Advanced mechanical vibrations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Alpha Science International
2006
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 468 S. Ill., graph. Darst. |
| ISBN: | 9781842652220 1842652222 |
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Datensatz im Suchindex
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| adam_text | ADVANCED MECHANICAL VIBRATIONS RAO V. DUKKIPATI ALPHA SCIENCE
INTERNATIONAL LTD. OXFORD, U.K. CONTENTS PREFACE T VII ACKNOWLEDGEMENTS
XI 1. INTRODUCTION 1 1.1 INTRODUCTION 1 1.2 CLASSIFICATION OF DYNAMIC
SYSTEM MODELS 1 1.3 CONSTRAINTS, GENERALIZED COORDINATES, AND DEGREES OF
FREEDOM 2 1.4 CLASSIFICATION OF VIBRATIONS 7 1.4.1 FREE AND FORCED
VIBRATIONS 8 1.4.2 LINEAR AND NON-LINEAR VIBRATIONS 8 1.4.3
DETERMINISTIC AND RANDOM VIBRATIONS 8 1.5 ELEMENTARY PARTS OF VIBRATING
SYSTEMS 9 1.5.1 EXAMPLES OF VIBRATING MOTION IO 1.5.2 SIMPLE HARMONIC
MOTION 10 1.5.3 PERIODIC MOTION 16 1.6 DISCRETE AND CONTINUOUS SYSTEMS
20 1.7 VIBRATION ANALYSIS 27 1.8 ELEMENTS OF VIBRATING SYSTEMS 24 1.8.1
SPRING ELEMENTS 25 1.8.2 POTENTIAL ENERGY OF LINEAR SPRINGS 29 1.8.3
EQUIVALENT SPRINGS 30 1.8.4 MASS OR INERTIA ELEMENTS 33 1.8.5 DAMPING
ELEMENTS 54 1.9 SUMMARY 38 PROBLEMS 39 I 2. TWO DEGREE OF FREEDOM
SYSTEMS 46 2.1 INTRODUCTION 46 2.2 EQUATIONS OF MOTION FOR A
TWO-DEGREE-OF FREEDOM SYSTEM 48 2.3 FREE VIBRATION OF UNDAMPED SYSTEMS
50 2.4 TORSIONAL SYSTEM 57 2.5 COORDINATE COUPLING AND
PRINCIPAL-COORDINATES 59 2.6 DAMPED FREE VIBRATIONS 64 2.7 FORCED
VIBRATION OF UNDAMPED SYSTEMS 67 2.8 FORCED VIBRATION WITH DAMPING 71
2.9 ORTHOGONALITY PRINCIPLE 74 2.10 SUMMARY 76 PROBLEMS 76 XIV CONTENTS
3. MULTI-DEGREE-OF-FREEDOM SYSTEMS 88 3.1 INTRODUCTION 88 3.2 EQUATIONS
OF MOTION 89 3.3 STIFFNESS INFLUENCE COEFFICIENTS 93 3.4 FLEXIBILITY
INFLUENCE COEFFICIENTS 95 3.5 MATRIX FORMULATION 96 3.6 INERTIA
INFLUENCE COEFFICIENTS 97 3.7 FREE VIBRATIONS OF MULTI-DEGREE-OF-FREEDOM
SYSTEMS 98 3.7.1 NORMAL MODE SOLUTION 98 3.7.2 NATURAL FREQUENCIES AND
MODE SHAPES 99 3.7.3 MODE SHAPE ORTHOGONALITY 104 3.8 FREE VIBRATIONS OF
UNDAMPED SYSTEMS 111 3.9 FREE VIBRATIONS OF DAMPED SYSTEMS 116 3.9.1
PROPORTIONAL DAMPING 116 3.9.2 GENERAL VISCOUS DAMPING 119 3.10 FORCED
VIBRATIONS OF MULTI-DEGREE OF FREEDOM SYSTEMS 720 3.10.1 HARMONIC
EXCITATIONS 727 3.10.2 LAPLACE TRANSFORM METHOD 124 3.11 MODAL ANALYSIS
FOR UNDAMPED SYSTEMS AND SYSTEMS WITH PROPORTIONAL DAMPING 727 3.11.1
