The far-field equations in linear elasticity - An inversion scheme

Gintides, D; Kiriaki, K

dc.contributor.author	Gintides, D	en
dc.contributor.author	Kiriaki, K	en
dc.date.accessioned	2014-03-01T01:17:15Z
dc.date.available	2014-03-01T01:17:15Z
dc.date.issued	2001	en
dc.identifier.issn	0044-2267	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14415
dc.subject	Linear Elasticity	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mechanics	en
dc.subject.other	RESONANCE REGION	en
dc.subject.other	SCATTERING	en
dc.subject.other	WAVES	en
dc.title	The far-field equations in linear elasticity - An inversion scheme	en
heal.type	journalArticle	en
heal.identifier.primary	10.1002/1521-4001(200105)81:5<305::AID-ZAMM305>3.0.CO;2-T	en
heal.identifier.secondary	http://dx.doi.org/10.1002/1521-4001(200105)81:5<305::AID-ZAMM305>3.0.CO;2-T	en
heal.language	English	en
heal.publicationDate	2001	en
heal.abstract	In this paper the far-field equations in linear elasticity for the rigid body and the cavity are considered. The direct scattering problem is formulated as a dyadic one. This imbedding of the vector problem for the displacement field into a dyadic field is enforced by the dyadic nature of the free space Green's function. Assuming that the incident field is produced by a superposition of plane dyadic incident waves it is proved that the scattered field is also expressed as the superposition of the corresponding scattered fields. A pair of integral equations of the first kind which hold independently of the boundary conditions are constructed in the far-field region. The properties of the Herglotz functions are used to derive solvability conditions and to build approximate far-field equations. Having this theoretical framework, approximate far-field equations are derived for a specific incidence which generates as far-field patterns simple known functions. An inversion scheme is proposed based on the unboundedness for the solutions of these approximate ""far-field equations"" and the support of the body is found by noting that the solutions of the integral equations are not bounded as the point of the location of the fundamental solution approaches the boundary of the scatterer from interioir points. It is also pointed that it is sufficient to recover the support of the body if only one approximate ""far-field equation"" is used. The case of the rigid sphere is considered to illuminate the unboundedness property on the boundary.	en
heal.publisher	WILEY-V C H VERLAG GMBH	en
heal.journalName	ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik	en
dc.identifier.doi	10.1002/1521-4001(200105)81:5<305::AID-ZAMM305>3.0.CO;2-T	en
dc.identifier.isi	ISI:000168641700002	en
dc.identifier.volume	81	en
dc.identifier.issue	5	en
dc.identifier.spage	305	en
dc.identifier.epage	316	en