In the past,convolutional neural network(CNN)has become one of the most popular deep learning frameworks,and has been widely used in Hyperspectral image classification tasks.Convolution(Conv)in CNN uses filter weights...In the past,convolutional neural network(CNN)has become one of the most popular deep learning frameworks,and has been widely used in Hyperspectral image classification tasks.Convolution(Conv)in CNN uses filter weights to extract features in local receiving domain,and the weight parameters are shared globally,which more focus on the highfrequency information of the image.Different from Conv,Transformer can obtain the long‐term dependence between long‐distance features through modelling,and adaptively focus on different regions.In addition,Transformer is considered as a low‐pass filter,which more focuses on the low‐frequency information of the image.Considering the complementary characteristics of Conv and Transformer,the two modes can be integrated for full feature extraction.In addition,the most important image features correspond to the discrimination region,while the secondary image features represent important but easily ignored regions,which are also conducive to the classification of HSIs.In this study,a complementary integrated Transformer network(CITNet)for hyperspectral image classification is proposed.Firstly,three‐dimensional convolution(Conv3D)and two‐dimensional convolution(Conv2D)are utilised to extract the shallow semantic information of the image.In order to enhance the secondary features,a channel Gaussian modulation attention module is proposed,which is embedded between Conv3D and Conv2D.This module can not only enhance secondary features,but suppress the most important and least important features.Then,considering the different and complementary characteristics of Conv and Transformer,a complementary integrated Transformer module is designed.Finally,through a large number of experiments,this study evaluates the classification performance of CITNet and several state‐of‐the‐art networks on five common datasets.The experimental results show that compared with these classification networks,CITNet can provide better classification performance.展开更多
The integrated hydraulic transformer has a compact structure and no throttling loss in the process of pressure regulation.It is widely used in the common pressure rail hydrostatic transmission system.The integrated hy...The integrated hydraulic transformer has a compact structure and no throttling loss in the process of pressure regulation.It is widely used in the common pressure rail hydrostatic transmission system.The integrated hydraulic transformer is realized by designing more than three ports on the distribution plate,and the voltage transformation characteristics of the integrated hydraulic transformer with different port numbers are different.In this paper,the influence of port number on the pressure ratio of integrated hydraulic transformer was studied,and the pressure ratio characteristics of 3⁃ports,4⁃ports,and 5⁃ports integrated hydraulic transformer were obtained,and an experimental platform was built for experimental verification,which shows that the simulation results are consistent with the experimental results and provides a theoretical basis for the design of integrated hydraulic transformer.展开更多
In this study,we aimto investigate certain triple integral transformand its application to a class of partial differentialequations.We discuss various properties of the new transformincluding inversion, linearity, exi...In this study,we aimto investigate certain triple integral transformand its application to a class of partial differentialequations.We discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution theorem.Further, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations aswell.Moreover,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables.展开更多
Based on the Euler-Bernoulli beam theory and Kelvin-Voigt model,a nonlinear model for the transverse vibration of a pipe under the combined action of base motion and pulsating internal flow is established.The governin...Based on the Euler-Bernoulli beam theory and Kelvin-Voigt model,a nonlinear model for the transverse vibration of a pipe under the combined action of base motion and pulsating internal flow is established.The governing partial differential equation is transformed into a nonlinear system of fourth-order ordinary differential equations by using the generalized integral transform technique(GITT).The effects of the combined excitation of base motion and pulsating internal flow on the nonlinear dynamic behavior of the pipe are investigated using a bifurcation diagram,phase trajectory diagram,power spectrum diagram,time-domain diagram,and Poincare map.The results show that the base excitation amplitude and frequency significantly affect the dynamic behavior of the pipe system.Some new resonance phenomena can be observed,such as the period-1 motion under the base excitation or the pulsating internal flow alone becomes the multi-periodic motion,quasi-periodic motion or even chaotic motion due to the combined excitation action.展开更多
