Advanced mechanical vibrations: physics, mathematics and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
2021
|
| Edition: | First edition |
| Subjects: | |
| Online Access: | TUM01 |
| Item Description: | Description based on publisher supplied metadata and other sources |
| Physical Description: | 1 Online-Ressource (xv, 321 Seiten) Illustrationen |
| ISBN: | 9781351008594 9781351008600 |
Staff View
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| 100 | 1 | |a Gatti, Paolo L. |d 1959- |e Verfasser |0 (DE-588)1146219415 |4 aut | |
| 245 | 1 | 0 | |a Advanced mechanical vibrations |b physics, mathematics and applications |c Paolo Luciano Gatti |
| 250 | |a First edition | ||
| 264 | 1 | |a Boca Raton ; London ; New York |b CRC Press |c 2021 | |
| 264 | 4 | |c © 2021 | |
| 300 | |a 1 Online-Ressource (xv, 321 Seiten) |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
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| 500 | |a Description based on publisher supplied metadata and other sources | ||
| 505 | 8 | |a Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Acknowledgements -- Frequently Used Acronyms -- 1 A Few Preliminary Fundamentals -- 1.1 Introduction -- 1.2 Modelling Vibrations and Vibrating Systems -- 1.3 Some Basic Concepts -- 1.3.1 The Phenomenon of Beats -- 1.3.2 Displacement, Velocity, Acceleration and Decibels -- 1.4 Springs, Dampers and Masses -- 2 Formulating the Equations Of Motion -- 2.1 Introduction -- 2.2 Systems of Material Particles -- 2.2.1 Generalised Co-Ordinates, Constraints and Degrees of Freedom -- 2.3 Virtual Work and d'Ahlembert's Principles - Lagrange and Hamilton Equations -- 2.3.1 Hamilton's Equations (HEs) -- 2.4 On the Properties and Structure of Lagrange's Equations -- 2.4.1 Invariance in the Form of Les and Monogenic Forces -- 2.4.2 The Structure of the Kinetic Energy and of Lagrange Equations -- 2.4.3 The Energy Function and the Conservation of Energy -- 2.4.4 Elastic Forces, Viscous Forces and Rayleigh Dissipation Function -- 2.4.5 More Co-Ordinates than DOFs: Lagrange's Multipliers -- 2.5 Hamilton's Principle -- 2.5.1 More than One Independent Variable: Continuous Systems and Boundary Conditions -- 2.6 Small-Amplitude Oscillations -- 2.7 A Few Complements -- 2.7.1 Motion in a Non-Inertial Frame of Reference -- 2.7.2 Uniformly Rotating Frame -- 2.7.3 Ignorable Co-Ordinates and the Routh Function -- 2.7.4 The Simple Pendulum Again: A Note on Non-Small Oscillations -- 3 Finite DOFs Systems: Free Vibration -- 3.1 Introduction -- 3.2 Free Vibration of 1-DOF Systems -- 3.2.1 Logarithmic Decrement -- 3.3 Free Vibration of MDOF Systems: The Undamped Case -- 3.3.1 Orthogonality of Eigenvectors and Normalisation -- 3.3.2 The General Solution of the Undamped Free-Vibration Problem -- 3.3.3 Normal Co-Ordinates -- 3.3.4 Eigenvalues and Eigenvectors Sensitivities | |
