Torsional vibration of a solid finite cylinder having transverse isotropy

Summary Stress and displacement components in a solid circular cylinder of transversely isotropic material under the torsional vibration set up by an impulsive twist applied at one and while the other end remains fixed, have been obtained by the application of Laplace transformation.     

Radial vibration of a composite cylindrical shell subjected to a magnetic field

Summary The radial vibration in a composite cylindrical shell under the effect of a magnetic field has been investigated by solving the equations of elasticity, taking into account electromagnetic equations of Maxwell. The frequency equation has been obtained at the final stage.     

Radial vibration of a composite spherical shell

Summary This paper deals with radial vibration of a composite spherical shell made up of orthotropic materials by the application of a periodic shearing stress on the outer surface. Two cases have been discussed. In the first the elastic constants of the material of the composite body are assumed to remain constant while in the second they are proportional to the distance from the centre of the composite body. Results were obtained in terms of Bessel functions.     

Torsional vibration of a twisted composite cylindrical shell of cylindrically aeolotropic materials

Summary The paper is concerned with the determination of torsional vibration of a twisted composite cylindrical shell assuming the elastic constants to be proportional to the square of the distance from the axis of the shell. The solution is obtained in the form of a series in terms of Bessel functions.     

On axisymmetric vibration in a transversely isotropic finite cylindrical shell acted upon by a magnetic field

Summary The present note seeks to investigate the axisymmetric vibration in a transversely isotropic finite cylindrical shell in presence of axial magnetic field by making use of the electromagnetic equations of Maxwell and the equations of elasticity. The frequency with its minimum value is obtained.     

Elastic wave mode separation for tilted transverse isotropy media

Seismic waves propagate through the earth as a superposition of different wave modes. Seismic imaging in areas characterized by complex geology requires techniques based on accurate reconstruction of the seismic wavefields. A crucial component of the methods in this category, collectively known as wave‐equation migration, is the imaging condition that extracts information about the discontinuities of physical properties from the reconstructed wavefields at every location in space. Conventional acoustic migration techniques image a scalar wavefield representing the P‐wave mode, in contrast to elastic migration techniques, which image a vector wavefield representing both the P‐ and S‐waves. For elastic imaging, it is desirable that the reconstructed vector fields are decomposed into pure wave modes, such that the imaging condition produces interpretable images, characterizing, for example, PP or PS reflectivity. In anisotropic media, wave mode separation can be achieved by projection of the reconstructed vector fields on the polarization vectors characterizing various wave modes. For heterogeneous media, because polarization directions change with position, wave mode separation needs to be implemented using space‐domain filters. For transversely isotropic media with a tilted symmetry axis, the polarization vectors depend on the elastic material parameters, including the tilt angles. Using these parameters, we separate the wave modes by constructing nine filters corresponding to the nine Cartesian components of the three polarization directions at every grid point. Since the S polarization vectors in transverse isotropic media are not defined in the singular directions, e.g., along the symmetry axes, we construct these vectors by exploiting the orthogonality between the SV and SH polarization vectors, as well as their orthogonality with the P polarization vector. This procedure allows one to separate all three modes, with better preserved P‐wave amplitudes than S‐wave amplitudes. Realistic synthetic examples show that this wave mode separation is effective for both 2D and 3D models with strong heterogeneity and anisotropy.     

On the vibration of a visco-elastic cylindrical shell and a composite visco-elastic cylinder with an isotropic core in an axial magnetic field

Summary The electrc-magnetic equations of Maxwell and the equations of mechanical motion have been used to investigate the vibrations of a cylindrical shell and also a cylinder with an isotropic core characterised by a visco-elasticity of Voigt tupe.     

Response of a circular cylindrical shell to disturbances in a half-space

The response of a circular cylindrical shell to disturbances in an elastic half-space is the subject of this paper. Two methods of solution are presented. The first is a method of matched asymptotic expansions, and the second is a method of successive reflections.     

斯通利波和弯曲波联合反演地层VTI各向异性的阵列声波处理方法

利用声波测井获取地层各向异性已成为储层油气评价的一项重要的课题.本文提出了一种单极和偶极振型联合反演地层各向异性的阵列声波处理方法,采用VTI（vertical transversely isotropic）介质斯通利波和弯曲波频散特征,分频段联合求取各向同性面内剪切模量,反演精度相比于传统方法得到了提高;研究了一种同时适用于单极和偶极声波测井的仪器标定方法,消除了仪器对井孔声传播的影响.通过对数值模拟数据的处理和现场测井数据的应用,验证了新方法的正确性和有效性.本文工作为利用阵列声波测井资料评价横观各向同性地层中横波速度的各向异性提供了有效的处理方法.

     

Forced vibration of a thin non-homogeneous circular plate having a central hole

Summary This paper deals with the forced vibration produced in a thin non-homogeneous circular plate having a central hole when a periodic force is acting on the internal boundary.     

On the transverse vibration of a circular membrane of varying density

Summary This paper deals with the solution of problem on the transverse vibration of a circular membrane of varying density by using Rayleigh-Ritz and perturbation method.     

Modal base forces in structures having a straight-line mode of vibration

The modal base forces in structures having a straight-line mode of vibration are investigated. Making use of the orthogonality relationship between the different modes, a relation between the modal base shears and base moments is found in all but the straight-line mode. This relation states that the contribution of the inertia forces to the modal overturning moments referred to the centre of rotation of the straight-line mode is identically null. The contributions of the vertical forces and lateral constraints must, however, be accounted for. For the special case of the straight-line mode being proportional to the height of each storey, the centre of rotation coincides with the base of the structure. For the case of the straight-line mode being a uniform displacement, the centre of rotation is at infinity and the contribution of the inertia forces to the modal base shears identically disappears in all but the straight-line mode.     

