The gravitational gradient tensor’s invariants and the related boundary conditions

Here we report new approaches of recovering the Earth gravitational field from GOCE (Gravity field and steady-state Ocean Circulation Explorer) gradiometric data with the help of the gradient tensor’s invariants. Our results only depend on GOCE satellite’s position and gradiometry, in other words, they are completely independent of the satellite attitude. First, starting from the invariants, linearization models are established, which can be referred as the general boundary conditions on the satellite’s orbit. Then, the spherical approximation expressions for the models are derived, and the corresponding solving methods for them are discussed. Furthermore, considering effects of J2-term, the spherical approximation models are improved so that the accuracies of the boundary conditions can be theoretically raised to O ( J 2/2 T), which is approximately equivalent to O(T2). Finally, some arithmetic examples are constructed from EGM96 model based on the derived theories, and the computational results illustrate that the spherical models have accuracies of 10-7 and the order recovering the gravitational field can reach up to 200, and the models with regard to effect of J2-term have accuracies of 10-8 and the order can reach up to 280.

THE EFFECTIVE PROPERTIES OF PIEZOCOMPOSITES, PART Ⅱ: THE EFFECTIVE ELECTROELASTIC MODULI

Since piezoelectric ceramic/polymer composites have been widely used as smart materials and smart structures, it is more and more important to obtain the closed-from solutions of the effective properties of piezocomposites with piezoelectric ellipsoidal inclusions. Based on the closed-from solutions of the electroe- lastic Eshelby's tensors obtained in the part I of this paper and the generalized Bu- diansky's energy-equivalence framework, the closed-form general relations of effective electroelastic moduli of the piezocomposites with piezoelectric ellipsoidal inclusions are given. The relations can be applicable for several micromechanics models, such as the dilute solution and the Mori-Tanaka's method. The difference among the various models is shown to be the way in which the average strain and the average electric field of the inclusion phase are evaluated. Comparison between predicted and exper- imental results shows that the theoretical values in this paper agree quite well with the experimental results. These expressions can be readily utilized in analysis and design of piezocomposites.

An approximate solution of green's tensor to homogeneous and transversely isotropic media

Fourier transform method is used to obtain an approximate solution of Green's tensor to homogeneous and transversely isotropic media like unidirectional fiber re-inforced composites and austenitic stainless steel materials in order to provide the theoretical basis for the scattering problems. A comparison to homogeneously isotropic media is presented and a brief discussion of the main features of the solution is given

Retrieval of Elastic Green’s Tensor near a Cylindrical Inhomogeneity from Vector Correlations

Multiple scattering of elastic waves in realistic media makes that averagefield intensities or energy densities follow diffusive processes. In such regime the successiveP to S energy conversions by distributed random inhomogeneities give rise toequipartition which means that in the phase space the available elastic energy is distributedin averagewith equal amounts among the possible states of P and S waves. Insuch diffusive regime the P to S energy ratio equilibrates in an universal way independentof the particular details of the scattering. It has been demonstrated that averagingthe cross correlations at any two points of an elastic medium subjected to diffuse elasticwavefields leads to the emergence of the Green function, which is the wave fieldthat would be observed at one position if an impulsive load is applied at the other. Inthis work we study the problem of the retrieval of the 2D tensor elastodynamic Greenfunction in an infinite elastic space containing a circular cylinder inclusion. We illuminateisotropically the elastic spacewith plane waves. We assume the spectra for both Pand S waves uniform but such that the energy ratio ES/EP=(a/b)2, which is the onepredicted by equipartition theory in two-dimensions. We then show that the Fouriertransform of azimuthal average of the cross-correlation of motion between two pointswithin an elastic medium is proportional to the imaginary part of the exact Green tensorfunction between these points. The numerical results presented here point out thepossibility of detection and imaging of diffractors and resonant diffractors by crosscorrelation even in presence of attenuation exists.