SYSTEMS WITH PROPORTIONAL DAMPING 729 3.11.2 GENERAL DAMPING 732 3.12
NUMERICAL SOLUTIONS 136 3.13 SUMMARY 737 PROBLEMS 737 4. ANALYTICAL
DYNAMICS 146 4.1 INTRODUCTION 146 4.2 DEGREES OF FREEDOM 146 4.3
GENERALIZED COORDINATES 148 4.4 CONSTRAINTS 149 4.5 PRINCIPLE OF VIRTUAL
WORK 757 4.6 D ALEMBERT S PRINCIPLE 757 4.7 GENERALIZED FORCE 759 *
4.8 LAGRANGE S EQUATIONS OF MOTION 762 4.8.1 HOLONOMIC SYSTEMS 762 4.8.2
NONHOLONOMIC SYSTEMS 765 4.9 RAYLEIGH DISSIPATION FUNCTION 766 4.10
IMPULSIVE MOTION 768 4.11 INTEGRALS OF THE MOTION 770 { 4.12 VARIATIONAL
PRINCIPLES 174 4.13 HAMILTON S PRINCIPLE 775 4.14 SUMMARY 779 PROBLEMS
180 CONTENTS XV 5. CONTINUOUS SYSTEMS 192 5.1 INTRODUCTION 792 5.2
TRANSVERSE VIBRATION OF A STRING 792 5.3 LONGITUDINAL VIBRATION OF RODS
795 5.4 TORSIONAL VIBRATION OF SHAFTS 202 5.5 TRANSVERSE VIBRATION OF
BEAMS 205 5.5.1 EFFECTS OF THE ROTARY INERTIA AND SHEAR DEFORMATION 270
5.5.2 EFFECT OF AXIAL FORCE 275 5.6 VIBRATION OF MEMBRANES 218 5.7
APPROXIMATE METHODS 223 5.7.1 RAYLEIGH S METHOD 223 5.7.2 RAYLEIGH-RITZ
METHOD 226 5.8 SUMMARY 229 PROBLEMS 229 6. NATURAL FREQUENCIES AND MODE
SHAPES 237 6.1 INTRODUCTION 237 6.2 DUNKERLEY S EQUATION 237 6.3
RAYLEIGH METHOD 241 6.4 RAYLEIGH-RITZ METHOD 246 6.5 HOLZER METHOD 247
6.6 JACOBI DIAGONALIZATION METHOD 250 6.7 CHOLESKY DECOMPOSITION METHOD
253 6.7.1 STANDARD EIGENVALUE PROBLEM 253 6.8 ITERATION METHODS 255
6.8.1 MATRIX ITERATION METHOD 256 6.8.2 INVERSE ITERATION METHOD 256
6.8.3 SIMULTANEOUS ITERATION METHOD 257 6.8.4 SUBSPACE ITERATION METHOD
258 6.9 SUMMARY 263 PROBLEMS 264 7. NUMERICAL METHODS 274 7.1
INTRODUCTION 274 I 7.2 SINGLE DEGREE OF FREEDOM SYSTEM 274 7.2.1 FINITE
DIFFERENCE METHOD 274 7.2.2 CENTRAL DIFFERENCE METHOD 276 7.2.3
RUNGE-KUTTA METHOD 278 7.3 MULTI DEGREE OF FREEDOM SYSTEM 281 1A
EXPLICIT SCHEMES 281 7.4.1 CENTRAL DIFFERENCE METHOD 2 82 7.4.2
TWO-CYCLE ITERATION WITH TRAPEZOIDAL RULE 289 7.4.3 FOURTH ORDER
RUNGE-KUTTA METHOD 297 XVI CONTENTS 7.5 IMPLICIT SCHEMES 292 7.5.1
HOUBOLT METHOD 292 7.5.2 WILSON THETA METHOD 296 7.5.3 NEWMARK BETA
METHOD 299 7.5.4 PARK STIFFLY STABLE METHOD 303 7.6 CASE STUDY 305 7.6.1
LINEAR DYNAMIC SYSTEM 305 7.7 SUMMARY 307 PROBLEMS 307 8. FINITE ELEMENT
METHOD 311 8.1 INTRODUCTION 372 8.2 BAR ELEMENT 314 8.3 BEAM-ELEMENT 376
8.4 GLOBAL MATRICES 318 8.5 TRANSFORMATION OF ELEMENT MATRICES AND
VECTORS 322 8.6 EQUATIONS OF MOTION OF THE COMPLETE SYSTEM OF FINITE
