The Eigenfrequency Spectra of the Interior Problems

Gavin R. Thomson () and Christian Constanda ()
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Gavin R. Thomson: A.C.C.A.
Christian Constanda: The University of Tulsa, Department of Mathematical and Computer Sciences

Chapter Chapter 5 in Stationary Oscillations of Elastic Plates, 2011, pp 61-74 from Springer

Abstract: Abstract As we saw in the previous chapter, each of the exterior boundary value problems has at most one regular solution. Unfortunately, this is not true for (Dω+) and (Nω+). We prove that (D0 ω+) and (N0 ω+) have nonzero solutions by establishing their equivalence to certain integral equations that are known to have such solutions. To do so, we construct the kernels of these integral equations—the so-called Green’s tensors. Throughout the chapter we exploit the close connection between system (4.1) and the corresponding homogeneous system governing the equilibrium bending of plates.

Keywords: Integral Equation; Regular Solution; Boundary Integral Equation; Representation Formula; Homogeneous Problem (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8241-5_5

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DOI: 10.1007/978-0-8176-8241-5_5

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