The nonlinear dynamic behaviors of viscoelastic axially functionally graded material(AFG)pipes conveying pulsating internal flow are very complex.And the dynamic behavior will induce the failure of the pipes,and resea...The nonlinear dynamic behaviors of viscoelastic axially functionally graded material(AFG)pipes conveying pulsating internal flow are very complex.And the dynamic behavior will induce the failure of the pipes,and research of vibration and stability of pipes becomes a major concern.Considering that the elastic modulus,density,and coefficient of viscoelastic damping of the pipe material vary along the axial direction,the transverse vibration equation of the viscoelastic AFG pipe conveying pulsating fluid is established based on the Euler-Bernoulli beam theory.The generalized integral transform technique(GITT)is used to transform the governing fourth-order partial differential equation into a nonlinear system of fourth-order ordinary differential equations in time.The time domain diagram,phase portraits,Poincarémap and power spectra diagram at different dimensionless pulsation frequencies,are discussed in detail,showing the characteristics of chaotic,periodic,and quasi-periodic motion.The results show that the distributions of the elastic modulus,density,and coefficient of viscoelastic damping have significant effects on the nonlinear dynamic behavior of the viscoelastic AFG pipes.With the increase of the material property coefficient k,the transition between chaotic,periodic,and quasi-periodic motion occurs,especially in the high-frequency region of the flow pulsation.展开更多
The present article mainly focuses on the fractional derivatives with an exponential kernel(“exponential fractional derivatives”for brevity).First,several extended integral transforms of the exponential fractional d...The present article mainly focuses on the fractional derivatives with an exponential kernel(“exponential fractional derivatives”for brevity).First,several extended integral transforms of the exponential fractional derivatives are proposed,including the Fourier transform and the Laplace transform.Then,the L2 discretisation for the exponential Caputo derivative with a∈(1,2)is established.The estimation of the truncation error and the properties of the coefficients are discussed.In addition,a numerical example is given to verify the correctness of the derived L2 discrete formula.展开更多
The transient response of two coplanar cracks in a piezoelectric ceramic under antiplane mechanical and inplane electric impacting loads is investigated in the present paper. Laplace and Fourier transforms are used to...The transient response of two coplanar cracks in a piezoelectric ceramic under antiplane mechanical and inplane electric impacting loads is investigated in the present paper. Laplace and Fourier transforms are used to reduce the mixed boundary value problems to Cauchy-type singular integral equations in Laplace transform domain, which are solved numerically. The dynamic stress and electric displacement factors are obtained as the functions of time and geometry parameters. The present study shows that the presence of the dynamic electric field will impede or enhance the propagation of the crack in piezoelectric ceramics at different stages of the dynamic electromechanical load. Moreover, the electromechanical response is greatly affected by the ratio of the space of the cracks and the crack length.展开更多
The generalized integral transform technique (GITT) is used to find a semianalytical numerical solution for dynamic response of an axially moving Timoshenko beam with clamped-clamped and simply-supported boundary co...The generalized integral transform technique (GITT) is used to find a semianalytical numerical solution for dynamic response of an axially moving Timoshenko beam with clamped-clamped and simply-supported boundary conditions, respectively. The implementation of GITT approach for analyzing the forced vibration equation eliminates the space variable and leads to systems of second-order ordinary differential equations (ODEs) in time. The MATHEMATICA built-in function, NDSolve, is used to numerically solve the resulting transformed ODE system. The good convergence behavior of the suggested eigenfunction expansions is demonstrated for calculating the transverse deflection and the angle of rotation of the beam cross-section. Moreover, parametric studies are performed to analyze the effects of the axially moving speed, the axial tension, and the amplitude of external distributed force on the vibration amplitude of axially moving Timoshenko beams.展开更多
A plane strain analysis based on the generalized Biot's equation is utilized to investigate the wave-induced response of a poro-elastic seabed with variable shear modulus. By employing integral transform and Frobenin...A plane strain analysis based on the generalized Biot's equation is utilized to investigate the wave-induced response of a poro-elastic seabed with variable shear modulus. By employing integral transform and Frobenins methods, the transient and steady solutions for the wave-inducod pore water pressure, effective stresses and displacements are analytically derived in detail. Verification is available through the reduction to the simple case of homogeneous seabed. The numerical results indicate that the inclusion of variable shear modulus significantly affects the wave-induced seabed response.展开更多
The small Hankel operators on weighted Bergman space of bounded symmetric domains Omega in C-n with symbols in L-2(Omega,dV(lambda)) are studied. Characterizations for the boundedness, compactness of the small Hankel ...The small Hankel operators on weighted Bergman space of bounded symmetric domains Omega in C-n with symbols in L-2(Omega,dV(lambda)) are studied. Characterizations for the boundedness, compactness of the small Hankel operators h(Phi) are presented in terms of a certain integral transform of the symbol Phi.展开更多
In this paper, the compatibility between the integral type gauge transformation and the additional symmetry of the constrained KP hierarchy is given. And the string-equation constraint in matrix models is also derived.