ELEMENTS 324 8.6.1 INCORPORATION OF BOUNDARY CONDITIONS 325 8.7
CONSISTENT AND LUMPED MASS MATRICES 325 8.7.1 LUMPED MASS MATRIX FOR BAR
AND BEAM ELEMENTS 326 8.8 MODEL REDUCTION 328 8.9 SUMMARY 345 PROBLEMS
346 9. NONLINEAR VIBRATIONS 350 9.1 INTRODUCTION 350 9.2 NONLINEAR
DYNAMIC SYSTEMS 350 9.3 EXACT METHODS FOR NONLINEAR SYSTEMS 357 9.4
APPROXIMATE METHODS FOR NONLINEAR SYSTEMS 354 9 A.I ITERATIVE METHOD 354
9.4.2 RITZ AVERAGING METHOD 357 9 A3 PERTURBATION METHOD 360 9.4.4
VARIATION OF PARAMETER METHOD 365 9.5 GRAPHICAL METHOD 366 , 9.5.1 PHASE
PLANE REPRESENTATION 366 9.5.2 ISOCLINE METHOD 368 9.5.3 PEU S METHOD
370 9.6 STABILITY OF EQUILIBRIUM 377 9.7 MULTIDEGREE OF FREEDOM SYSTEMS
378 9.8 SUMMARY 378 , PROBLEMS 379 CONTENTS XVII 10. RANDOM VIBRATIONS
385 10.1 INTRODUCTION 385 10.2 RANDOM VIBRATIONS 385 10.3 PROBABILITY
DENSITY FUNCTION 387 10.4 AUTOCORRELATION FUNCTION 390 10.5 GAUSSIAN
RANDOM PROCESS 390 10.6 FOURIER ANALYSIS 397 10.6.1 FOURIER SERIES 397
10.6.2 FOURIER INTEGRAL 392 10.7 RESPONSE OF A SINGLE DEGREE OF FREEDOM
VIBRATIONS SYSTEM 394 10.7.1 IMPULSE RESPONSE METHOD 394 10.7.2
FREQUENCY RESPONSE METHOD 396 10.8 POWER SPECTRAL DENSITY FUNCTION 398
10.9 JOINT PROBABILITY DENSITY FUNCTION 399 10.10 CROSS-CORRELATION
FUNCTION 400 10.11 APPLICATION OF GSDS TO VEHICLE DYNAMICS 400 10.12
RESPONSE OF A SDOF SYSTEM TO A RANDOM INPUT 407 10.13 RESPONSE OF MDOF
SYSTEMS TO RANDOM INPUTS 403 10.14 SUMMARY 406 PROBLEMS 406 GLOSSARY OF
TERMS 411 GLOSSARY OF SYMBOLS 424 ANSWERS TO THE SELECTED PROBLEMS 426
BIBLIOGRAPHY 452 INDEX 462
|
| adam_txt |
ADVANCED MECHANICAL VIBRATIONS RAO V. DUKKIPATI ALPHA SCIENCE
INTERNATIONAL LTD. OXFORD, U.K. CONTENTS PREFACE T VII ACKNOWLEDGEMENTS
XI 1. INTRODUCTION 1 1.1 INTRODUCTION 1 1.2 CLASSIFICATION OF DYNAMIC
SYSTEM MODELS 1 1.3 CONSTRAINTS, GENERALIZED COORDINATES, AND DEGREES OF
FREEDOM 2 1.4 CLASSIFICATION OF VIBRATIONS 7 1.4.1 FREE AND FORCED
VIBRATIONS 8 1.4.2 LINEAR AND NON-LINEAR VIBRATIONS 8 1.4.3
DETERMINISTIC AND RANDOM VIBRATIONS 8 1.5 ELEMENTARY PARTS OF VIBRATING
SYSTEMS 9 1.5.1 EXAMPLES OF VIBRATING MOTION IO 1.5.2 SIMPLE HARMONIC
MOTION 10 1.5.3 PERIODIC MOTION 16 1.6 DISCRETE AND CONTINUOUS SYSTEMS
20 1.7 VIBRATION ANALYSIS 27 1.8 ELEMENTS OF VIBRATING SYSTEMS 24 1.8.1
SPRING ELEMENTS 25 1.8.2 POTENTIAL ENERGY OF LINEAR SPRINGS 29 1.8.3
EQUIVALENT SPRINGS 30 1.8.4 MASS OR INERTIA ELEMENTS 33 1.8.5 DAMPING
