In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and ...In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.展开更多
This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initial...This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes.The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located.After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied.The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration.Numerical results on the influence of the initial stress,anisotropy properties of the plate material,the crack’s length and its distance from the face planes of the plate on the values of the ERR,are presented and discussed.In particular,it is established that for the relatively greater length of the crack’s band,the initial stretching of the plate causes a decrease,but the initial compression causes an increase in the values of the ERR.展开更多
Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional （1D） equations for a piezoelectric semiconductor beam are obtained. The...Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional （1D） equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degen- erated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic be- haviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.展开更多
The work investigated surface and mechanical properties of untreated and treated three-layered weftknitted spacer fabrics.In order to optimize the mechanical properties of weft-knitted spacer fabrics,silica aerogels(S...The work investigated surface and mechanical properties of untreated and treated three-layered weftknitted spacer fabrics.In order to optimize the mechanical properties of weft-knitted spacer fabrics,silica aerogels(SAs)coating was employed.Scanning electron microscopy(SEM)images of untreated and treated spacer fabrics were analyzed to ensure the presence of SAs on the coated spacer fabrics.The basic properties of uncoated and coated weftknitted spacer fabrics were studied and compared.Tensile strength and initial modulus were studied according to the GB/T3923 test standard YG026 MB-250 by testing machine.Moreover,compression properties of spacer fabrics were also tested by HD026 G test instrument.In this testing,work of compression,the linearity of compression,recovery work of compression and other parameters were calculated from stress and strain curves.It was found that SAs coating has a significant influence on the mechanical properties of weftknitted spacer fabrics.The statistical analysis also verified the significant performance(P value smaller than 0.05)of treated fabric samples at the 0.05 level.展开更多
The effects of SO_2 on the initial atmospheric corrosion of AZ91D magnesiumalloy were investigated in laboratory. Met-allographic observation, SEM (Scanning ElectronMicroscopy), XRD (X-ray Diffraction) and XPS (X-ray ...The effects of SO_2 on the initial atmospheric corrosion of AZ91D magnesiumalloy were investigated in laboratory. Met-allographic observation, SEM (Scanning ElectronMicroscopy), XRD (X-ray Diffraction) and XPS (X-ray Proton Spectrograph) were used to analyze anddiscuss the initial surface morphology of corrosion layers and corrosion products. The corrosionrate of the alloy increases with increasing the content of SO_2. The initial attack has thecharacteristics of localized corrosion and preferentially concentrates on a phase. MgO and Mg(OH)_2form at first, which provide a protective layer, then the existence of SO_2 decreases the pH of thethin solution on the alloy, accelerates dissolution process, and promotes the formation of MgSO_3centre dot 6H_2O and MgSO_4 centre dot 6H_2O, meanwhile cracks were found on the corrosion productswith corrosion continuation. These soluble corrosion products and the cracks provide the paths forfiltering oxygen and corrosion pollutants into the matrix, which results in severe localizedcorrosion and the loss of protective function of film.展开更多
Forced and natural vibrations of a rectangular pre-stressed orthotropic compositeplate containing two neighboring cylindrical cavities whose cross sections are rectangularwith rounded-off corners are investigated nume...Forced and natural vibrations of a rectangular pre-stressed orthotropic compositeplate containing two neighboring cylindrical cavities whose cross sections are rectangularwith rounded-off corners are investigated numerically. It is assumed that all the end surfacesof the rectangular pre-stressed composite plate are simply supported and subjected to auniformly distributed normal time-harmonic force on the upper face plane. The consideredproblem is formulated within the Three-Dimensional Linearized Theory of Elastic Waves inInitially Stressed Bodies (TDLTEWISB). The influence of mechanical and geometricalparameters as well as the initial stresses and the effect of cylindrical cavities on the dynamicalcharacteristics of the rectangular orthotropic composite plate are analyzed and discussed.展开更多
In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables （2D）. Applying the notion of the ε-regular map we show the unique existence of ...In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables （2D）. Applying the notion of the ε-regular map we show the unique existence of global solutions for initial data with low regularity and the existence of the global attractor.展开更多
The inverse problem for the 1-dimensional acoustic wave equation is discussed to deter-mine propagation velocity from impulse response. A relation between the propagation velocityand the wavefield can be established f...The inverse problem for the 1-dimensional acoustic wave equation is discussed to deter-mine propagation velocity from impulse response. A relation between the propagation velocityand the wavefield can be established from the analysis of propagation of discontinuities forhyperbolic equations. As a result, the inverse problem discussed in this paper is reduced to aparticular initial value problem of a semilinear system of P. D. E.. The Picard iteration forsolving this initial value problem is constructed and the convergence of iteration is proved.The main results are the following: (i) the propagation velocity can always be recovered fromthe impulse response, unless the inverse problem contains a singular point, where the propa-gation velocity is infinite or zero, or its total variation in the neighborhood of the singularpoint is infinite; (ii) the stability behaviour of the solutions of this inverse problem is es-sentially dependent on the total variation of logarithm of propagation velocity.展开更多