| 505 | 8 | |a 3.3.5 Light Damping as a Perturbation of an Undamped System -- 3.3.6 More Orthogonality Conditions -- 3.3.7 Eigenvalue Degeneracy -- 3.3.8 Unrestrained Systems: Rigid-Body Modes -- 3.4 Damped Systems: Classical and Non-Classical Damping -- 3.4.1 Rayleigh Damping -- 3.4.2 Non-Classical Damping -- 3.5 GEPs and QEPs: Reduction to Standard Form -- 3.5.1 Undamped Systems -- 3.5.2 Viscously Damped Systems -- 3.6 Eigenvalues Sensitivity of Viscously Damped Systems -- 4 Finite-DOFs Systems: Response to External Excitation -- 4.1 Introduction -- 4.2 Response in the Time-, Frequency- and S-Domains: IRF, Duhamel's Integral, FRF and TF -- 4.2.1 Excitation Due to Base Displacement, Velocity or Acceleration -- 4.3 Harmonic and Periodic Excitation -- 4.3.1 A Few Notes on Vibration Isolation -- 4.3.2 Eccentric Excitation -- 4.3.3 Other Forms of FRFs -- 4.3.4 Damping Evaluation -- 4.3.5 Response Spectrum -- 4.4 MDOF Systems: Classical Damping -- 4.4.1 Mode 'Truncation' and the Mode-Acceleration Solution -- 4.4.2 The Presence of Rigid-Body Modes -- 4.5 MDOF Systems: Non-Classical Viscous Damping, a State-Space Approach -- 4.5.1 Another State-Space Formulation -- 4.6 Frequency Response Functions of a 2-DOF System -- 4.7 A Few Further Remarks on FRFs -- 5 Vibrations of Continuous Systems -- 5.1 Introduction -- 5.2 The Flexible String -- 5.2.1 Sinusoidal Waveforms and Standing Waves -- 5.2.2 Finite Strings: The Presence of Boundaries and the Free Vibration -- 5.3 Free Longitudinal and Torsional Vibration of Bars -- 5.4 A Short Mathematical Interlude: Sturm-Liouville Problems -- 5.5 A Two-Dimensional System: Free Vibration of a Flexible Membrane -- 5.5.1 Circular Membrane with Fixed Edge -- 5.6 Flexural (Bending) Vibrations of Beams -- 5.7 Finite Beams With Classical BCs -- 5.7.1 On the Orthogonality of Beam Eigenfunctions -- 5.7.2 Axial Force Effects | |
| 505 | 8 | |a 5.7.3 Shear Deformation and Rotary Inertia (Timoshenko Beam) -- 5.8 Bending Vibrations of Thin Plates -- 5.8.1 Rectangular Plates -- 5.8.2 Circular Plates -- 5.8.3 On the Orthogonality of Plate Eigenfunctions -- 5.9 A Few Additional Remarks -- 5.9.1 Self-Adjointness and Positive-Definiteness of the Beam and Plate Operators -- 5.9.2 Analogy with Finite-DOFs Systems -- 5.9.3 The Free Vibration Solution -- 5.10 Forced Vibrations: The Modal Approach -- 5.10.1 Alternative Closed-Form for FRFs -- 5.10.2 A Note on Green's Functions -- 6 Random Vibrations -- 6.1 Introduction -- 6.2 The Concept of Random Process, Correlation and Covariance Functions -- 6.2.1 Stationary Processes -- 6.2.2 Main Properties of Correlation and Covariance Functions -- 6.2.3 Ergodic Processes -- 6.3 Some Calculus for Random Processes -- 6.4 Spectral Representation of Stationary Random Processes -- 6.4.1 Main Properties of Spectral Densities -- 6.4.2 Narrowband and Broadband Processes -- 6.5 Response of Linear Systems to Stationary Random Excitation -- 6.5.1 SISO (Single Input-Single Output) Systems -- 6.5.2 SDOF-System Response to Broadband Excitation -- 6.5.3 SDOF Systems: Transient Response -- 6.5.4 A Note on Gaussian (Normal) Processes -- 6.5.5 MIMO (Multiple Inputs-Multiple Outputs) Systems -- 6.5.6 Response of MDOF Systems -- 6.5.7 Response of a Continuous System to Distributed Random Excitation: A Modal Approach -- 6.6 Threshold Crossing Rates and Peaks Distribution of Stationary Narrowband Processes -- Appendix A: On Matrices and Linear Spaces -- Appendix B: Fourier Series, Fourier and Laplace Transforms -- References and Further Reading -- Index | |
| 650 | 4 | |a Vibration | |