The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be d...The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.展开更多
The plane elastic problem for a semi-strip with a transverse crack is inves- tigated. The initial problem is reduced to a one-dimensional continuous problem by use of an integral transformation method with a generaliz...The plane elastic problem for a semi-strip with a transverse crack is inves- tigated. The initial problem is reduced to a one-dimensional continuous problem by use of an integral transformation method with a generalized scheme. The one-dimensional problem is first formulated as a vector boundary problem, and then reduced to a system of three singular integral equations (SIEs). The system is solved by use of an orthogonal polynomial method and a special generalized method. The contribution of this work is the consideration of kernel fixed singularities in solving the system. The crack length and its location relative to the semi-strip's lateral sides are investigated to simplify the problem's statement. This simplification reduces the initial problem to a system of two SIEs.展开更多
Based on the principle of linear superposition, this paper proves generalized Duhamel's integral which reserves moving dynamical load problem to fixed dynamical load problem. Laplace transform and Fourier transfor...Based on the principle of linear superposition, this paper proves generalized Duhamel's integral which reserves moving dynamical load problem to fixed dynamical load problem. Laplace transform and Fourier transform are used to solve patial differential equation of infinite beam. The generalized Duhamel's integral and deflection impulse response function of the beam make it easy for us to obtain final solution of moving line load problem. Deep analyses indicate that the extreme value of dynamic response always lies in the center of the line load and travels with moving load at the same speed. Additionally, the authors also present definition of moving dynamic coefficient which reflects moving effect.展开更多
A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special Junction was introduced to transform the inhomogeneous bound...A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special Junction was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel Junctions, the equation With respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.展开更多
This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method. Based on the numerical results, the effect of non-Newtonian coeff...This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method. Based on the numerical results, the effect of non-Newtonian coefficient Hc and other parameters on the flow are analysed. It is shown that the annular flow has a shorter characteristic time than the general pipe flow while the correspondent velocity, average velocity have a ... nailer value for a given Hc. Else, when radii ratio keeps unchanged, the shear stress of inner wall of annular flow will change with the inner radius -compared with the general pipe flow and is always smaller than that of the outer wall.展开更多
Using the Weyl ordering of operators expansion formula (Hong-Yi Fan, J. Phys.A 25 (1992) 3443) this paper finds a kind of two-fold integration transformation about the Wigner operator △( q',p) q-number transf...Using the Weyl ordering of operators expansion formula (Hong-Yi Fan, J. Phys.A 25 (1992) 3443) this paper finds a kind of two-fold integration transformation about the Wigner operator △( q',p) q-number transform) in phase space quantum mechanics,∫∫∞-∞dp'dq'/π △(q',p')e-2i( p-p')( q-q')=δ( p-P)δ( q-Q),∫∫∞-∞dqdpδ(p-P)δ(q-Q)e2i(p-p')(q-q')=△(q',p'),whereQ,P are the coordinate and momentum operators, respectively. We apply it to study mutual converting formulae among Q-P ordering, P-Q ordering and Weyl ordering of operators. In this way, the contents of phase space quantum mechanics can be enriched. The formula of the Weyl ordering of operators expansion and the technique of integration within the Weyl ordered product of operators are used in this discussion.展开更多
This article studies on Cauchy’s function f (z) and its integral, (2πi)J[ f (z)] ≡ ■C f (t)dt/(t z) taken along a closed simple contour C, in regard to their comprehensive properties over the entire z =...This article studies on Cauchy’s function f (z) and its integral, (2πi)J[ f (z)] ≡ ■C f (t)dt/(t z) taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x + iy plane consisted of the simply connected open domain D + bounded by C and the open domain D outside C. (1) With f (z) assumed to be C n (n ∞-times continuously differentiable) z ∈ D + and in a neighborhood of C, f (z) and its derivatives f (n) (z) are proved uniformly continuous in the closed domain D + = [D + + C]. (2) Cauchy’s integral formulas and their derivatives z ∈ D + (or z ∈ D ) are proved to converge uniformly in D + (or in D = [D +C]), respectively, thereby rendering