Wave propagation in graded rings with rectangular cross-sections

In this paper, a double orthogonal polynomial series method is proposed to investigate the guided wave propagation in a two-dimensional (2-D) structure, namely, a FGM ring with a rectangular cross-section. Two kinds of graded rings are considered: material gradient directions being in the radial direction and in the axial direction respectively. Numerical comparison with available reference results for a straightly homogeneous rectangular bar illustrates the validity of the proposed method. The dispersion curves and displacement distributions of various FGM rings, which have different radius to thickness ratios, different material gradient directions and different thickness to height ratios, are calculated to reveal the guided wave characteristics.     

An algorithm of the method of difference potentials for domains with cuts

The method of Difference Potentials (DPM) is applied to solving a Dirichlet problem for the Laplace equation in a square with a cut. The DPM approach has been modified to achieve a more efficient numerical algorithm with respect to computational time. The considered problem can be a prototype for other problems formulated in domains with cuts including elastic problems related to cracks.     

Dynamic point sources in laminated media via the thin-layer method

This paper presents closed-form expressions for the Greens functions associated with harmonic point sources acting within horizontally layered media. These expressions are intended for use with the highly efficient Thin-Layer Method (TLM) described elsewhere, which is now being used widely for diverse engineering purposes. Among the dynamic sources considered are point forces, force dipoles (cracks and moments) , blast loads, seismic double couples with no net resultant, and bimoments (moment dipoles) . Comparisons with known analytical solutionsfor homogenous media demonstrate the accuracy of the formulation. However, the main field ofapplication is laminated media, for which no analytical solutions can be obtained. On the otherhand, it should be noted that the computational effort in this method does not depend on whetherthe system is layered. The resulting Greens functions could be used to efficiently model elasticwaves in complex media by means of the Boundary Integral Method.     

Approximate dynamic boundary conditions for a thin piezoelectric layer

Approximate dynamic boundary conditions of different orders are derived for the case of a thin piezoelectric coating layer bonded to an elastic material. The approximate boundary conditions are derived using series expansions of the elastic displacements and the electric potential in the thickness coordinate of the layer. All the expansion functions are then eliminated with the aid of the equations of motion and boundary/interface conditions of the layer. This results in boundary conditions on the elastic material that may be truncated to different orders in the thickness of the layer to obtain approximate boundary conditions. The approximate boundary conditions may be used as a replacement for the piezoelectric layer and thus simplify the analysis significantly. Numerical examples show that the approximate boundary conditions give good results for low frequencies and/or thin piezoelectric layers.