| 650 | 0 | 7 | |a Mechanische Schwingung |0 (DE-588)4138305-9 |2 gnd |9 rswk-swf |
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| 776 | 0 | 8 | |i Erscheint auch als |a Gatti, Paolo Luciano |t Advanced Mechanical Vibrations |d Milton : Taylor & Francis Group,c2021 |n Druck-Ausgabe, Hardcover |z 978-1-138-54228-0 |
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Record in the Search Index
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| author | Gatti, Paolo L. 1959- |
| author_GND | (DE-588)1146219415 |
| author_facet | Gatti, Paolo L. 1959- |
| author_role | aut |
| author_sort | Gatti, Paolo L. 1959- |
| author_variant | p l g pl plg |
| building | Verbundindex |
| bvnumber | BV047442228 |
| classification_tum | PHY 011 MSR 328 PHY 204 |
| collection | ZDB-30-PQE |
| contents | Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Acknowledgements -- Frequently Used Acronyms -- 1 A Few Preliminary Fundamentals -- 1.1 Introduction -- 1.2 Modelling Vibrations and Vibrating Systems -- 1.3 Some Basic Concepts -- 1.3.1 The Phenomenon of Beats -- 1.3.2 Displacement, Velocity, Acceleration and Decibels -- 1.4 Springs, Dampers and Masses -- 2 Formulating the Equations Of Motion -- 2.1 Introduction -- 2.2 Systems of Material Particles -- 2.2.1 Generalised Co-Ordinates, Constraints and Degrees of Freedom -- 2.3 Virtual Work and d'Ahlembert's Principles - Lagrange and Hamilton Equations -- 2.3.1 Hamilton's Equations (HEs) -- 2.4 On the Properties and Structure of Lagrange's Equations -- 2.4.1 Invariance in the Form of Les and Monogenic Forces -- 2.4.2 The Structure of the Kinetic Energy and of Lagrange Equations -- 2.4.3 The Energy Function and the Conservation of Energy -- 2.4.4 Elastic Forces, Viscous Forces and Rayleigh Dissipation Function -- 2.4.5 More Co-Ordinates than DOFs: Lagrange's Multipliers -- 2.5 Hamilton's Principle -- 2.5.1 More than One Independent Variable: Continuous Systems and Boundary Conditions -- 2.6 Small-Amplitude Oscillations -- 2.7 A Few Complements -- 2.7.1 Motion in a Non-Inertial Frame of Reference -- 2.7.2 Uniformly Rotating Frame -- 2.7.3 Ignorable Co-Ordinates and the Routh Function -- 2.7.4 The Simple Pendulum Again: A Note on Non-Small Oscillations -- 3 Finite DOFs Systems: Free Vibration -- 3.1 Introduction -- 3.2 Free Vibration of 1-DOF Systems -- 3.2.1 Logarithmic Decrement -- 3.3 Free Vibration of MDOF Systems: The Undamped Case -- 3.3.1 Orthogonality of Eigenvectors and Normalisation -- 3.3.2 The General Solution of the Undamped Free-Vibration Problem -- 3.3.3 Normal Co-Ordinates -- 3.3.4 Eigenvalues and Eigenvectors Sensitivities 3.3.5 Light Damping as a Perturbation of an Undamped System -- 3.3.6 More Orthogonality Conditions -- 3.3.7 Eigenvalue Degeneracy -- 3.3.8 Unrestrained Systems: Rigid-Body Modes -- 3.4 Damped Systems: Classical and Non-Classical Damping -- 3.4.1 Rayleigh Damping -- 3.4.2 Non-Classical Damping -- 3.5 GEPs and QEPs: Reduction to Standard Form -- 3.5.1 Undamped Systems -- 3.5.2 Viscously Damped Systems -- 3.6 Eigenvalues Sensitivity of Viscously Damped Systems -- 4 Finite-DOFs Systems: Response to External Excitation -- 4.1 Introduction -- 4.2 Response in the Time-, Frequency- and S-Domains: IRF, Duhamel's Integral, FRF and TF -- 4.2.1 Excitation Due to Base Displacement, Velocity or Acceleration -- 4.3 Harmonic and Periodic Excitation -- 4.3.1 A Few Notes on Vibration Isolation -- 4.3.2 Eccentric Excitation -- 4.3.3 Other Forms of FRFs -- 4.3.4 Damping Evaluation -- 4.3.5 Response Spectrum -- 4.4 MDOF Systems: Classical Damping -- 4.4.1 Mode 'Truncation' and the Mode-Acceleration Solution -- 4.4.2 The Presence of Rigid-Body Modes -- 4.5 MDOF Systems: Non-Classical Viscous Damping, a State-Space Approach -- 4.5.1 Another State-Space Formulation -- 4.6 Frequency Response Functions of a 2-DOF System -- 4.7 A Few Further Remarks on FRFs -- 5 Vibrations of Continuous Systems -- 5.1 Introduction -- 5.2 The Flexible String -- 5.2.1 Sinusoidal Waveforms and Standing Waves -- 5.2.2 Finite Strings: The Presence of Boundaries and the Free Vibration -- 5.3 Free Longitudinal and Torsional Vibration of Bars -- 5.4 A Short Mathematical Interlude: Sturm-Liouville Problems -- 5.5 A Two-Dimensional System: Free Vibration of a Flexible Membrane -- 5.5.1 Circular Membrane with Fixed Edge -- 5.6 Flexural (Bending) Vibrations of Beams -- 5.7 Finite Beams With Classical BCs -- 5.7.1 On the Orthogonality of Beam Eigenfunctions -- 5.7.2 Axial Force Effects 5.7.3 Shear Deformation and Rotary Inertia (Timoshenko Beam) -- 5.8 Bending Vibrations of Thin Plates -- 5.8.1 Rectangular Plates -- 5.8.2 Circular Plates -- 5.8.3 On the Orthogonality of Plate Eigenfunctions -- 5.9 A Few Additional Remarks -- 5.9.1 Self-Adjointness and Positive-Definiteness of the Beam and Plate Operators -- 5.9.2 Analogy with Finite-DOFs Systems -- 5.9.3 The Free Vibration Solution -- 5.10 Forced Vibrations: The Modal Approach -- 5.10.1 Alternative Closed-Form for FRFs -- 5.10.2 A Note on Green's Functions -- 6 Random Vibrations -- 6.1 Introduction -- 6.2 The Concept of Random Process, Correlation and Covariance Functions -- 6.2.1 Stationary Processes -- 6.2.2 Main Properties of Correlation and Covariance Functions -- 6.2.3 Ergodic Processes -- 6.3 Some Calculus for Random Processes -- 6.4 Spectral Representation of Stationary Random Processes -- 6.4.1 Main Properties of Spectral Densities -- 6.4.2 Narrowband and Broadband Processes -- 6.5 Response of Linear Systems to Stationary Random Excitation -- 6.5.1 SISO (Single Input-Single Output) Systems -- 6.5.2 SDOF-System Response to Broadband Excitation -- 6.5.3 SDOF Systems: Transient Response -- 6.5.4 A Note on Gaussian (Normal) Processes -- 6.5.5 MIMO (Multiple Inputs-Multiple Outputs) Systems -- 6.5.6 Response of MDOF Systems -- 6.5.7 Response of a Continuous System to Distributed Random Excitation: A Modal Approach -- 6.6 Threshold Crossing Rates and Peaks Distribution of Stationary Narrowband Processes -- Appendix A: On Matrices and Linear Spaces -- Appendix B: Fourier Series, Fourier and Laplace Transforms -- References and Further Reading -- Index |
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| dewey-full | 620.3 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
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| dewey-search | 620.3 |
| dewey-sort | 3620.3 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik |
