Holdings: Wave propagation in viscoelastic and poroelastic continua

Wave propagation in viscoelastic and poroelastic continua: a boundary element approach

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Bibliographic Details
Main Author:	Schanz, Martin (Author)
Format:	Book
Language:	English
Published:	Berlin ; Heidelberg ; New York ; Barcelona ; Hongkong ; London ; Springer 2001
Series:	Lecture notes in applied mechanics 2
Subjects:	Boundary element methods Viscoelasticity Wave-motion, Theory of Poröser Stoff Viskoelastisches Medium Randelemente-Methode Wellenausbreitung Elastische Welle Hochschulschrift
Online Access:	Inhaltsverzeichnis
Item Description:	Zugl.: Braunschweig, Techn. Univ., Habil.-Schr., 2001
Physical Description:	X, 170 S. Ill., graph. Darst.
ISBN:	3540416323

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adam_text	CONTENTS 1. INTRODUCTION * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 1 2. CONVOLUTION QUADRATURE METHOD * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 7 2.1 BASIC THEORY OF THE CONVOLUTION QUADRATURE METHOD . . . . . . . . . . . . . . 7 2.2 NUMERICAL TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.1 SERIES EXPANSION OF THE TEST FUNCTIONS F 1 AND F 2 . . . . . . . . . . . 12 2.2.2 COMPUTING THE INTEGRATION WEIGHTS * N . . . . . . . . . . . . . . . . . . . 14 2.2.3 NUMERICAL CONVOLUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3. VISCOELASTICALLY SUPPORTED EULER-BERNOULLI BEAM * * * * * * * * * * * * * * * * * 23 3.1 INTEGRAL EQUATION FOR A BEAM RESTING ON VISCOELASTIC FOUNDATION . . . . 23 3.1.1 FUNDAMENTAL SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1.2 INTEGRAL EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 NUMERICAL EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.1 FIXED-SIMPLY SUPPORTED BEAM . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2.2 FIXED-FREE VISCOELASTIC SUPPORTED BEAM . . . . . . . . . . . . . . . . . . 37 4. TIME DOMAIN BOUNDARY ELEMENT FORMULATION * * * * * * * * * * * * * * * * * * * * 39 4.1 INTEGRAL EQUATION FOR ELASTODYNAMICS. . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.2 BOUNDARY ELEMENT FORMULATION FOR ELASTODYNAMICS . . . . . . . . . . . . . . . 44 4.3 VALIDATION OF PROPOSED METHOD: WAVE PROPAGATION IN A ROD . . . . . . . . 46 4.3.1 INFLUENCE OF THE SPATIAL AND TIME DISCRETIZATION . . . . . . . . . . . . 47 4.3.2 COMPARISON WITH THE CLASSICAL TIME DOMAIN BE FORMULATION 53 5. VISCOELASTODYNAMIC BOUNDARY ELEMENT FORMULATION * * * * * * * * * * * * * * * 57 5.1 VISCOELASTIC CONSTITUTIVE EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.2 BOUNDARY INTEGRAL EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.3 BOUNDARY ELEMENT FORMULATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.4 VALIDATION OF THE METHOD AND PARAMETER STUDY . . . . . . . . . . . . . . . . . . . 66 5.4.1 THREE-DIMENSIONAL ROD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.4.2 ELASTIC FOUNDATION ON VISCOELASTIC HALF SPACE . . . . . . . . . . . . . 71 X CONTENTS 6. POROELASTODYNAMIC BOUNDARY ELEMENT FORMULATION * * * * * * * * * * * * * * * 77 6.1 BIOTS THEORY OF POROELASTICITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.1.1 ELASTIC SKELETON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.1.2 VISCOELASTIC SKELETON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6.2 FUNDAMENTAL SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.3 POROELASTIC BOUNDARY INTEGRAL FORMULATION . . . . . . . . . . . . . . . . . . . . . 86 6.3.1 BOUNDARY INTEGRAL EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.3.2 BOUNDARY ELEMENT FORMULATION . . . . . . . . . . . . . . . . . . . . . . . . . 91 6.4 NUMERICAL STUDIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.4.1 INFLUENCE OF TIME STEP SIZE AND MESH SIZE . . . . . . . . . . . . . . . . 93 6.4.2 POROELASTIC HALF SPACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 7. WAVE PROPAGATION * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 105 7.1 WAVE PROPAGATION IN POROELASTIC ONE-DIMENSIONAL COLUMN . . . . . . . . . 105 7.1.1 ANALYTICAL SOLUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7.1.2 POROELASTIC RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.1.3 POROVISCOELASTIC RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 7.2 WAVES IN HALF SPACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.2.1 RAYLEIGH SURFACE WAVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7.2.2 SLOW COMPRESSIONAL WAVE IN POROELASTIC HALF SPACE . . . . . . . . 