Expression of contour vibration modes of a square plate by scalar and vector velocity potentials.

2007

Acoust. Sci. & Tech.

Self Cite

The finite-difference time-domain (FDTD) numerical method has the unique characteristic that it can separately calculate the far-field scattered waves and near-field total waves at the same time, where total waves refer to a mixture of incident plane waves and scattered waves. This formulation is called the total-field/scattered-field (TF/SF) formulation and is very effective for the analysis of scattering problems in nondestructive evaluation (NDE). In this report, a TF/SF formulation of the elastic wave fields in solids is described. Specifically, scalar and vector potentials are used for the formulation. Using these potentials is beneficial for two reasons. First, the longitudinal waves and shear waves are initially separated. Therefore, the scattering phenomenon can be clearly recognized. Second, it is facile to use the potentials for setting the absorbing boundaries. The FDTD TF/SF formulation using potentials has been proved effective in the analysis of the scattering of a longitudinal plane wave incident to a square hole.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of the finite-difference time-domain method and total-field/scattered field formulation to scattering phenomena in solids

2007

Acoust. Sci. & Tech.

Self Cite

“…5,6) The author and his colleagues also have previously considered the application of the FDTD method to the analysis of time-domain problems of elastic wave fields in solids and piezoelectric materials. [7][8][9][10][11][12][13][14][15] If a solid is assumed to be elastically isotropic, longitudinal and shear waves propagate individually without interaction or mode conversion in a homogeneous region and can be analyzed independently using derived scalar and vector potentials. Generally, velocity potentials are derived from the particle velocity components already calculated.…”

Section: Introductionmentioning

confidence: 99%

Finite-Difference Time-Domain Numerical Analysis of Elastic Wave Fields Using both Elastic and Velocity Potential Variables

2006

jjap

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The use of both elastic variables and velocity potentials is proposed for the analysis of elastic wave fields in isotropic solids by finite-difference time-domain (FDTD) methods. The term 'elastic variables' refers to stresses and particle velocities. Velocity potentials can be directly derived using the same leap-frog finite-difference scheme as in the FDTD method. In some situations, for example, where an absorbing boundary is present, it is more straightforward to calculate using velocity potentials. This approach also provides an easy way to handle of complex elastic wave phenomena. On the other hand, many other types of boundary conditions are often expressed in terms of elastic variables. In these situations, it is more convenient to use elastic variables for calculation. Some examples are introduced here to illustrate the efficiency of the proposed technique. First, the method was used for the case of an absorbing boundary. In the model, almost all analysis was carried out using values of stress and particle velocity, but velocity potentials were applied near the absorbing boundary on the truncated interface. Second, an interface between elastic variables and velocity potentials, namely a stress-velocity/potentials interface, was constructed around a scattering object. External to the interface, stresses and particle velocities were used for calculation, and potential variables were applied inside the interface. In a third example, calculations were made over almost the entire analytical region using potential values, but in the neighborhood of the free boundary, elastic variables were used. All the examples above were analyzed numerically using the FDTD method, and the results confirmed the usefulness of the method.

“…Sato and coworkers have previously investigated the application of the FDTD numerical method to the analysis of time domain problems of elastic wave fields [1][2][3][4][5][6]. However, only isotropic solids are considered in their studies.…”

Section: Introductionmentioning

confidence: 99%

Implementation of initial and boundary conditions in the finite-difference time-domain numerical solution of elastic wave fields in anisotropic solids

2006

Acoust. Sci. & Tech.

Self Cite

Methods of treating initial and boundary conditions when applying the finite difference time domain (FDTD) numerical method to the analysis of elastic wave fields in anisotropic solids have been considered with reference to an electrical circuit analogy. It was found that the staggered lattice of the FDTD analysis of anisotropic solids is expressed by the superposition of two electric circuit networks of identical configurations. One of these circuits is translated relative to the other by one grid length in both the y and z directions, and is then superposed onto the other circuit to yield the final overall circuit. The two circuits are connected by the mutual capacitance between the capacitances loaded at the normal stress nodes of one of the circuits, and the shear stress nodes of the other circuit, which are positioned on the same stress nodes. From the configurations of the circuits, it can be concluded that the initial and boundary conditions should be applied to both the circuit networks. The theory was confirmed by considering two model problems.