| discipline_str_mv | Physik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik |
| edition | First edition |
| format | Electronic eBook |
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and the Routh Function -- 2.7.4 The Simple Pendulum Again: A Note on Non-Small Oscillations -- 3 Finite DOFs Systems: Free Vibration -- 3.1 Introduction -- 3.2 Free Vibration of 1-DOF Systems -- 3.2.1 Logarithmic Decrement -- 3.3 Free Vibration of MDOF Systems: The Undamped Case -- 3.3.1 Orthogonality of Eigenvectors and Normalisation -- 3.3.2 The General Solution of the Undamped Free-Vibration Problem -- 3.3.3 Normal Co-Ordinates -- 3.3.4 Eigenvalues and Eigenvectors Sensitivities</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3.3.5 Light Damping as a Perturbation of an Undamped System -- 3.3.6 More Orthogonality Conditions -- 3.3.7 Eigenvalue Degeneracy -- 3.3.8 Unrestrained Systems: Rigid-Body Modes -- 3.4 Damped Systems: Classical and Non-Classical Damping -- 3.4.1 Rayleigh Damping -- 3.4.2 Non-Classical Damping -- 3.5 GEPs and QEPs: Reduction to Standard Form -- 3.5.1 Undamped Systems -- 3.5.2 Viscously Damped Systems -- 3.6 Eigenvalues Sensitivity 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| id | DE-604.BV047442228 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T18:01:24Z |
| indexdate | 2024-07-10T09:12:16Z |
| institution | BVB |
| isbn | 9781351008594 9781351008600 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032844380 |
| oclc_num | 1206400943 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM |
| owner_facet | DE-91 DE-BY-TUM |
| physical | 1 Online-Ressource (xv, 321 Seiten) Illustrationen |
| psigel | ZDB-30-PQE ZDB-30-PQE TUM_PDA_PQE_Kauf |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Gatti, Paolo L. 1959- Verfasser (DE-588)1146219415 aut Advanced mechanical vibrations physics, mathematics and applications Paolo Luciano Gatti First edition Boca Raton ; London ; New York CRC Press 2021 © 2021 1 Online-Ressource (xv, 321 Seiten) Illustrationen txt rdacontent c rdamedia cr rdacarrier Description based on publisher supplied metadata and other sources Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Acknowledgements -- Frequently Used Acronyms -- 1 A Few Preliminary Fundamentals -- 1.1 Introduction -- 1.2 Modelling Vibrations and Vibrating Systems -- 1.3 Some Basic Concepts -- 1.3.1 The Phenomenon of Beats -- 1.3.2 Displacement, Velocity, Acceleration and Decibels -- 1.4 Springs, Dampers and Masses -- 2 Formulating the Equations Of Motion -- 2.1 Introduction -- 2.2 Systems of Material Particles -- 2.2.1 Generalised Co-Ordinates, Constraints and Degrees of Freedom -- 2.3 Virtual Work and d'Ahlembert's Principles - Lagrange and Hamilton Equations -- 2.3.1 Hamilton's Equations (HEs) -- 2.4 On the Properties and Structure of Lagrange's Equations -- 2.4.1 Invariance in the Form of Les and Monogenic Forces -- 2.4.2 The Structure of the Kinetic Energy and of Lagrange Equations -- 2.4.3 The Energy Function and the Conservation of Energy -- 2.4.4 Elastic Forces, Viscous Forces and Rayleigh Dissipation Function -- 2.4.5 More Co-Ordinates than DOFs: Lagrange's Multipliers -- 2.5 Hamilton's Principle -- 2.5.1 More than One Independent Variable: