In this paper the elastic properties of SiOx film are investigated quantitatively for local fixed point and qualitatively for overall area by atomic force acoustic microscopy （AFAM） in which the sample is vibrated a...In this paper the elastic properties of SiOx film are investigated quantitatively for local fixed point and qualitatively for overall area by atomic force acoustic microscopy （AFAM） in which the sample is vibrated at the ultrasonic frequency while the sample surface is touched and scanned with the tip contacting the sample respectively for fixed point and continuous measurements. The SiOx films on the silicon wafers are prepared by the plasma enhanced chemical vapour deposition （PECVD）, The local contact stiffness of the tip-SiOx film is calculated from the contact resonance spectrum measured with the atomic force acoustic microscopy. Using the reference approach, indentation modulus of SiOx film for fixed point is obtained. The images of cantilever amplitude are also visualized and analysed when the SiOx surface is excited at a fixed frequency. The results show that the acoustic amplitude images can reflect the elastic properties of the sample.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
The formation of singularity and breakdown of classical solutions to the three- dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite...The formation of singularity and breakdown of classical solutions to the three- dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite-time formation of singularity in classical solu- tions is proved for certain initial data. For the compressible viscoelastic fluids, a criterion in term of the temporal integral of the velocity gradient is obtained for the breakdown of smooth solutions.展开更多
A buckling model of Timoshenko micro-beam with local thickness defects is established based on a modified gradient elasticity.By introducing the local thickness defects function of the micro-beam,the variable coeffici...A buckling model of Timoshenko micro-beam with local thickness defects is established based on a modified gradient elasticity.By introducing the local thickness defects function of the micro-beam,the variable coefficient differential equations of the buckling problem are obtained with the variational principle.Combining the eigensolution series of the complete micro-beam with the Galerkin method,we obtain the critical load and buckling modes of the micro-beam with defects.The results show that the depth and location of the defect are the main factors affecting the critical load,and the combined effect of boundary conditions and defects can significantly change the buckling mode of the micro-beam.The effect of defect location on buckling is related to the axial gradient of the rotation angle,and defects should be avoided at the maximum axial gradient of the rotation angle.The model and method are also applicable to the static deformation and vibration of the micro-beam.展开更多
The influence of the transfer payments from the central government to the local governments on the local governments＇ efforts on taxation must be taken into consideration by every country for the design of the transf...The influence of the transfer payments from the central government to the local governments on the local governments＇ efforts on taxation must be taken into consideration by every country for the design of the transfer payments. Based on the theoretical analysis on the influence of the transfer payments from the central government to the local governments＇ on the local governments＇ payments＇, this paper indicates that the local governments＇ efforts on taxation depends on the demand elasticity of the district for public goods, It increases with the increase of the elasticity. Judge the degree of the local govet：nment＇s efforts on taxation by measure 2. After an empirical analysis on the transJer payments from the central government to the local governments＇from 2000 to 2004, this paper gets the con- clusion that the local governments＇ effbrts on taxation ctbates with the increase of supporting payments or with the increase of the ratio of transfer payments to local wiliing public paymentS. Under speCific Circumstances, the higher the ratio of transfer payments to the local fiscal expenditure is. the smaller the local governments＇ efforts＇ on taxation is＂ under the central payments, whereas＇ the higher the local income is, the higher the efforts is under the central pav- ments. Based on this＇, this paper gives the meaning of its eOrresponding pofiCieS. ＂展开更多
The current study presents a new protocol for local pulse wave velocity (PWV) measurement using dynamic MR sequences, which have a high temporal resolution (TR < 6 ms). MR images were obtained at two positions alon...The current study presents a new protocol for local pulse wave velocity (PWV) measurement using dynamic MR sequences, which have a high temporal resolution (TR < 6 ms). MR images were obtained at two positions along the common carotid artery, separated by a distance of 5 cm. In each phase of a MR series, carotid region was automatically extracted and then its area distension waveform could be obtained. Sixteen volunteers with no symptoms of cardiovascular diseases were studied. For local PWV estimation, three delay estimation principles were tested and produced the following values: intersecting tangents method (M1): 4.72 ± 1.40 m/s, second derivative method (M2): 4.94 ± 1.68 m/s and cross-correlation method (M3): 5.03 ± 1.17 m/s. The cross-correlation method showed a relative high reliability as its least standard deviation.展开更多
