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Exact axisymmetric solutions for laminated transversely isotropic piezoelectric circular plate (Ⅰ)——Exact solutions for piezoelectric circular plate

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Science China(Technological Sciences) 1999年第4期42卷 388-395页

作者：丁皓江徐荣桥国凤林 Department of Civil Engineering Zhejiang University Hangzhou China

Based on three-dimensional elastic equations for piezoelectric materials, the state equations for piezoelectric circular plate under axisymmetric deformation are derived. Applying Hankel transform to them and letting the free boundary terms resulting from Hankel transform be zero, a set of ordinary differential equations with constant coefficients and associated boundary conditions are obtained. Furthermore, two exact solutions corresponding to generalized rigid slipping and generalized elastic simple support are deduced. Then, the governing equations obtained reduce to equations for axisymmetric problem of transversely isotropic circular plate. Under the two types of boundary conditions of elastic simple support and rigid slipping, exact solutions are derived. Finally, numerical results are presented and applicability of the classical plate theory is discussed.

关键词： transversely isotropy axisymmetric deformation exact solution piezoelectric circular plate.

Fundamental solutions for transversely isotropic magneto-electro-elastic media and boundary integral formulation

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Science China(Technological Sciences) 2003年第6期46卷 607-619页

作者：丁皓江江爱民 Department of Civil Engineering Zhejiang University Hangzhou 310027 China West Branch of Zhejiang University of Technology Quzhou 324006 China

To obtain the fundamental solutions for computation of magneto-electro-elastic media by the boundary element method, the general solutions in the case of distinct eigenvalues are de-rived and expressed in five harmonic functions from the governing equations and the strict differ-ential operator theorem. On the basis of these general solutions, the fundamental solution of infi-nite magneto-electro-elastic solid are obtained with the method of trial-and-error. Finally, the boundary integral formulation is derived and the corresponding boundary element method program is implemented to perform two numerical calculations(a column under uni-axial tension, uniform electric displacement or uniform magnetic induction, an annular plate simply-supported on outer and inner surfaces under axial loads). The numerical results agree well with the analytical ones.

关键词： transversely isotropic magneto-electro-elastic media, fundamental solution, boundary integral formulation.

A modified nearly analytic discrete method and wavefield simulations in transversely isotropic media

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Science China Earth Sciences 2005年第8期48卷 1321-1328页

作者： LU Ming YANG Dinghui Department of Mathematical Sciences Tsinghua University Beijing 100084 China Department of Mathematical Sciences Tsinghua University Beijing 100084 China

Nearly analytic discrete method (NADM) is a higher accurate method for elastic wave equation that can suppress effectively numerical dispersion caused by discretizing the wave equation. In this paper we investigate the efficient implementation of NADM and present a refinement of the original NADM. Our theoretical analyses show that the modified NADM can improve significantly over the original one in numerous perspectives including numerical errors, storage spaces, and computational costs. Three-component synthetic VSP seismograms in 3-layered transversely isotropic (TI) media generated by the modified NADM are also reported. Theoretical analyses and numerical results show that the modified NADM can reduce storage space about 53 percent and computational costs about 30 percent compared with the original NADM. Moreover the accuracy of the modified NADM in time increases from 2-order of the original NADM to 4-order. Numerical results suggest that the modified NADM is more suitable to large-scale modeling because the modified method has little numerical dispersions even when too-coarse grids are used.

关键词： nearly analytic discrete method (NADM), elastic wave, three-component VSP seismogram, transversely isotropic(TI), seismic wave.

The 3-D non-axisymmetrical Lamb's problem in transversely isotropic saturated poroelastic media

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Science China(Technological Sciences) 2004年第5期47卷 526-549页

作者： HUANG Yi1 & WANG Xiaogang1,2 1. School of Civil Engineering, Xian University of Architecture & Technology, Xian 710055, China 2. Department of Civil Engineering, Qinghai University, Xining 810016, China Correspondence should be addressed to Huang Yi (email: huangyih@***) Received April 15, 2004 revised July 12, 2004 School of Civil Engineering Xi’an University of Architecture & Technology Xi’an China Department of Civil Engineering Qinghai University Xining China

Based on Biots theory on fluid-saturated porous media, the displacement functions are adopted to convert the 3-D Biots wave equations in the cylindrical coordinate for transversely isotropic saturated poroelastic media into two棗one 6-order and one 2-order棗uncoupling differential governing equations. Then, the differential equations are solved by the Fourier expanding and Hankel integral transform method. Integral solutions of soil skeleton displacements and pore pressure as well as the total stresses for poroelastic media are obtained. Furthermore, the systematic study on Lambs problems for the transversely isotropic saturated poroelastic media is performed. Integral solutions for surface radial, vertical and circumferential displacements are obtained in both cases of drained surface and undrained surface under the vertical and horizontal harmonic excitation force. In the end of this paper, the numerical examples are presented. The calculation results indicate that the difference between the model of isotropic saturated poroelastic media and that of transversely isotropic saturated poroelastic media is obvious.

关键词： transversely isotropic saturated poroelastic media, Biot's wave equations, Lamb's problems.