The nose shape effect on long-rod penetration was investigated by establishing numerical 2D models with different original nose shapes.The variations in nose shapes and the mass erosion rate of the rods in the transie...The nose shape effect on long-rod penetration was investigated by establishing numerical 2D models with different original nose shapes.The variations in nose shapes and the mass erosion rate of the rods in the transient phase,primary penetration phase,and secondary penetration phase were adequately analyzed by two dimensionless parameters,i.e.,the nose shape factor N* and the diameter ratio of the rod nose and shank n.In general,N*,η and the mass erosion rate of the rod vary distinctly in different phases,i.e.,unsteady in the initial transient and the secondary penetration phases,and quasi-steady in the primary penetration phase.Furthermore,a relationship between the mass erosion of the rod and the variation in the nose shape was established.A three-phase 2D model of long-rod penetration was further constructed by considering the variations in nose shape.This research may provide a reference to improve the theoretical model of long-rod penetration.展开更多
We consider the Cauchy problem for one-dimensional(1D)barotropic compressible Navier-Stokes equations with density-depending viscosity and large external forces.Under a general assumption on the densitydepending visco...We consider the Cauchy problem for one-dimensional(1D)barotropic compressible Navier-Stokes equations with density-depending viscosity and large external forces.Under a general assumption on the densitydepending viscosity,we prove that the Cauchy problem admits a unique global strong(classical)solution for the large initial data with vacuum.Moreover,the density is proved to be bounded from above time-independently.As a consequence,we obtain the large time behavior of the solution without external forces.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11922209,11991031 and 12021002)。
文摘In this work,the three-dimensional(3 D)propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP)and quasi-shear(qS_(1) and qS_(2))modes are derived.Based on the transfer and stiffness matrices,band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap property,and the tunability of the nonreciprocal transmission by the initial stress is discussed.This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.
文摘This paper deals with the mathematical modelling and 3D FEM study of the energy release rate(ERR)in the band crack’s front contained in the orthotropic thick rectangular plate which is stretched or compressed initially before the loading of the crack's edge planes.The initial stretching or compressing of the plate causes uniformly distributed normal stress to appear acting in the direction which is parallel to the plane on which the band crack is located.After the appearance of the initial stress in the plate it is assumed that the crack's edge planes are loaded with additional uniformly distributed normal forces and the ERR caused with this additional loading is studied.The corresponding boundary value problem is formulated within the scope of the so-called 3D linearized theory of elasticity which allows the initial stress on the values of the ERR to be taken into consideration.Numerical results on the influence of the initial stress,anisotropy properties of the plate material,the crack’s length and its distance from the face planes of the plate on the values of the ERR,are presented and discussed.In particular,it is established that for the relatively greater length of the crack’s band,the initial stretching of the plate causes a decrease,but the initial compression causes an increase in the values of the ERR.
基金Project supported by the National Natural Science Foundation of China(Nos.11672223,11402187,and 51178390)the China Postdoctoral Science Foundation(No.2014M560762)the Fundamental Research Funds for the Central Universities of China(No.xjj2015131)
文摘Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional （1D） equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degen- erated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic be- haviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.
文摘The work investigated surface and mechanical properties of untreated and treated three-layered weftknitted spacer fabrics.In order to optimize the mechanical properties of weft-knitted spacer fabrics,silica aerogels(SAs)coating was employed.Scanning electron microscopy(SEM)images of untreated and treated spacer fabrics were analyzed to ensure the presence of SAs on the coated spacer fabrics.The basic properties of uncoated and coated weftknitted spacer fabrics were studied and compared.Tensile strength and initial modulus were studied according to the GB/T3923 test standard YG026 MB-250 by testing machine.Moreover,compression properties of spacer fabrics were also tested by HD026 G test instrument.In this testing,work of compression,the linearity of compression,recovery work of compression and other parameters were calculated from stress and strain curves.It was found that SAs coating has a significant influence on the mechanical properties of weftknitted spacer fabrics.The statistical analysis also verified the significant performance(P value smaller than 0.05)of treated fabric samples at the 0.05 level.