A non-local solution for a functionally graded piezoelectric nano-rod is pre- sented by accounting the surface effect. This solution is used to evaluate the charac- teristics of the wave propagation in the rod structu...A non-local solution for a functionally graded piezoelectric nano-rod is pre- sented by accounting the surface effect. This solution is used to evaluate the charac- teristics of the wave propagation in the rod structure. The model is loaded under a two-dimensional （2D） electric potential and an initially applied voltage at the top of the rod. The mechanical and electrical properties are assumed to be variable along the thick- ness direction of the rod according to the power law. The Hamilton principle is used to derive the governing differential equations of the electromechanical system. The effects of some important parameters such as the applied voltage and gradation of the material properties on the wave characteristics of the rod are studied.展开更多
Recent experiments revealed many new phenomena of the macroscopic domain patterns in the stress-induced phase transformation of a superelastic polycrystalline NiTi tube during tensile loading. The new phenomena includ...Recent experiments revealed many new phenomena of the macroscopic domain patterns in the stress-induced phase transformation of a superelastic polycrystalline NiTi tube during tensile loading. The new phenomena include deformation instability with the formation of a helical domain, domain topology transition from helix to cylinder, domain-front branching and loading-path dependence of domain patterns. In this paper, we model the polycrystal as an elastic continuum with nonconvex strain energy and adopt the non-local strain gradient energy to account for the energy of the diffusive domain front. We simulate the equilibrium domain patterns and their evolution in the tubes under tensile loading by a non-local Finite Element Method （FEM）. It is revealed that the observed loading-path dependence and topology transition of do- main patterns are due to the thermodynamic metastability of the tube system. The computation also shows that the tube-wall thickness has a significant effect on the domain patterns： with fixed material properties and interfacial energy density, a large tube-wall thickness leads to a long and slim helical domain and a severe branching of the cylindrical-domain front.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.50775005)
文摘In this paper the elastic properties of SiOx film are investigated quantitatively for local fixed point and qualitatively for overall area by atomic force acoustic microscopy （AFAM） in which the sample is vibrated at the ultrasonic frequency while the sample surface is touched and scanned with the tip contacting the sample respectively for fixed point and continuous measurements. The SiOx films on the silicon wafers are prepared by the plasma enhanced chemical vapour deposition （PECVD）, The local contact stiffness of the tip-SiOx film is calculated from the contact resonance spectrum measured with the atomic force acoustic microscopy. Using the reference approach, indentation modulus of SiOx film for fixed point is obtained. The images of cantilever amplitude are also visualized and analysed when the SiOx surface is excited at a fixed frequency. The results show that the acoustic amplitude images can reflect the elastic properties of the sample.
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 in part by the National Science Foundationthe Office of Naval Research
文摘The formation of singularity and breakdown of classical solutions to the three- dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite-time formation of singularity in classical solu- tions is proved for certain initial data. For the compressible viscoelastic fluids, a criterion in term of the temporal integral of the velocity gradient is obtained for the breakdown of smooth solutions.
基金National High-Technology Research &Development Program of China (2007AA03Z330)National Key Development Programfor Basic Research of China(2009CB623305)+3 种基金Foundation for Innovative Research Groups of the National Natural ScienceFoundation of China (50821004)National Science Foundation of China (1077411310876041)Nanotechnology Project of Shanghai Science and Technology Committee (0852nm06900)
基金Project supported by the Young Core Instructor and Domestic Visitor Foundation from the Education Commission of Hunan Province(No.21B0315)。
文摘A buckling model of Timoshenko micro-beam with local thickness defects is established based on a modified gradient elasticity.By introducing the local thickness defects function of the micro-beam,the variable coefficient differential equations of the buckling problem are obtained with the variational principle.Combining the eigensolution series of the complete micro-beam with the Galerkin method,we obtain the critical load and buckling modes of the micro-beam with defects.The results show that the depth and location of the defect are the main factors affecting the critical load,and the combined effect of boundary conditions and defects can significantly change the buckling mode of the micro-beam.The effect of defect location on buckling is related to the axial gradient of the rotation angle,and defects should be avoided at the maximum axial gradient of the rotation angle.The model and method are also applicable to the static deformation and vibration of the micro-beam.