Continuous Systems and Boundary Conditions -- 2.6 Small-Amplitude Oscillations -- 2.7 A Few Complements -- 2.7.1 Motion in a Non-Inertial Frame of Reference -- 2.7.2 Uniformly Rotating Frame -- 2.7.3 Ignorable Co-Ordinates and the Routh Function -- 2.7.4 The Simple Pendulum Again: A Note on Non-Small Oscillations -- 3 Finite DOFs Systems: Free Vibration -- 3.1 Introduction -- 3.2 Free Vibration of 1-DOF Systems -- 3.2.1 Logarithmic Decrement -- 3.3 Free Vibration of MDOF Systems: The Undamped Case -- 3.3.1 Orthogonality of Eigenvectors and Normalisation -- 3.3.2 The General Solution of the Undamped Free-Vibration Problem -- 3.3.3 Normal Co-Ordinates -- 3.3.4 Eigenvalues and Eigenvectors Sensitivities 3.3.5 Light Damping as a Perturbation of an Undamped System -- 3.3.6 More Orthogonality Conditions -- 3.3.7 Eigenvalue Degeneracy -- 3.3.8 Unrestrained Systems: Rigid-Body Modes -- 3.4 Damped Systems: Classical and Non-Classical Damping -- 3.4.1 Rayleigh Damping -- 3.4.2 Non-Classical Damping -- 3.5 GEPs and QEPs: Reduction to Standard Form -- 3.5.1 Undamped Systems -- 3.5.2 Viscously Damped Systems -- 3.6 Eigenvalues Sensitivity of Viscously Damped Systems -- 4 Finite-DOFs Systems: Response to External Excitation -- 4.1 Introduction -- 4.2 Response in the Time-, Frequency- and S-Domains: IRF, Duhamel's Integral, FRF and TF -- 4.2.1 Excitation Due to Base Displacement, Velocity or Acceleration -- 4.3 Harmonic and Periodic Excitation -- 4.3.1 A Few Notes on Vibration Isolation -- 4.3.2 Eccentric Excitation -- 4.3.3 Other Forms of FRFs -- 4.3.4 Damping Evaluation -- 4.3.5 Response Spectrum -- 4.4 MDOF Systems: Classical Damping -- 4.4.1 Mode 'Truncation' and the Mode-Acceleration Solution -- 4.4.2 The Presence of Rigid-Body Modes -- 4.5 MDOF Systems: Non-Classical Viscous Damping, a State-Space Approach -- 4.5.1 Another State-Space Formulation -- 4.6 Frequency Response Functions of a 2-DOF System -- 4.7 A Few Further Remarks on FRFs -- 5 Vibrations of Continuous Systems -- 5.1 Introduction -- 5.2 The Flexible String -- 5.2.1 Sinusoidal Waveforms and Standing Waves -- 5.2.2 Finite Strings: The Presence of Boundaries and the Free Vibration -- 5.3 Free Longitudinal and Torsional Vibration of Bars -- 5.4 A Short Mathematical Interlude: Sturm-Liouville Problems -- 5.5 A Two-Dimensional System: Free Vibration of a Flexible Membrane -- 5.5.1 Circular Membrane with Fixed Edge -- 5.6 Flexural (Bending) Vibrations of Beams -- 5.7 Finite Beams With Classical BCs -- 5.7.1 On the Orthogonality of Beam Eigenfunctions -- 5.7.2 Axial Force Effects 5.7.3 Shear Deformation and Rotary Inertia (Timoshenko Beam) -- 5.8 Bending Vibrations of Thin Plates -- 5.8.1 Rectangular Plates -- 5.8.2 Circular Plates -- 5.8.3 On the Orthogonality of Plate Eigenfunctions -- 5.9 A Few Additional Remarks -- 5.9.1 Self-Adjointness and Positive-Definiteness of the Beam and Plate Operators -- 5.9.2 Analogy with Finite-DOFs Systems -- 5.9.3 The Free Vibration Solution -- 5.10 Forced Vibrations: The Modal Approach -- 5.10.1 Alternative Closed-Form for FRFs -- 5.10.2 A Note on Green's Functions -- 6 Random Vibrations -- 6.1 Introduction -- 6.2 The Concept of Random Process, Correlation and Covariance Functions -- 