Propagation of surface (seismic) waves: Ordinary differential equations with strongly nonlinear damping

Andriotaki, PN

dc.contributor.author	Andriotaki, PN	en
dc.date.accessioned	2014-03-01T01:22:59Z
dc.date.available	2014-03-01T01:22:59Z
dc.date.issued	2005	en
dc.identifier.issn	0167-8442	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16751
dc.subject	Exact solutions	en
dc.subject	Nonlinear ordinary differential equations	en
dc.subject	Nonlinear surface seismic waves	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Crack propagation	en
dc.subject.other	Damping	en
dc.subject.other	Differential equations	en
dc.subject.other	Seismic waves	en
dc.subject.other	Surface waves	en
dc.subject.other	Nonlinear mechanics	en
dc.subject.other	Nonlinear seismic waves (NLSW)	en
dc.subject.other	Ordinary differential equations (ODE)	en
dc.subject.other	Wave motions	en
dc.subject.other	Wave propagation	en
dc.subject.other	seismic wave	en
dc.subject.other	wave propagation	en
dc.title	Propagation of surface (seismic) waves: Ordinary differential equations with strongly nonlinear damping	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.tafmec.2005.03.002	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.tafmec.2005.03.002	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	Second-order ordinary differential equations (ODEs) with strongly nonlinear damping (cubic nonlinearities) govern surface wave motions that entail nonlinear surface seismic motions. They apply to dynamic crack propagation and nonlinear oscillation problems in physics and nonlinear mechanics. It is shown that the nonlinear surface seismic wave equation (Rayleigh equation) admits several functional transformations and it is possible to reduce it to an equivalent first-order Abel ODE of the second kind in normal form. Based on a recently developed methodology concerning the construction of exact analytic solutions for the type of Abel equations under consideration, exact solutions are obtained for the nonlinear seismic wave (NLSW) equation for initial conditions of the physical problem. The method employed is general and can be applied to a large class of relevant ODEs in mathematical physics and nonlinear mechanics. (c) 2005 Elsevier Ltd. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Theoretical and Applied Fracture Mechanics	en
dc.identifier.doi	10.1016/j.tafmec.2005.03.002	en
dc.identifier.isi	ISI:000230742900002	en
dc.identifier.volume	43	en
dc.identifier.issue	3	en
dc.identifier.spage	308	en
dc.identifier.epage	323	en