the integral formulas valid over the entire z-plane. (3) The same claims (as for f (z) and J[ f (z)]) are shown extended to hold for the complement function F(z), defined to be C n z ∈ D and about C. (4) The uniform convergence theorems for f (z) and F(z) shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle |z| = 1 such that the four general- ized Hilbert-type integral transforms are proved. (5) Further, the singularity distribution of f (z) in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . (6) A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. (7) Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. (8) Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f (z) in domain D , based on the continuous numerical value of f (z) z ∈ D + = [D + + C], is presented for resolution as a conjecture.展开更多
The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic mater...The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic material, which contains an edge crack perpendicular to and terminating at the interface. Fourier transforms and asymptotic analysis are employed to reduce the problem to a singular integral equation which is numerically solved using Gauss-Chebyshev quadrature formulae. Furthermore, a parametric study is carried out to investigate the effects of elastic and geometric characteristics of the composite on the values of stress intensity factor.展开更多
The adhesion failure has become one dominant factor in determining the reliability and service life of miniaturized devices subject to loadings with arbitrary orientations.This article establishes an adhesive full sti...The adhesion failure has become one dominant factor in determining the reliability and service life of miniaturized devices subject to loadings with arbitrary orientations.This article establishes an adhesive full stick contact model between an elastic half-space and a rigid cylinder loaded in any direction.Using the Papkovich-Neuber functions,the Fourier integral transform,and the asymmetric bipolar coordinates,the exact solution is obtained.Unlike the Johnson-Kendall-Roberts(JKR)model,the present adhesive contact model takes into account the effects of the load direction as well as the coupling of the normal and tangential contact stresses.Besides,it considers the full stick contact which has large values of the friction coefficient between contacting surfaces,contrary to the frictionless contact supposed in the JKR model.The result shows that suitable angles can be found,which makes the contact surfaces difficult to be peeled off or easy to be pressed into.展开更多
基金funded in part by the National Natural Science Foundation of China(42271409,62071084)in part by the Heilongjiang Science Foundation Project of China under Grant LH2021D022in part by the Leading Talents Project of the State Ethnic Affairs Commission,and in part by the Fundamental Research Funds in Heilongjiang Provincial Universities of China under Grant 145209149.
文摘In the past,convolutional neural network(CNN)has become one of the most popular deep learning frameworks,and has been widely used in Hyperspectral image classification tasks.Convolution(Conv)in CNN uses filter weights to extract features in local receiving domain,and the weight parameters are shared globally,which more focus on the highfrequency information of the image.Different from Conv,Transformer can obtain the long‐term dependence between long‐distance features through modelling,and adaptively focus on different regions.In addition,Transformer is considered as a low‐pass filter,which more focuses on the low‐frequency information of the image.Considering the complementary characteristics of Conv and Transformer,the two modes can be integrated for full feature extraction.In addition,the most important image features correspond to the discrimination region,while the secondary image features represent important but easily ignored regions,which are also conducive to the classification of HSIs.In this study,a complementary integrated Transformer network(CITNet)for hyperspectral image classification is proposed.Firstly,three‐dimensional convolution(Conv3D)and two‐dimensional convolution(Conv2D)are utilised to extract the shallow semantic information of the image.In order to enhance the secondary features,a channel Gaussian modulation attention module is proposed,which is embedded between Conv3D and Conv2D.This module can not only enhance secondary features,but suppress the most important and least important features.Then,considering the different and complementary characteristics of Conv and Transformer,a complementary integrated Transformer module is designed.Finally,through a large number of experiments,this study evaluates the classification performance of CITNet and several state‐of‐the‐art networks on five common datasets.The experimental results show that compared with these classification networks,CITNet can provide better classification performance.