ELEMENTS 54 1.9 SUMMARY 38 PROBLEMS 39 I 2. TWO DEGREE OF FREEDOM
SYSTEMS 46 2.1 INTRODUCTION 46 2.2 EQUATIONS OF MOTION FOR A
TWO-DEGREE-OF FREEDOM SYSTEM 48 2.3 FREE VIBRATION OF UNDAMPED SYSTEMS
50 2.4 TORSIONAL SYSTEM 57 2.5 COORDINATE COUPLING AND
PRINCIPAL-COORDINATES 59 2.6 DAMPED FREE VIBRATIONS 64 2.7 FORCED
VIBRATION OF UNDAMPED SYSTEMS 67 2.8 FORCED VIBRATION WITH DAMPING 71
2.9 ORTHOGONALITY PRINCIPLE 74 2.10 SUMMARY 76 PROBLEMS 76 XIV CONTENTS
3. MULTI-DEGREE-OF-FREEDOM SYSTEMS 88 3.1 INTRODUCTION 88 3.2 EQUATIONS
OF MOTION 89 3.3 STIFFNESS INFLUENCE COEFFICIENTS 93 3.4 FLEXIBILITY
INFLUENCE COEFFICIENTS 95 3.5 MATRIX FORMULATION 96 3.6 INERTIA
INFLUENCE COEFFICIENTS 97 3.7 FREE VIBRATIONS OF MULTI-DEGREE-OF-FREEDOM
SYSTEMS 98 3.7.1 NORMAL MODE SOLUTION 98 3.7.2 NATURAL FREQUENCIES AND
MODE SHAPES 99 3.7.3 MODE SHAPE ORTHOGONALITY 104 3.8 FREE VIBRATIONS OF
UNDAMPED SYSTEMS 111 3.9 FREE VIBRATIONS OF DAMPED SYSTEMS 116 3.9.1
PROPORTIONAL DAMPING 116 3.9.2 GENERAL VISCOUS DAMPING 119 3.10 FORCED
VIBRATIONS OF MULTI-DEGREE OF FREEDOM SYSTEMS 720 3.10.1 HARMONIC
EXCITATIONS 727 3.10.2 LAPLACE TRANSFORM METHOD 124 3.11 MODAL ANALYSIS
FOR UNDAMPED SYSTEMS AND SYSTEMS WITH PROPORTIONAL DAMPING 727 3.11.1
SYSTEMS WITH PROPORTIONAL DAMPING 729 3.11.2 GENERAL DAMPING 732 3.12
NUMERICAL SOLUTIONS 136 3.13 SUMMARY 737 PROBLEMS 737 4. ANALYTICAL
DYNAMICS 146 4.1 INTRODUCTION 146 4.2 DEGREES OF FREEDOM 146 4.3
GENERALIZED COORDINATES 148 4.4 CONSTRAINTS 149 4.5 PRINCIPLE OF VIRTUAL
WORK 757 4.6 D'ALEMBERT'S PRINCIPLE 757 4.7 GENERALIZED FORCE 759 * '
4.8 LAGRANGE'S EQUATIONS OF MOTION 762 4.8.1 HOLONOMIC SYSTEMS 762 4.8.2
NONHOLONOMIC SYSTEMS 765 4.9 RAYLEIGH DISSIPATION FUNCTION 766 4.10
IMPULSIVE MOTION 768 4.11 INTEGRALS OF THE MOTION 770 { 4.12 VARIATIONAL
PRINCIPLES 174 4.13 HAMILTON'S PRINCIPLE 775 4.14 SUMMARY 779 PROBLEMS
180 CONTENTS XV 5. CONTINUOUS SYSTEMS 192 5.1 INTRODUCTION 792 5.2
TRANSVERSE VIBRATION OF A STRING 792 5.3 LONGITUDINAL VIBRATION OF RODS
795 5.4 TORSIONAL VIBRATION OF SHAFTS 202 5.5 TRANSVERSE VIBRATION OF
BEAMS 205 5.5.1 EFFECTS OF THE ROTARY INERTIA AND SHEAR DEFORMATION 270
5.5.2 EFFECT OF AXIAL FORCE 275 5.6 VIBRATION OF MEMBRANES 218 5.7
APPROXIMATE METHODS 223 5.7.1 RAYLEIGH'S METHOD 223 5.7.2 RAYLEIGH-RITZ
METHOD 226 5.8 SUMMARY 229 PROBLEMS 229 6. NATURAL FREQUENCIES AND MODE
SHAPES 237 6.1 INTRODUCTION 237 6.2 DUNKERLEY'S EQUATION 237 6.3
