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Title:	Nonlinear dynamics of continuous elastic systems
From:	Jan Awrejcewicz ; Vadim A. Krys'ko ; A. F. Vakakis
Person:	Awrejcewicz, Jan 1952- Verfasser aut Krysʹko, Vadim A. Vakakis, Alexander F. 1937-
Main Authors:	Awrejcewicz, Jan 1952- (Author), Krysʹko, Vadim A. 1937- (Author), Vakakis, Alexander F. (Author)
Format:	Book
Language:	English
Published:	Berlin u.a. Springer 2004
Subjects:	Dynamics Elastic plates and shells Nonlinear theories Nichtlineare Dynamik Elastische Platte Elastische Schale
Online Access:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010615491&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XI, 341 S. Ill., graph. Darst.
ISBN:	3540205152

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Record in the Search Index

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adam_text	J. AWREJCEWICZ * V. KRYS KO * A.F. VAKAKIS NONLINEAR DYNAMICS OF CONTINUOUS ELASTIC SYSTEMS WITH 125 FIGURES AND 27 TABLES SPRINGER TABLE OF CONTENTS PREFACE V TABLE OF CONTENTS IX 1 VIBRATION OF PLATES AND SHELLS WITH ADDED MASSES 1 1.1 INTRODUCTION 1 1.2 3D-THEORY OF ORTHOTROPIC SHALLOW SHELLS WITH ADDED MASSES 4 1.2.1 CURVILINEAR ORTHOGONAL COORDINATES 4 1.2.2 FUNDAMENTAL RELATIONS AND HYPOTHESES 9 1.2.3 VARIATIONAL EQUATIONS 10 1.2.4 DIFFERENTIAL EQUATIONS, BOUNDARY AND INITIAL CONDITIONS 20 1.3 ANALYSIS OF ORTHOTROPIC SHALLOW SHELLS WITH ADDED MASSES... 23 1.3.1 TWO DIMENSIONAL THEORY 23 1.3.2 SIMPLIFIED MODEL 29 1.3.3 ADDED MASSES STIFFNESS 33 1.3.4 DETERMINATION OF DYNAMICAL CHARACTERISTICS 38 1.3.5 ALGORITHMS AND NUMERICAL RESULTS 51 1.4 DYNAMICAL CHARACTERISTICS OF PLATES WITH ADDED MASSES 56 1.4.1 TIMOSHENKO S KINEMATIC MODEL 56 1.4.2 SPATIAL THEORY OF ELASTICITY 59 1.4.3 THREE DIMENSIONAL PROBLEM 65 1.4.4 ALGORITHMS 69 1.4.5 FREQUENCY SPECTRA COMPARISON OF THREE DIMENSIONAL AND APPROXIMATE THEORIES 73 1.4.6 INFLUENCE OF THE ADDED MASSES - NUMERICAL INVESTIGATION 82 1.4.7 FUNDAMENTAL CONCLUSIONS 91 2 RATIONAL DESIGN OF PLATES AND SHELLS 9 3 2.1 INTRODUCTION 93 2.2 ORTHOTROPIC PLATES AND SHELLS WITH VARIABLE THICKNESS AND LOW STIFFNESS 94 2.2.1 FREQUENCY SPECTRA PROPERTIES OF ORTHOTROPIC SHELLS WITH VARIABLE THICKNESS 94 2.2.2 FINITE DIMENSIONAL APPROXIMATION OF FREE VIBRATIONS OF THE TIMOSHENKO LIKE SHELL 101 X TABLE OF CONTENTS 2.2.3 ALGORITHMS FOR THE MB AND MVI METHODS 107 2.2.4 ANALYSIS OF FREE VIBRATIONS OF TRANSVERSAL-ISOTROPIC PLATES 122 2.3 RATIONAL DESIGN OF PLATES WITH FINITE TRANSVERSAL STIFFNESS ... 125 2.3.1 PLATES AND SHELLS MASS OPTIMIZATION WITH FREE VIBRATION FREQUENCIES CONSTRAINTS 126 2.3.2 FINITE DIMENSIONAL APPROXIMATIONS OF THE RATIONAL DESIGN OF PLATES AND SHELLS 129 2.3.3 TIMOSHENKO-LIKE RECTANGULAR PLATES WITH STIFF AND ROLLING SUPPORTS 134 2.4 OPTIMIZATION OF PLATES AND SHELLS SURFACES WITH CONSTRAINTS . 144 2.4.1 SHELLS OPTIMIZATION - FORMULATION OF THE PROBLEM .... 144 2.4.2 ALGORITHM FOR OPTIMAL SURFACE SEARCH 147 2.4.3 DESIGN OF PLATES AND SHELLS WITH CONSTANT THICKNESS AND ROLLING SUPPORTS 151 2.5 VIBROISOLATION OF A CONSTRUCTION WITH SHELLS ELEMENTS 159 2.5.1 NONLINEAR FORCED VIBRATIONS OF THE TIMOSHENKO LIKE SHELLS 160 2.5.2 OPTIMAL VIBROISOLATION-FORMULATION OF THE PROBLEM AND VIBROISOLATION HARMONIE EXCITATION 170 2.5.3 ALGORITHM OF THE OPTIMAL VIBROISOLATION OF TIMOSHENKO-LIKE SHELLS 175 2.6 GENERALISATIONS 175 3 ORDER REDUCTION BY PROPER ORTHOGONAL DECOMPOSITION (POD) ANALYSIS 177 3.1 THE POD METHOD 177 3.1.1 INTRODUCTION 177 3.1.2 THEORETICAL BASIS 179 3.2 APPLICATION OF POD TO VIBRO-IMPACT CONTINUOUS OSCILLATORS . 