgaps are discussed.The results show that the metamaterial with a non-uniform stiffness gradient pattern is capable of opening a broad fusion bandgap and effectively attenuating the longitudinal waves within a broad frequency region.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10904068,10834009,11174138,11174139Research Fund for the Doctoral Program(for new scholar)of Higher Education of China under Grant No 20100091120039A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘Broadband acoustic transmission enhancement(ATE)is realized for a periodically structured stiff plate without any opening that is conventionally thought to be only capable of supporting narrowband ATE,by introducing locally resonant(LR)elements.This exotic phenomenon is interpreted by analyzing the vibration pattern of the structure-induced LR modes,and is well modeled by a simple"spring-mass"system which reveals the contribution of the LR effect to the important broadband performance.Our findings should help to better understand the physical mechanism of ATE and may have potential impact on ultrasonic applications such as broadband acoustic filters or compact acoustic devices in subwavelength scale.
基金supported by the Climbling Project of Taishan Scholar in Shandong Province (No.tspd20210313)National Natural Science Foundation of China (Grant No.51874190,52079068,41941019,52090081 and 52074168)+3 种基金Taishan Scholar in Shandong Province (No.tsqn202211150)Outstanding Youth Fund Project in Shandong Province (No.ZQ2022YQ49)the State Key Laboratory of Hydroscience and Engineering,China (No.2021-KY-04)support from the G.Albert Shoemaker endowment.
文摘Multi-seam mining often leads to the retention of a significant number of coal pillars for purposes such as protection,safety,or water isolation.However,stress concentration beneath these residual coal pillars can significantly impact their strength and stability when mining below them,potentially leading to hydraulic support failure,surface subsidence,and rock bursting.To address this issue,the linkage between the failure and instability of residual coal pillars and rock strata during multi-seam mining is examined in this study.Key controls include residual pillar spalling,safety factor(f.),local mine stiffness(LMS),and the post-peak stiffness(k)of the residual coal pillar.Limits separating the two forms of failure,progressive versus dynamic,are defined.Progressive failure results at lower stresses when the coal pillar transitions from indefinitely stable(f,>1.5)to failing(f,<1.5)when the coal pillar can no longer remain stable for an extended duration,whereas sud-den(unstable)failure results when the strength of the pillar is further degraded and fails.The transition in mode of failure is defined by the LMS/k ratio.Failure transitions from quiescent to dynamic as LMS/k.<1,which can cause chain pillar instability propagating throughout the mine.This study provides theoretical guidance to define this limit to instability of residual coal pillars for multi-seam mining in similar mines.