Turam response of a permeable inhomogeneous cylindrical conductor surrounded by a thin shell

Summary Electromagnetic response characteristics of an inhomogeneous permeable cylinder surrounded by a thin insulated concentric dissipative shell is obtained in presence of a line-source of current. The 3-layer boundary value problem is solved by assuming the thickness of the shell to be much smaller than the skin-depth in the shell. Numerically computed results are presented in the form of argand diagrams to examine the influence of the shell parameters (conductivity and its proximity with the core) and magnetic contrast. The multi-frequency response of the system is also given which resolves the two conducting layers and analyzes the frequency dependence of screening behavior of the shell.N.G.R.I. Contribution No. 282.     

Magnetoelastic disturbances in a perfectly conducting cylindrical shell in a constant magnetic field

Summary The paper deals with the problem of determining the displacements, stresses, magnetic and the electric fields of an infinite shell placed in vacuum and subjected to an impulsive excitation load.     

Dynamic interaction analysis of a circular cylindrical shell of finite length in a half-space

A study on the transient response of a circular cylindrical shell of finite length embedded in a homogeneous, isotropic and linear elastic half-space is presented. The soil-structure system is subjected to suddenly applied explosion waves. The numerical method employed is a combination of the time domain semi-analytical boundary element method used for the semi-infinite soil medium and the finite strip method used for the circular cylindrical shell. The two methods are combined through equilibrium and compatibility conditions at the soil-structure interface. The dynamic responses at the interface between the soil medium and the structure for every time step are obtained. Numerical examples are presented in detail to demonstrate the use and versatility of the proposed method. The following parameters are found to affect the response: (1) the slenderness ratio of the length over the diameter of the shell, L/D; (2) the relative wall thickness, h/a; (3) the relative stiffness ratio between the shell and the medium, E_s/E_m; and (4) the incidence angle of the explosion wave, α.     

Torsional vibration of a finite cylindrical cavity in a two-layer transversely isotropic half-space

The aim of this paper is to present a rigorous investigation for a two-layered transversely isotropic linear elastic half-space containing a circular cylindrical cavity of length equal to the top layer undergoing mono-harmonic ring shape shear stress applied either on the vertical cylindrical surface or on the base of the cavity. To this end, a combination of Fourier cosine integral transform for depth and Hankel integral transform for radial distance are used, which translate the boundary value problem to a singular integral equation for the shear stress comes out from the continuity of two layers. The integral equation is solved for some collocation points with a smoothed variable of distance, which is adapted with the use of a free parameter. It is shown that, although the shear stress is highly singular, it does not highly depend on this free parameter. Both the analytical and numerical results are verified with both the static isotropic and dynamic transversely isotropic homogeneous cases. In addition, some new graphical results are presented for more understanding in engineering point of view.     

Propagation of surface waves on the surface of a non-homogeneous aeolotropic cylindrical shell

Summary The object of the present paper is to investigate the propagation of surface waves on a non-homogeneous aeolotropic cylindrical shell surrounded by vacuum. The elastic constantsc _ij (i, j=1,2...) and density of the material of the shell are assumed to be of the form and respectively, where _ij, ₀ are constants andk ₁,k ₂ are any integers.     

Anisotropic azimuthal surface-wave inversion for a vertically fractured and transverse isotropy medium: Theory and examples from a controlled field experiment

Fractures in elastic media add compliance to a rock in the direction normal to the fracture strike. Therefore, elastic wave velocities in a fractured rock will vary as a function of the energy propagation direction relative to the orientation of the aligned fracture set. Anisotropic Thomson–Haskell matrix Rayleigh-wave equations for a vertically transverse isotropic media can be used to model surface-wave dispersion along the principal axes of a vertically fractured and transversely isotropic medium. Furthermore, a workflow combining first-break analysis and azimuthal anisotropic Rayleigh-wave inversion can be used to estimate P-wave and S-wave velocities, Thomsen's ε, and Thomsen's δ along the principal axes of the orthorhombic symmetry. In this work, linear slip theory is used to map our inversion results to the equivalent vertically fractured and transversely isotropic medium coefficients. We carried out this inversion on a synthetic example and a field example. The synthetic data example results show that joint estimation of S-wave velocities with Thomsen's parameters ε and δ along normal and parallel to the vertical fracture set is reliable and, when mapped to the corresponding vertically fractured and transversely isotropic medium, provides insight into the fracture compliances. When the inversion was carried out on the field data, results indicated that the fractured rock is more compliant in the azimuth normal to the visible fracture set orientation and that the in situ normal fracture compliance to tangential fracture compliance ratio is less than half, which implies some cementation may have occurred along the fractures. Such an observation has significant implications when modelling the transport properties of the rock and its strength. Both synthetic and field examples show the potential of azimuthal anisotropic Rayleigh-wave inversion as the method can be further expanded to a more general case where the vertical fracture set orientation is not known a priori.     

Scattering of elastic wave by a cylindrical shell deeply embeded in saturated soils

The compression of soil grain and pore fluid as well as viscid coupling of pore fluid and soil skeleton is considered, the scattering problem of incident plane P1 wave （fast compressional wave） by an infinite cylindrical shell deeply embedded in isotropic saturated soils is studied by adopting the amended Biot model, amplitude equations about potential functions of scattering and refracting fields are obtained, and the effect of dimensionless frequencies and shell thickness on the back-scattering spectra and dynamic stress concentration factors of two types of cylindrical shells with high and low rigidity are numerically computed and analyzed.