基金the National Key Research and Development Plan Projects(Grant No.2018YFB2001200)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant Nos.19KJB460026,19KJA140002)the Six Talent Peak Training Projects in Jiangsu Province(Grant No.JXQC-36).
文摘The integrated hydraulic transformer has a compact structure and no throttling loss in the process of pressure regulation.It is widely used in the common pressure rail hydrostatic transmission system.The integrated hydraulic transformer is realized by designing more than three ports on the distribution plate,and the voltage transformation characteristics of the integrated hydraulic transformer with different port numbers are different.In this paper,the influence of port number on the pressure ratio of integrated hydraulic transformer was studied,and the pressure ratio characteristics of 3⁃ports,4⁃ports,and 5⁃ports integrated hydraulic transformer were obtained,and an experimental platform was built for experimental verification,which shows that the simulation results are consistent with the experimental results and provides a theoretical basis for the design of integrated hydraulic transformer.
文摘In this study,we aimto investigate certain triple integral transformand its application to a class of partial differentialequations.We discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution theorem.Further, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations aswell.Moreover,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52171288,51890914)the Key Research and Development Program of Shandong Province(Major Innovation Project)(Grant No.2022CXGC020405)+1 种基金the National Ministry of Industry and Information Technology Innovation Special Project-Engineering Demonstration Application of Subsea Oil and Gas Production SystemSubject 4:Research on Subsea Christmas Tree and Wellhead Offshore Testing Technology(Grant No.MC-201901-S01-04)CNPq,CAPES and FAPERJ of Brazil。
文摘Based on the Euler-Bernoulli beam theory and Kelvin-Voigt model,a nonlinear model for the transverse vibration of a pipe under the combined action of base motion and pulsating internal flow is established.The governing partial differential equation is transformed into a nonlinear system of fourth-order ordinary differential equations by using the generalized integral transform technique(GITT).The effects of the combined excitation of base motion and pulsating internal flow on the nonlinear dynamic behavior of the pipe are investigated using a bifurcation diagram,phase trajectory diagram,power spectrum diagram,time-domain diagram,and Poincare map.The results show that the base excitation amplitude and frequency significantly affect the dynamic behavior of the pipe system.Some new resonance phenomena can be observed,such as the period-1 motion under the base excitation or the pulsating internal flow alone becomes the multi-periodic motion,quasi-periodic motion or even chaotic motion due to the combined excitation action.
基金supported by the National Natural Science Foundation of China(52171288,51890914)the Key Research and Development Program of Shandong Province(Major Innovation Project)(2022CXGC020405)+3 种基金the National Ministry of Industry and Information Technology Innovation Special Project-Engineering Demonstration Application of Subsea Oil and Gas Production System-Subject 4“Research on Subsea Christmas Tree and Wellhead Offshore Testing Technology”[MC-201901-S01-04]the Fundamental Research Funds for the Central Universities(20CX02410A)the Development Fund of Shandong Key Laboratory of Oil&Gas Storage and Transportation SafetyCNPq,CAPES and FAPERJ of Brazil。
文摘The nonlinear dynamic behaviors of viscoelastic axially functionally graded material(AFG)pipes conveying pulsating internal flow are very complex.And the dynamic behavior will induce the failure of the pipes,and research of vibration and stability of pipes becomes a major concern.Considering that the elastic modulus,density,and coefficient of viscoelastic damping of the pipe material vary along the axial direction,the transverse vibration equation of the viscoelastic AFG pipe conveying pulsating fluid is established based on the Euler-Bernoulli beam theory.The generalized integral transform technique(GITT)is used to transform the governing fourth-order partial differential equation into a nonlinear system of fourth-order ordinary differential equations in time.The time domain diagram,phase portraits,Poincarémap and power spectra diagram at different dimensionless pulsation frequencies,are discussed in detail,showing the characteristics of chaotic,periodic,and quasi-periodic motion.The results show that the distributions of the elastic modulus,density,and coefficient of viscoelastic damping have significant effects on the nonlinear dynamic behavior of the viscoelastic AFG pipes.With the increase of the material property coefficient k,the transition between chaotic,periodic,and quasi-periodic motion occurs,especially in the high-frequency region of the flow pulsation.
