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Numerical simulations on resonance poles - The trapping case of two plane cracks

By Carlos Alves Centro and Carlos J. S. Alves


In this paper a proof for the existence of acoustic resonance poles with Robin boundary conditions is presented. The analysis of the elastic crack scattering problem allows us to distinguish two types of resonance poles -- normal or tangential, and we present some numerical results based on a variational boundary element method. Considering two plane cracks, we present some estimates to justify the difference between simulation results when the cracks lay on the same plane or on different ones, including a trapping case. Keywords: resonance poles; elastic waves; acoustic waves; crack shapes AMS classification: 73D25 1 Introduction It is well known that an acoustic plane wave u inc (x) = e ikd:x with real frequency k ? 0 scattered by an object produces a scattered wave u sc which has the asymptotic behavior u sc (x) = e ikjxj jxj ` u1 (x) + O( 1 jxj ) ' ; when jxj !1: where x = x=jxj; and u1 is an analytical function defined on the sphere S 2 , called the far fie..

Topics: resonance poles, elastic waves, acoustic waves, crack shapes
Year: 2007
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