文摘The influence of the transfer payments from the central government to the local governments on the local governments＇ efforts on taxation must be taken into consideration by every country for the design of the transfer payments. Based on the theoretical analysis on the influence of the transfer payments from the central government to the local governments＇ on the local governments＇ payments＇, this paper indicates that the local governments＇ efforts on taxation depends on the demand elasticity of the district for public goods, It increases with the increase of the elasticity. Judge the degree of the local govet：nment＇s efforts on taxation by measure 2. After an empirical analysis on the transJer payments from the central government to the local governments＇from 2000 to 2004, this paper gets the con- clusion that the local governments＇ effbrts on taxation ctbates with the increase of supporting payments or with the increase of the ratio of transfer payments to local wiliing public paymentS. Under speCific Circumstances, the higher the ratio of transfer payments to the local fiscal expenditure is. the smaller the local governments＇ efforts＇ on taxation is＂ under the central payments, whereas＇ the higher the local income is, the higher the efforts is under the central pav- ments. Based on this＇, this paper gives the meaning of its eOrresponding pofiCieS. ＂
文摘The current study presents a new protocol for local pulse wave velocity (PWV) measurement using dynamic MR sequences, which have a high temporal resolution (TR < 6 ms). MR images were obtained at two positions along the common carotid artery, separated by a distance of 5 cm. In each phase of a MR series, carotid region was automatically extracted and then its area distension waveform could be obtained. Sixteen volunteers with no symptoms of cardiovascular diseases were studied. For local PWV estimation, three delay estimation principles were tested and produced the following values: intersecting tangents method (M1): 4.72 ± 1.40 m/s, second derivative method (M2): 4.94 ± 1.68 m/s and cross-correlation method (M3): 5.03 ± 1.17 m/s. The cross-correlation method showed a relative high reliability as its least standard deviation.
基金supported by the University of Kashan(No.463865/13)the Iranian Nanotechnology Development Committee
文摘A non-local solution for a functionally graded piezoelectric nano-rod is pre- sented by accounting the surface effect. This solution is used to evaluate the charac- teristics of the wave propagation in the rod structure. The model is loaded under a two-dimensional （2D） electric potential and an initially applied voltage at the top of the rod. The mechanical and electrical properties are assumed to be variable along the thick- ness direction of the rod according to the power law. The Hamilton principle is used to derive the governing differential equations of the electromechanical system. The effects of some important parameters such as the applied voltage and gradation of the material properties on the wave characteristics of the rod are studied.
文摘Recent experiments revealed many new phenomena of the macroscopic domain patterns in the stress-induced phase transformation of a superelastic polycrystalline NiTi tube during tensile loading. The new phenomena include deformation instability with the formation of a helical domain, domain topology transition from helix to cylinder, domain-front branching and loading-path dependence of domain patterns. In this paper, we model the polycrystal as an elastic continuum with nonconvex strain energy and adopt the non-local strain gradient energy to account for the energy of the diffusive domain front. We simulate the equilibrium domain patterns and their evolution in the tubes under tensile loading by a non-local Finite Element Method （FEM）. It is revealed that the observed loading-path dependence and topology transition of do- main patterns are due to the thermodynamic metastability of the tube system. The computation also shows that the tube-wall thickness has a significant effect on the domain patterns： with fixed material properties and interfacial energy density, a large tube-wall thickness leads to a long and slim helical domain and a severe branching of the cylindrical-domain front.