The refined theory of transversely isotropic piezoelectric rectangular beams

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Science China(Physics,Mechanics & Astronomy) 2006年第4期49卷 473-486页

作者： GAO Yang1 & WANG Minzhong2 1. College of Science, China Agricultural University, Beijing 100083, China 2. State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engi- neering Science, Peking University, Beijing 100871, China College of Science China Agricultural University Beijing China State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science Peking University Beijing China

The problem of deducing one-dimensional theory from two-dimensional theory for a transversely isotropic piezoelectric rectangular beam is investigated. Based on the piezoelasticity theory, the refined theory of piezoelectric beams is derived by using the general solution of transversely isotropic piezoelasticity and Lur'e method without ad hoc assumptions. Based on the refined theory of piezoelectric beams, the exact equations for the beams without transverse surface loadings are derived, which consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beams under transverse loadings are derived directly from the refined beam theory. As a special case, the governing differential equations for transversely isotropic elastic beams are obtained from the corresponding equations of piezoelectric beams. To illustrate the application of the beam theory developed, a uniformly loaded and simply supported piezoelectric beam is examined.

关键词： rectangular beams, the refined theory, piezoelectric, transversely isotropic.

Deformation analysis of transversely isotropic coal-rock mass with porous and cracks

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International Journal of Mining Science and Technology 2012年第6期22卷 814-820页

作者： Xue Dongjie Zhou Hongwei Kong Lin Tang Xianli Zhao Tian Yi Haiyang Zhao Yufeng School of Mechanics Architecture and Civil EngineeringChina University of Mining & Technology

Coal-rock as a typical sedimentary rock has obvious stratification,namely it has transversely isotropic feature.Meanwhile,deformation leads to coal-rock mass having the characteristics of different porous and crack structures as well as local anisotropy.Equivalent axial and circumferential strain' formulas of the pure coal-rock mass specimen with a single crack were derived through the establishment of equivalent mechanical model of standard cylindrical coal-rock specimen,and have been widely used to a variety of media combined different structures containing multiple cracks.The complete stress strain curve of a real coal-rock specimen was obtained by the CTC test.Additionally,according to the comparison with the theoretical value,the theoretical mechanical model could well explain the deformation characteristics of coal-rock mass and verify its validity.Further,following features were analyzed:strain normalized coefficient and elastic modulus(Poisson's ratio) in vertical and parallel direction to the stratification,stratification angle,porosity,pore radius,normal and tangential stiffness of crack,and the relationship of different crack width with different tangential stiffness of crack.Through the analysis above,it substantiate this claim that the theoretical model with better reliability reflects the transversely isotropic nature of the coal-rock and the local anisotropy caused by the porous and cracks.

关键词： Coal-rock mass transversely isotropic Porous and crack Mechanical model

Plane Vibrations in a transversely Isotropic Infinite Hollow Cylinder Under Effect of the Rotation and Magnetic Field

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Computer Modeling in Engineering & Sciences 2017年第2期113卷 151-170页

作者： F.S.Bayones A.M.Abd-Alla Math.Dept. Faculty of ScienceTaif UniversitySaudi Arabia Mathematics Department Faculty of ScienceSohagEgypt

The aim of this paper is to study the effects of rotation and magnetic field on the plane vibrations in a transversely isotropic material of an infinite hollow cylinder.The natural frequency of the plane vibrations in the case of harmonic vibrations has been obtained.The natural frequencies are calculated numerically and the effects of rotation and magnetic field are discussed.The numerical results obtained have been illustrated graphically to understand the behavior of frequency equation with different values of frequencyωunder effects the rotation and magnetic field.Comparison was made with the results obtained in the presence and absence of the rotation and magnetic field.The results indicate that the effect of rotation and magnetic field are very pronounced.

关键词： Plane transversely isotropic rotating magnetic field homogeneous transversely isotropic Natural frequencies

Completeness of General Solutions to Axisymmetric Problems of transversely Isotropic Body

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Science China Mathematics 1994年第5期37卷 580-596页

作者：王炜徐新生王敏中 Department of Mechanics Peking UniversityBeijing 100871PRC

In this paper a kind of problems,which are a little wider than the axisymmetric problems of a transversely isotropic elastic body,are considered in a rectangular coordinates system.Two new general solutions of the axisymmetric problems of a transversely isotropic body are concisely obtained in a cylindrical coordinates system.Their completeness is also proved.It is worth while pointing out thai whether the meridional half-section is simply connected or multiply connected,both the new general solutions are single-valued.Using these results eight special general solutions are derived,including some known famous solutions.

关键词： transversely isotropic axisymmetric problem elastic general solution completeness

A Study on Propagation of Waves in a transversely Isotropic Poroelastic Layer Bounded between Two Viscous Liquids

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Open Journal of Acoustics 2019年第1期9卷 1-12页

作者： Nageswaranath Chinta Ahmed Shah Syed Ramesh Modem Venkata Ramanamurthy Mangipudi Department of Mathematics BVRITH College of Engineering for Women Hyderabad India Department of Mathematics Deccan College of Engineering and Technology Hyderabad India Department of Mathematics University College of Technology Osmania University Hyderabad India Department of Mathematics Osmania University Hyderabad India

Propagation of Love waves in a transversely isotropic poroelastic layer bounded between two compressible viscous liquids is presented. The equations of motion in a transversely isotropic poroelastic solid are formulated in the framework of Biot’s theory. A closed-form solution for the propagation of Love waves is obtained in a transversely isotropic poroelastic layer. The complex frequency equation for phase velocity and attenuation of Love waves is derived for a transversely isotropic poroelastic layer when it is bounded between two viscous liquids and the results are compared with that of the poroelastic layer. The effect of viscous liquids on the propagation of Love waves is discussed. It is observed that the presence of viscous liquids decreases phase velocity in both transversely isotropic poroelastic layer and poroelastic layer. Results related to the case without viscous liquids have been compared with some of the earlier results and comparison shows good agreement.

关键词： Viscosity Love Waves Wave Number Dissipation Coefficient transversely Isotropic Poroelastic Layer