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Journal of Ocean Engineering and Science 2023年第6期8卷 636-646页

作者： Nazek A.Obeidat Daniel E.Bentil Department of Mathematics and Statistics University of VermontBurlingtonVermont 05405USA

In this research work,we present proof of the existence and uniqueness of solution for a novel method called tempered fractional natural transforms(TFNT)and give error *** efficient method is applied to models,such as the time-space tempered fractional convection-diffusion equation(FCDE)and tempered fractional Black-Scholes equation(FBSE).We obtain exact solutions for these models using our methodology,which is very important for knowing the wave behavior in ocean engineering models and for the studies related to marine science and *** exact solutions to tempered fractional differential equations(TFDEs)is far from ***,the proposed method is an excellent addition to the myriad of techniques for solving TFDE problems.

关键词： Tempered fractional calculus Diffusion equation Caputo derivative Riemann-Liouville derivative integral transforms

Non-local theory solution to two collinear limited-permeable mode-I cracks in a piezoelectric/piezomagnetic material plane

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Science China(Physics,Mechanics & Astronomy) 2012年第7期55卷 1272-1290页

作者： ZHOU ZhenGong TANG YuLing WU LinZhi Center for Composite Materials and Structures Harbin Institute of Technology Harbin 150080China

The non-local theory solution to two collinear limited-permeable mode-1 cracks in a piezoelectric/piezomagnetic medium was investigated by using the generalized Almansi＇s theorem and the Schmidt method in the present paper. The problem was for- mulated through Fourier transformation into two pairs of dual integral equations, in which the unknown variables are the dis- placement jumps across the crack surfaces. For solving the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of the crack length, the distance between the two collinear cracks, the lattice parameter, the electric permittivity and the magnetic permeability of the air inside the crack on the stress fields, the electric displacement fields and the magnetic flux fields near the crack tips in a piezoeleetric/piezomaguetic medium. Different from the classical solutions, the present solution exhibits no stress, electric displacement and magnetic flux singularities at the crack tips in a piezoelectric/piezomagnetic medium.

关键词： piezoelectric/piezomagnetic medium fracture mechanics the non-local theory integral transforms

JACOBI POLYNOMIALS USED TO INVERT THE LAPLACE TRANSFORM

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Analysis in Theory and Applications 2004年第1期20卷 28-34页

作者： A.Al-Shuaibi F.Al-Rawjih King Fahd University of Petroleum and Minerals Dhahran Saudi ArabiaCollege For Girls Dammam Saudi Arabia

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find on approximation to f(t) by the use of the dassical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series ex-pansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.

关键词： Inverse Laplace transform Jacobi polynomials integral transforms Ill-posed problems

材料特性对输送脉动流体的粘弹性轴向功能梯度管非线性动力行为的影响

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哈尔滨工程大学学报（英文版） 2023年第2期22卷 247-259页

作者：付光明庹宇航张贺恩苏健孙宝江王锴娄敏 Key Laboratory of Unconventional Oil&Gas Development(China University of Petroleum(East China)) Ministry of EducationQingdao 266580China China Petroleum Pipeline Engineering Co. Ltd.Langfang 065201China CNPC Offshore Engineering Company Limited Beijing 100028China Nuclear Engineering Department COPPEFederal University of Rio de JaneiroRio de Janeiro 21941-972Brazil

The nonlinear dynamic behaviors of viscoelastic axially functionally graded material(AFG)pipes conveying pulsating internal flow are very *** the dynamic behavior will induce the failure of the pipes,and research of vibration and stability of pipes becomes a major *** 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 *** 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 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 *** 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 *** 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.

关键词： Axially functionally graded pipe Pipe conveying pulsating flow integral transforms Nonlinear dynamics Chaotic motion Quasi-periodic motion

Representation Theory of Three-Dimensional Elliptical Crack Under Dynamic Loading

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Journal of Beijing Institute of Technology 2000年第2期9卷 138-141页

作者：范天佑北京理工大学材料科学研究中心北京100081

The relation between the normal displacement on the surface of a dynamical elliptical crack and the normal stress over the crack surface was studied. The three dimensional elastodynamic equations and Fourier Laplace transforms are used. Based on the influence function and the inversion of integral transforms, one can find that if the distribution of normal displacement on the surface of a dynamic elliptical crack is a polynomial of degree n in x 1 and x 2 , then the normal pressure acting over the ellipse is also a polynomial P n(x 1,x 2) of the same degree in x 1 and x 2 .

关键词： dynamic elliptical crack elastodynamics integral transforms representation theory