基金This work was financially supported by the National Natural Science Foundation of China (No. 50171011 )the 973 Science Foundation of China (No. 19990650).
文摘The effects of SO_2 on the initial atmospheric corrosion of AZ91D magnesiumalloy were investigated in laboratory. Met-allographic observation, SEM (Scanning ElectronMicroscopy), XRD (X-ray Diffraction) and XPS (X-ray Proton Spectrograph) were used to analyze anddiscuss the initial surface morphology of corrosion layers and corrosion products. The corrosionrate of the alloy increases with increasing the content of SO_2. The initial attack has thecharacteristics of localized corrosion and preferentially concentrates on a phase. MgO and Mg(OH)_2form at first, which provide a protective layer, then the existence of SO_2 decreases the pH of thethin solution on the alloy, accelerates dissolution process, and promotes the formation of MgSO_3centre dot 6H_2O and MgSO_4 centre dot 6H_2O, meanwhile cracks were found on the corrosion productswith corrosion continuation. These soluble corrosion products and the cracks provide the paths forfiltering oxygen and corrosion pollutants into the matrix, which results in severe localizedcorrosion and the loss of protective function of film.
文摘Forced and natural vibrations of a rectangular pre-stressed orthotropic compositeplate containing two neighboring cylindrical cavities whose cross sections are rectangularwith rounded-off corners are investigated numerically. It is assumed that all the end surfacesof the rectangular pre-stressed composite plate are simply supported and subjected to auniformly distributed normal time-harmonic force on the upper face plane. The consideredproblem is formulated within the Three-Dimensional Linearized Theory of Elastic Waves inInitially Stressed Bodies (TDLTEWISB). The influence of mechanical and geometricalparameters as well as the initial stresses and the effect of cylindrical cavities on the dynamicalcharacteristics of the rectangular orthotropic composite plate are analyzed and discussed.
基金This work is supported by National Natural Science Foundation of China under Grant nos, 10001013 and 10471047 and Natural Science Foundation of Guangdong Province of China under Grant no. 004020077.
文摘In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables （2D）. Applying the notion of the ε-regular map we show the unique existence of global solutions for initial data with low regularity and the existence of the global attractor.
基金Project supported by National Natural Science Foundation of China.
文摘The inverse problem for the 1-dimensional acoustic wave equation is discussed to deter-mine propagation velocity from impulse response. A relation between the propagation velocityand the wavefield can be established from the analysis of propagation of discontinuities forhyperbolic equations. As a result, the inverse problem discussed in this paper is reduced to aparticular initial value problem of a semilinear system of P. D. E.. The Picard iteration forsolving this initial value problem is constructed and the convergence of iteration is proved.The main results are the following: (i) the propagation velocity can always be recovered fromthe impulse response, unless the inverse problem contains a singular point, where the propa-gation velocity is infinite or zero, or its total variation in the neighborhood of the singularpoint is infinite; (ii) the stability behaviour of the solutions of this inverse problem is es-sentially dependent on the total variation of logarithm of propagation velocity.
基金supported by the National Natural Science Foundation of China(Grant Nos.11872118 and 12002293).
文摘The nose shape effect on long-rod penetration was investigated by establishing numerical 2D models with different original nose shapes.The variations in nose shapes and the mass erosion rate of the rods in the transient phase,primary penetration phase,and secondary penetration phase were adequately analyzed by two dimensionless parameters,i.e.,the nose shape factor N* and the diameter ratio of the rod nose and shank n.In general,N*,η and the mass erosion rate of the rod vary distinctly in different phases,i.e.,unsteady in the initial transient and the secondary penetration phases,and quasi-steady in the primary penetration phase.Furthermore,a relationship between the mass erosion of the rod and the variation in the nose shape was established.A three-phase 2D model of long-rod penetration was further constructed by considering the variations in nose shape.This research may provide a reference to improve the theoretical model of long-rod penetration.
基金supported by Undergraduate Research Fund of Beijing Normal University(Grant Nos.2017-150 and 201810027047)National Natural Science Foundation of China(Grant Nos.11601218 and 11771382)。
文摘We consider the Cauchy problem for one-dimensional(1D)barotropic compressible Navier-Stokes equations with density-depending viscosity and large external forces.Under a general assumption on the densitydepending viscosity,we prove that the Cauchy problem admits a unique global strong(classical)solution for the large initial data with vacuum.Moreover,the density is proved to be bounded from above time-independently.As a consequence,we obtain the large time behavior of the solution without external forces.