RAYLEIGH METHOD 241 6.4 RAYLEIGH-RITZ METHOD 246 6.5 HOLZER METHOD 247
6.6 JACOBI DIAGONALIZATION METHOD 250 6.7 CHOLESKY DECOMPOSITION METHOD
253 6.7.1 STANDARD EIGENVALUE PROBLEM 253 6.8 ITERATION METHODS 255
6.8.1 MATRIX ITERATION METHOD 256 6.8.2 INVERSE ITERATION METHOD 256
6.8.3 SIMULTANEOUS ITERATION METHOD 257 6.8.4 SUBSPACE ITERATION METHOD
258 6.9 SUMMARY 263 PROBLEMS 264 7. NUMERICAL METHODS 274 7.1
INTRODUCTION 274 I 7.2 SINGLE DEGREE OF FREEDOM SYSTEM 274 7.2.1 FINITE
DIFFERENCE METHOD 274 7.2.2 CENTRAL DIFFERENCE METHOD 276 7.2.3
RUNGE-KUTTA METHOD 278 7.3 MULTI DEGREE OF FREEDOM SYSTEM 281 1A
EXPLICIT SCHEMES 281 7.4.1 CENTRAL DIFFERENCE METHOD 2'82 7.4.2
TWO-CYCLE ITERATION WITH TRAPEZOIDAL RULE 289 7.4.3 FOURTH ORDER
RUNGE-KUTTA METHOD 297 XVI CONTENTS 7.5 IMPLICIT SCHEMES 292 7.5.1
HOUBOLT METHOD 292 7.5.2 WILSON THETA METHOD 296 7.5.3 NEWMARK BETA
METHOD 299 7.5.4 PARK STIFFLY STABLE METHOD 303 7.6 CASE STUDY 305 7.6.1
LINEAR DYNAMIC SYSTEM 305 7.7 SUMMARY 307 PROBLEMS 307 8. FINITE ELEMENT
METHOD 311 8.1 INTRODUCTION 372 8.2 BAR ELEMENT 314 8.3 BEAM-ELEMENT 376
8.4 GLOBAL MATRICES 318 8.5 TRANSFORMATION OF ELEMENT MATRICES AND
VECTORS 322 8.6 EQUATIONS OF MOTION OF THE COMPLETE SYSTEM OF FINITE
ELEMENTS 324 8.6.1 INCORPORATION OF BOUNDARY CONDITIONS 325 8.7
CONSISTENT AND LUMPED MASS MATRICES 325 8.7.1 LUMPED MASS MATRIX FOR BAR
AND BEAM ELEMENTS 326 8.8 MODEL REDUCTION 328 8.9 SUMMARY 345 PROBLEMS
346 9. NONLINEAR VIBRATIONS 350 9.1 INTRODUCTION 350 9.2 NONLINEAR
DYNAMIC SYSTEMS 350 9.3 EXACT METHODS FOR NONLINEAR SYSTEMS 357 9.4
APPROXIMATE METHODS FOR NONLINEAR SYSTEMS 354 9 A.I ITERATIVE METHOD 354
9.4.2 RITZ AVERAGING METHOD 357 9 A3 PERTURBATION METHOD 360 9.4.4
VARIATION OF PARAMETER METHOD 365 9.5 GRAPHICAL METHOD 366 , 9.5.1 PHASE
PLANE REPRESENTATION 366 9.5.2 ISOCLINE METHOD 368 9.5.3 PEU'S METHOD
370 9.6 STABILITY OF EQUILIBRIUM 377 9.7 MULTIDEGREE OF FREEDOM SYSTEMS
378 9.8 SUMMARY 378 , ' PROBLEMS 379 CONTENTS XVII 10. RANDOM VIBRATIONS
385 10.1 INTRODUCTION 385 10.2 RANDOM VIBRATIONS 385 10.3 PROBABILITY
DENSITY FUNCTION 387 10.4 AUTOCORRELATION FUNCTION 390 10.5 GAUSSIAN
RANDOM PROCESS 390 10.6 FOURIER ANALYSIS 397 10.6.1 FOURIER SERIES 397
10.6.2 FOURIER INTEGRAL 392 10.7 RESPONSE OF A SINGLE DEGREE OF FREEDOM
VIBRATIONS SYSTEM 394 10.7.1 IMPULSE RESPONSE METHOD 394 10.7.2
FREQUENCY RESPONSE METHOD 396 10.8 POWER SPECTRAL DENSITY FUNCTION 398
10.9 JOINT PROBABILITY DENSITY FUNCTION 399 10.10 CROSS-CORRELATION