文摘The present article mainly focuses on the fractional derivatives with an exponential kernel(“exponential fractional derivatives”for brevity).First,several extended integral transforms of the exponential fractional derivatives are proposed,including the Fourier transform and the Laplace transform.Then,the L2 discretisation for the exponential Caputo derivative with a∈(1,2)is established.The estimation of the truncation error and the properties of the coefficients are discussed.In addition,a numerical example is given to verify the correctness of the derived L2 discrete formula.
文摘The transient response of two coplanar cracks in a piezoelectric ceramic under antiplane mechanical and inplane electric impacting loads is investigated in the present paper. Laplace and Fourier transforms are used to reduce the mixed boundary value problems to Cauchy-type singular integral equations in Laplace transform domain, which are solved numerically. The dynamic stress and electric displacement factors are obtained as the functions of time and geometry parameters. The present study shows that the presence of the dynamic electric field will impede or enhance the propagation of the crack in piezoelectric ceramics at different stages of the dynamic electromechanical load. Moreover, the electromechanical response is greatly affected by the ratio of the space of the cracks and the crack length.
基金Project supported by the Science Foundation of China University of Petroleum in Beijing(No.2462013YJRC003)
文摘The generalized integral transform technique (GITT) is used to find a semianalytical numerical solution for dynamic response of an axially moving Timoshenko beam with clamped-clamped and simply-supported boundary conditions, respectively. The implementation of GITT approach for analyzing the forced vibration equation eliminates the space variable and leads to systems of second-order ordinary differential equations (ODEs) in time. The MATHEMATICA built-in function, NDSolve, is used to numerically solve the resulting transformed ODE system. The good convergence behavior of the suggested eigenfunction expansions is demonstrated for calculating the transverse deflection and the angle of rotation of the beam cross-section. Moreover, parametric studies are performed to analyze the effects of the axially moving speed, the axial tension, and the amplitude of external distributed force on the vibration amplitude of axially moving Timoshenko beams.
基金This project is supported by the National Natural Science Foundation of China (Grant No50479045)
文摘A plane strain analysis based on the generalized Biot's equation is utilized to investigate the wave-induced response of a poro-elastic seabed with variable shear modulus. By employing integral transform and Frobenins methods, the transient and steady solutions for the wave-inducod pore water pressure, effective stresses and displacements are analytically derived in detail. Verification is available through the reduction to the simple case of homogeneous seabed. The numerical results indicate that the inclusion of variable shear modulus significantly affects the wave-induced seabed response.
文摘The small Hankel operators on weighted Bergman space of bounded symmetric domains Omega in C-n with symbols in L-2(Omega,dV(lambda)) are studied. Characterizations for the boundedness, compactness of the small Hankel operators h(Phi) are presented in terms of a certain integral transform of the symbol Phi.
基金supported by the Fundamental Research Funds for the Central Universities(2015QNA43)
文摘In this paper, the compatibility between the integral type gauge transformation and the additional symmetry of the constrained KP hierarchy is given. And the string-equation constraint in matrix models is also derived.
基金This work was supported by the National Natural Science Foundation of China(No.19772064)by the project of CAS KJ 951-1-20
文摘The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.
文摘The plane elastic problem for a semi-strip with a transverse crack is inves- tigated. The initial problem is reduced to a one-dimensional continuous problem by use of an integral transformation method with a generalized scheme. The one-dimensional problem is first formulated as a vector boundary problem, and then reduced to a system of three singular integral equations (SIEs). The system is solved by use of an orthogonal polynomial method and a special generalized method. The contribution of this work is the consideration of kernel fixed singularities in solving the system. The crack length and its location relative to the semi-strip's lateral sides are investigated to simplify the problem's statement. This simplification reduces the initial problem to a system of two SIEs.
文摘Based on the principle of linear superposition, this paper proves generalized Duhamel's integral which reserves moving dynamical load problem to fixed dynamical load problem. Laplace transform and Fourier transform are used to solve patial differential equation of infinite beam. The generalized Duhamel's integral and deflection impulse response function of the beam make it easy for us to obtain final solution of moving line load problem. Deep analyses indicate that the extreme value of dynamic response always lies in the center of the line load and travels with moving load at the same speed. Additionally, the authors also present definition of moving dynamic coefficient which reflects moving effect.
