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2 Computer Assisted Mechanics and Engineering Sciences

2 2004

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Modal analysis of wave mototion in inhomogeneous waveguides which are modelled by FEM

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Špacapan I. , Premrov M.

Computer Assisted Mechanics and Engineering Sciences

2004

tom Vol. 11, No. 2-3

137-144

This paper presents a simple computing procedure for the analysis of the wave motion in infinite layered waveguides via the analysis of the propagating wave modes. Waveguides may have irregular inclusions, which yields complicated reflections of waves, and an analytical solution is practically not feasible. The section of the waveguide, where we want to analyze the displacements and stress waves, is modelled by finite elements using standard programs for FEM. The external problem is solved as an internal one, while the radiation conditions are satisfied exactly. The procedure only some simple mathematical manipulations and is performed in the frequency domain. It yields exact results and a clear insight into the propagating wave modes. The results of the first presented numerical example are compared to the exact ones, while in the second example the foundation represents an irregularity in the waveguide composed of two layers.

Solving wave problems in infinite domain by using variable local DtN operators

100%

Premrov M. , Špacapan I.

Computer Assisted Mechanics and Engineering Sciences

2004

tom Vol. 11, No. 2-3

145-153

This paper presents an iterative method for solving two-dimensional wave problems in infinite domains. The method yields a solution that satisfies Sommerfeld's radiation condition, as required for the correct solution of infinite domains excited only locally. This problem occurs in the solution of the wave equation in infinite domains when using an asymptotic local DtN (Dirichlet-to-Neumann) map in computational procedures applied to a finite domain. We are demonstrating that the amplitudes of the reflected fictive harmonics depend upon the wave number, the location of the fictive boundary, as well as on the DtN operator used in the computations. A constant value of the operator cannot sufficiently eliminate the amplitudes of all reflected waves, while the results are poor especially for higher harmonics. Thus, we are proposing an iterative method, which varies the tangential dependence of the operator in each computational step.