FUNCTION 400 10.11 APPLICATION OF GSDS TO VEHICLE DYNAMICS 400 10.12
RESPONSE OF A SDOF SYSTEM TO A RANDOM INPUT 407 10.13 RESPONSE OF MDOF
SYSTEMS TO RANDOM INPUTS 403 10.14 SUMMARY 406 PROBLEMS 406 GLOSSARY OF
TERMS 411 GLOSSARY OF SYMBOLS 424 ANSWERS TO THE SELECTED PROBLEMS 426
BIBLIOGRAPHY 452 INDEX 462 |
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| dewey-ones | 531 - Classical mechanics |
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| id | DE-604.BV021807700 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:49:49Z |
| indexdate | 2024-07-09T20:45:05Z |
| institution | BVB |
| isbn | 9781842652220 1842652222 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015020045 |
| oclc_num | 254896189 |
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| owner | DE-91G DE-BY-TUM |
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| physical | XVII, 468 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
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| publisher | Alpha Science International |
| record_format | marc |
| spelling | Dukkipati, Rao V. 1945- Verfasser (DE-588)131484265 aut Advanced mechanical vibrations Rao V. Dukkipati Oxford Alpha Science International 2006 XVII, 468 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mechanische Schwingung (DE-588)4138305-9 gnd rswk-swf Mechanische Schwingung (DE-588)4138305-9 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015020045&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dukkipati, Rao V. 1945- Advanced mechanical vibrations Mechanische Schwingung (DE-588)4138305-9 gnd |
| subject_GND | (DE-588)4138305-9 |
| title | Advanced mechanical vibrations |
| title_auth | Advanced mechanical vibrations |
| title_exact_search | Advanced mechanical vibrations |
| title_exact_search_txtP | Advanced mechanical vibrations |
| title_full | Advanced mechanical vibrations Rao V. Dukkipati |
| title_fullStr | Advanced mechanical vibrations Rao V. Dukkipati |
| title_full_unstemmed | Advanced mechanical vibrations Rao V. Dukkipati |
| title_short | Advanced mechanical vibrations |
| title_sort | advanced mechanical vibrations |
| topic | Mechanische Schwingung (DE-588)4138305-9 gnd |
| topic_facet | Mechanische Schwingung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015020045&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dukkipatiraov advancedmechanicalvibrations |