文摘A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special Junction was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel Junctions, the equation With respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.
文摘This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method. Based on the numerical results, the effect of non-Newtonian coefficient Hc and other parameters on the flow are analysed. It is shown that the annular flow has a shorter characteristic time than the general pipe flow while the correspondent velocity, average velocity have a ... nailer value for a given Hc. Else, when radii ratio keeps unchanged, the shear stress of inner wall of annular flow will change with the inner radius -compared with the general pipe flow and is always smaller than that of the outer wall.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174)Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘Using the Weyl ordering of operators expansion formula (Hong-Yi Fan, J. Phys.A 25 (1992) 3443) this paper finds a kind of two-fold integration transformation about the Wigner operator △( q',p) q-number transform) in phase space quantum mechanics,∫∫∞-∞dp'dq'/π △(q',p')e-2i( p-p')( q-q')=δ( p-P)δ( q-Q),∫∫∞-∞dqdpδ(p-P)δ(q-Q)e2i(p-p')(q-q')=△(q',p'),whereQ,P are the coordinate and momentum operators, respectively. We apply it to study mutual converting formulae among Q-P ordering, P-Q ordering and Weyl ordering of operators. In this way, the contents of phase space quantum mechanics can be enriched. The formula of the Weyl ordering of operators expansion and the technique of integration within the Weyl ordered product of operators are used in this discussion.
文摘This article studies on Cauchy’s function f (z) and its integral, (2πi)J[ f (z)] ≡ ■C f (t)dt/(t z) taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x + iy plane consisted of the simply connected open domain D + bounded by C and the open domain D outside C. (1) With f (z) assumed to be C n (n ∞-times continuously differentiable) z ∈ D + and in a neighborhood of C, f (z) and its derivatives f (n) (z) are proved uniformly continuous in the closed domain D + = [D + + C]. (2) Cauchy’s integral formulas and their derivatives z ∈ D + (or z ∈ D ) are proved to converge uniformly in D + (or in D = [D +C]), respectively, thereby rendering the integral formulas valid over the entire z-plane. (3) The same claims (as for f (z) and J[ f (z)]) are shown extended to hold for the complement function F(z), defined to be C n z ∈ D and about C. (4) The uniform convergence theorems for f (z) and F(z) shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle |z| = 1 such that the four general- ized Hilbert-type integral transforms are proved. (5) Further, the singularity distribution of f (z) in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . (6) A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. (7) Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. (8) Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f (z) in domain D , based on the continuous numerical value of f (z) z ∈ D + = [D + + C], is presented for resolution as a conjecture.
文摘The present work is concerned with the problem of mode Ⅲ crack perpendicular to the interface of a bi-strip composite. One of these strips is made of a functionally graded material and the other of an isotropic material, which contains an edge crack perpendicular to and terminating at the interface. Fourier transforms and asymptotic analysis are employed to reduce the problem to a singular integral equation which is numerically solved using Gauss-Chebyshev quadrature formulae. Furthermore, a parametric study is carried out to investigate the effects of elastic and geometric characteristics of the composite on the values of stress intensity factor.
基金supported by the National Natural Science Foundation of China(Nos.11972257,11832014,and 11472193)the China Scholarship Council(CSC)the Fundamental Research Funds for the Central Universities(No.22120180223)。
文摘The adhesion failure has become one dominant factor in determining the reliability and service life of miniaturized devices subject to loadings with arbitrary orientations.This article establishes an adhesive full stick contact model between an elastic half-space and a rigid cylinder loaded in any direction.Using the Papkovich-Neuber functions,the Fourier integral transform,and the asymmetric bipolar coordinates,the exact solution is obtained.Unlike the Johnson-Kendall-Roberts(JKR)model,the present adhesive contact model takes into account the effects of the load direction as well as the coupling of the normal and tangential contact stresses.Besides,it considers the full stick contact which has large values of the friction coefficient between contacting surfaces,contrary to the frictionless contact supposed in the JKR model.The result shows that suitable angles can be found,which makes the contact surfaces difficult to be peeled off or easy to be pressed into.