131 8. CONCLUSIONS * APPLICATIONS * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 135 8.1 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 8.2 OUTLOOK ON FURTHER APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 A. MATHEMATIC PRELIMINARIES * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 143 A.1 DISTRIBUTIONS OR GENERALIZED FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 143 A.2 CONVOLUTION INTEGRALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 A.3 LAPLACE TRANSFORM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 A.4 LINEAR MULTISTEP METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 B. BEM DETAILS * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 151 B.1 FUNDAMENTAL SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 B.1.1 VISCO- AND ELASTODYNAMIC FUNDAMENTAL SOLUTIONS . . . . . . . . . . 151 B.1.2 POROELASTODYNAMIC FUNDAMENTAL SOLUTIONS. . . . . . . . . . . . . . . . 152 B.2 CLASSICAL TIME DOMAIN BE FORMULATION . . . . . . . . . . . . . . . . . . . . . . . 154 NOTATION INDEX * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 157 REFERENCES * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 159 INDEX * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 169
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spelling	Schanz, Martin Verfasser aut Wave propagation in viscoelastic and poroelastic continua a boundary element approach Martin Schanz Berlin ; Heidelberg ; New York ; Barcelona ; Hongkong ; London ; Springer 2001 X, 170 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in applied mechanics 2 Zugl.: Braunschweig, Techn. Univ., Habil.-Schr., 2001 Boundary element methods Viscoelasticity Wave-motion, Theory of Poröser Stoff (DE-588)4046811-2 gnd rswk-swf Viskoelastisches Medium (DE-588)4426217-6 gnd rswk-swf Randelemente-Methode (DE-588)4076508-8 gnd rswk-swf Wellenausbreitung (DE-588)4121912-0 gnd rswk-swf Elastische Welle (DE-588)4151684-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Viskoelastisches Medium (DE-588)4426217-6 s Elastische Welle (DE-588)4151684-9 s Wellenausbreitung (DE-588)4121912-0 s Randelemente-Methode (DE-588)4076508-8 s DE-604 Poröser Stoff (DE-588)4046811-2 s Lecture notes in applied mechanics 2 (DE-604)BV013785088 2 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009303819&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Schanz, Martin Wave propagation in viscoelastic and poroelastic continua a boundary element approach Lecture notes in applied mechanics Boundary element methods Viscoelasticity Wave-motion, Theory of Poröser Stoff (DE-588)4046811-2 gnd Viskoelastisches Medium (DE-588)4426217-6 gnd Randelemente-Methode (DE-588)4076508-8 gnd Wellenausbreitung (DE-588)4121912-0 gnd Elastische Welle (DE-588)4151684-9 gnd
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title	Wave propagation in viscoelastic and poroelastic continua a boundary element approach
title_auth	Wave propagation in viscoelastic and poroelastic continua a boundary element approach
title_exact_search	Wave propagation in viscoelastic and poroelastic continua a boundary element approach
title_full	Wave propagation in viscoelastic and poroelastic continua a boundary element approach Martin Schanz
title_fullStr	Wave propagation in viscoelastic and poroelastic continua a boundary element approach Martin Schanz
title_full_unstemmed	Wave propagation in viscoelastic and poroelastic continua a boundary element approach Martin Schanz
title_short	Wave propagation in viscoelastic and poroelastic continua
title_sort	wave propagation in viscoelastic and poroelastic continua a boundary element approach
title_sub	a boundary element approach
topic	Boundary element methods Viscoelasticity Wave-motion, Theory of Poröser Stoff (DE-588)4046811-2 gnd Viskoelastisches Medium (DE-588)4426217-6 gnd Randelemente-Methode (DE-588)4076508-8 gnd Wellenausbreitung (DE-588)4121912-0 gnd Elastische Welle (DE-588)4151684-9 gnd
topic_facet	Boundary element methods Viscoelasticity Wave-motion, Theory of Poröser Stoff Viskoelastisches Medium Randelemente-Methode Wellenausbreitung Elastische Welle Hochschulschrift
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009303819&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV013785088
work_keys_str_mv	AT schanzmartin wavepropagationinviscoelasticandporoelasticcontinuaaboundaryelementapproach

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