183 3.2.1 VIBRO-IMPACTING BEAM 183 3.2.2 OVERHUNG ROTOR 191 3.3 COHERENT SPATIAL STRUCTURES IN EXTENDED SYSTEMS 200 3.3.1 COMPUTATION OF THE TRANSIENT DYNAMICS 201 3.3.2 POD ANALYSIS OF THE TRUSS DYNAMICS 210 3.3.3 POD BASED REDUCED-ORDER MODELS 213 3.3.4 EXPERIMENTAL RESULTS 222 3.4 POD STUDY OF THE INTERACTION OF SLOW AND FAST DYNAMICS ... 228 3.4.1 FORMULATION OF THE PROBLEM 228 3.4.2 REGULAER MOTIONS 231 3.4.3 CHAOTIC MOTIONS 233 TABLE OF CONTENTS XI 4 ANALYTIC MODELLING OF DISCRETENESS EFFECTS IN CONTINUOUS SYSTEMS 239 4.1 THE METHOD OF NON-SMOOTH TRANSFORMATIONS 239 4.2 ELASTIC CONTINUUM ON DISCRETE ELASTIC NONLINEAR FOUNDATION . 245 4.2.1 ASYMPTOTIC ANALYSIS 245 4.3 STATIC BUECKLING OF A CIRCULAR RING COMPRESSIVE LOADS 256 5 CONTINUOUS SYSTEMS WITH NON-SMOOTH NONLINEARITIES ..... 269 5.1 TRANSIENT LOCALIZATION DUE TO BACKLASH NONLINEARITIES 269 5.1.1 TRANSIENT LOCALIZATION AND BEAT PHENOMENA DUE TO CLEARANCE 270 5.1.2 ORDER REDUCTION AND RESPONSE RECONSTRUCTION 274 5.1.3 NONLINEAR ANALYSIS 279 5.1.4 ADDITIONAL EXAMPLES 282 5.2 NONLINEAR LOCALIZATION IN SYSTEMS OF VIBRO-IMPACTING BEAMS 286 5.2.1 NUMERICAL RESULTS - NONLINEAR LOCALIZATION DUE TO VIBRO-IMPACTS 290 5.2.2 EXPERIMENTAL RESULTS - NONLINEAR LOCALIZATION DUE TO VIBRO-IMPACTS 298 5.3 VIBRO-IMPACT MOTIONS OF A ROTARY SYSTEM 303 REFERENCES 315 INDEX 329
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spellingShingle	Awrejcewicz, Jan 1952- Krysʹko, Vadim A. 1937- Vakakis, Alexander F. Nonlinear dynamics of continuous elastic systems Dynamics Elastic plates and shells Nonlinear theories Nichtlineare Dynamik (DE-588)4126141-0 gnd Elastische Platte (DE-588)4151682-5 gnd Elastische Schale (DE-588)4151689-8 gnd
subject_GND	(DE-588)4126141-0 (DE-588)4151682-5 (DE-588)4151689-8
title	Nonlinear dynamics of continuous elastic systems
title_auth	Nonlinear dynamics of continuous elastic systems
title_exact_search	Nonlinear dynamics of continuous elastic systems
title_full	Nonlinear dynamics of continuous elastic systems Jan Awrejcewicz ; Vadim A. Krys'ko ; A. F. Vakakis
title_fullStr	Nonlinear dynamics of continuous elastic systems Jan Awrejcewicz ; Vadim A. Krys'ko ; A. F. Vakakis
title_full_unstemmed	Nonlinear dynamics of continuous elastic systems Jan Awrejcewicz ; Vadim A. Krys'ko ; A. F. Vakakis
title_short	Nonlinear dynamics of continuous elastic systems
title_sort	nonlinear dynamics of continuous elastic systems
topic	Dynamics Elastic plates and shells Nonlinear theories Nichtlineare Dynamik (DE-588)4126141-0 gnd Elastische Platte (DE-588)4151682-5 gnd Elastische Schale (DE-588)4151689-8 gnd
topic_facet	Dynamics Elastic plates and shells Nonlinear theories Nichtlineare Dynamik Elastische Platte Elastische Schale
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010615491&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT awrejcewiczjan nonlineardynamicsofcontinuouselasticsystems AT krysʹkovadima nonlineardynamicsofcontinuouselasticsystems AT vakakisalexanderf nonlineardynamicsofcontinuouselasticsystems

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