000			03844nam a22004935i 4500
001			978-0-8176-8241-5
003			DE-He213
005			20140220083711.0
007			cr nn 008mamaa
008			110627s2011 xxu| s |||| 0|eng d
020			_a9780817682415 _9978-0-8176-8241-5
024	7		_a10.1007/978-0-8176-8241-5 _2doi
050		4	_aQA431
072		7	_aPBKL _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.45 _223
100	1		_aThomson, Gavin R. _eauthor.
245	1	0	_aStationary Oscillations of Elastic Plates _h[electronic resource] : _bA Boundary Integral Equation Analysis / _cby Gavin R. Thomson, Christian Constanda.
264		1	_aBoston : _bBirkhäuser Boston, _c2011.
300			_aXIII, 230p. 4 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPreface -- The Mathematical Models -- Layer Potentials -- The Nonhomogenous System -- The Question of Uniqueness for the Exterior Problems -- The Eigenfrequency Spectra of the Interior Problems -- The Question of Solvability -- The Direct Boundary Equation Formulation -- Modified Fundamental Solutions -- Problems with Robin Boundary Conditions -- The Transmission Problem -- The Null Field Equations -- Appendices -- References -- Index.
520			_aElliptic partial differential equations are important for approaching many problems in mathematical physics, and boundary integral methods play a significant role in their solution. This monograph investigates the latter as they arise in the theory characterizing stationary vibrations of thin elastic plates. The techniques used reduce the complexity of classical three-dimensional elasticity to a system of two independent variables, using eigenfrequencies to model problems with flexural-vibrational elastic body deformation and simplifying these problems to manageable, uniquely solvable integral equations. In under 250 pages, Stationary Oscillations of Elastic Plates develops an impressive amount of theoretical machinery. After introducing the equations describing the vibrations of elastic plates in the first chapter, the book proceeds to explore topics including the single-layer and double-layer plate potentials; the Newtonian potential; the exterior boundary value problems; the direct boundary integral equation method; the Robin boundary value problems; the boundary-contact problem; the null field equations. Throughout, ample time is allotted to laying the groundwork necessary for establishing the existence and uniqueness of solutions to the problems discussed. The book is meant for readers with a knowledge of advanced calculus and some familiarity with functional analysis. It is a useful tool for professionals in pure and applied mathematicians, as well as for theoretical physicists and mechanical engineers with practices involving elastic plates. Graduate students in these fields would also benefit from the monograph as a supplementary text for courses relating to theories of elasticity or flexural vibrations.
650		0	_aMathematics.
650		0	_aIntegral equations.
650		0	_aDifferential equations, partial.
650		0	_aMathematical physics.
650		0	_aVibration.
650	1	4	_aMathematics.
650	2	4	_aIntegral Equations.
650	2	4	_aVibration, Dynamical Systems, Control.
650	2	4	_aMathematical Methods in Physics.
650	2	4	_aPartial Differential Equations.
700	1		_aConstanda, Christian. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817682408
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-8241-5
912			_aZDB-2-SMA
999			_c105100 _d105100