Three-dimensional inverse problem for inhomogeneous transversely isotropic media

1988 ◽  
Vol 32 (2) ◽  
pp. 136-143 ◽  
Author(s):  
Jiří Jech ◽  
I. Pšenčík
Keyword(s):  
Inverse Problem ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Complete solutions of three-dimensional problems in transversely isotropic media

2018 ◽  
Vol 32 (3) ◽  
pp. 775-802 ◽  
Author(s):  
Francesco Marmo ◽  
Salvatore Sessa ◽  
Nicoló Vaiana ◽  
Daniela De Gregorio ◽  
Luciano Rosati
Keyword(s):  
Three Dimensional ◽  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Complete Solutions

scholarly journals Stress field formulation of linear electro-magneto-elastic materials

2019 ◽  
Vol 24 (12) ◽  
pp. 3806-3822
Author(s):  
A Amiri-Hezaveh ◽  
P Karimi ◽  
M Ostoja-Starzewski
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Governing Equations ◽  
Field Equations ◽  
Elastic Solids ◽  
Elastic Materials ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
Sufficient Set

A stress-based approach to the analysis of linear electro-magneto-elastic materials is proposed. Firstly, field equations for linear electro-magneto-elastic solids are given in detail. Next, as a counterpart of coupled governing equations in terms of the displacement field, generalized stress equations of motion for the analysis of three-dimensional (3D) problems Are obtained – they supply a more convenient basis when mechanical boundary conditions are entirely tractions. Then, a sufficient set of conditions for the corresponding solution of generalized stress equations of motion to be unique are detailed in a uniqueness theorem. A numerical passage to obtain the solution of such equations is then given by generalizing a reciprocity theorem in terms of stress for such materials. Finally, as particular cases of the general 3D form, the stress equations of motion for planar problems (plane strain and Generalized plane stress) for transversely isotropic media are formulated.

The inverse problem for transversely isotropic media

Wave Motion ◽  
1991 ◽  
Vol 14 (3) ◽  
pp. 233-242
Author(s):  
S.M. Kelly ◽  
M.A. Hooshyar
Keyword(s):  
Inverse Problem ◽  
Transversely Isotropic ◽  
Transversely Isotropic Media ◽  
Isotropic Media

3-D Exact Free Vibration Analysis of Transversely Isotropic Cylindrical Panels

1998 ◽  
Vol 120 (4) ◽  
pp. 982-986 ◽  
Author(s):  
Chen Weiqiu ◽  
Cai Jinbiao ◽  
Ye Guiru ◽  
Ding Haojiang
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Transversely Isotropic ◽  
Function Solution ◽  
Transversely Isotropic Media ◽  
Cylindrical Panels ◽  
Isotropic Media ◽  
Three Dimensional Elasticity

This paper presents an exact analysis of the free vibration of simply supported, transversely isotropic cylindrical panels. Based on the three dimensional elasticity for transversely isotropic media, three displacement functions are introduced so that the equations of motion are uncoupled and simplified. After expanding these functions with orthogonal series, the equations of free vibration problems are further reduced to three second order ordinary differential equations. A modified Bessel function solution with complex arguments is then directly used for the case of complex eigenvalues, which, to the authors’ knowledge, has never been reported before. To clarify the correctness and effectiveness of the developed method, numerical examples are presented and compared to the results of existent papers.

Stability Conditions for Wave Simulation in 3-D Anisotropic Media with the Pseudospectral Method

2012 ◽  
Vol 12 (3) ◽  
pp. 703-720 ◽  
Author(s):  
Wensheng Zhang
Keyword(s):  
Inverse Problem ◽  
Wave Propagation ◽  
Pseudospectral Method ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Stability Conditions ◽  
Wave Simulation ◽  
Transversely Isotropic Media ◽  
Isotropic Media ◽  
D Wave

AbstractSimulation of elastic wave propagation has important applications in many areas such as inverse problem and geophysical exploration. In this paper, stability conditions for wave simulation in 3-D anisotropic media with the pseudospectral method are investigated. They can be expressed explicitly by elasticity constants which are easy to be applied in computations. The 3-D wave simulation for two typical anisotropic media, transversely isotropic media and orthorhombic media, are carried out. The results demonstrate some satisfactory behaviors of the pseudospectral method.

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