6.2.1 Stationary Processes -- 6.2.2 Main Properties of Correlation and Covariance Functions -- 6.2.3 Ergodic Processes -- 6.3 Some Calculus for Random Processes -- 6.4 Spectral Representation of Stationary Random Processes -- 6.4.1 Main Properties of Spectral Densities -- 6.4.2 Narrowband and Broadband Processes -- 6.5 Response of Linear Systems to Stationary Random Excitation -- 6.5.1 SISO (Single Input-Single Output) Systems -- 6.5.2 SDOF-System Response to Broadband Excitation -- 6.5.3 SDOF Systems: Transient Response -- 6.5.4 A Note on Gaussian (Normal) Processes -- 6.5.5 MIMO (Multiple Inputs-Multiple Outputs) Systems -- 6.5.6 Response of MDOF Systems -- 6.5.7 Response of a Continuous System to Distributed Random Excitation: A Modal Approach -- 6.6 Threshold Crossing Rates and Peaks Distribution of Stationary Narrowband Processes -- Appendix A: On Matrices and Linear Spaces -- Appendix B: Fourier Series, Fourier and Laplace Transforms -- References and Further Reading -- Index Vibration Mechanische Schwingung (DE-588)4138305-9 gnd rswk-swf Mechanische Schwingung (DE-588)4138305-9 s DE-604 Erscheint auch als Gatti, Paolo Luciano Advanced Mechanical Vibrations Milton : Taylor & Francis Group,c2021 Druck-Ausgabe, Hardcover 978-1-138-54228-0 |
| spellingShingle | Gatti, Paolo L. 1959- Advanced mechanical vibrations physics, mathematics and applications Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- Acknowledgements -- Frequently Used Acronyms -- 1 A Few Preliminary Fundamentals -- 1.1 Introduction -- 1.2 Modelling Vibrations and Vibrating Systems -- 1.3 Some Basic Concepts -- 1.3.1 The Phenomenon of Beats -- 1.3.2 Displacement, Velocity, Acceleration and Decibels -- 1.4 Springs, Dampers and Masses -- 2 Formulating the Equations Of Motion -- 2.1 Introduction -- 2.2 Systems of Material Particles -- 2.2.1 Generalised Co-Ordinates, Constraints and Degrees of Freedom -- 2.3 Virtual Work and d'Ahlembert's Principles - Lagrange and Hamilton Equations -- 2.3.1 Hamilton's Equations (HEs) -- 2.4 On the Properties and Structure of Lagrange's Equations -- 2.4.1 Invariance in the Form of Les and Monogenic Forces -- 2.4.2 The Structure of the Kinetic Energy and of Lagrange Equations -- 2.4.3 The Energy Function and the Conservation of Energy -- 2.4.4 Elastic Forces, Viscous Forces and Rayleigh Dissipation Function -- 2.4.5 More Co-Ordinates than DOFs: Lagrange's Multipliers -- 2.5 Hamilton's Principle -- 2.5.1 More than One Independent Variable: Continuous Systems and Boundary Conditions -- 2.6 Small-Amplitude Oscillations -- 2.7 A Few Complements -- 2.7.1 Motion in a Non-Inertial Frame of Reference -- 2.7.2 Uniformly Rotating Frame -- 2.7.3 Ignorable Co-Ordinates and the Routh Function -- 2.7.4 The Simple Pendulum Again: A Note on Non-Small Oscillations -- 3 Finite DOFs Systems: Free Vibration -- 3.1 Introduction -- 3.2 Free Vibration of 1-DOF Systems -- 3.2.1 Logarithmic Decrement -- 3.3 Free Vibration of MDOF Systems: The Undamped Case -- 3.3.1 Orthogonality of Eigenvectors and Normalisation -- 3.3.2 The General Solution of the Undamped Free-Vibration Problem -- 3.3.3 Normal Co-Ordinates -- 3.3.4 Eigenvalues and Eigenvectors Sensitivities 3.3.5 Light Damping as a Perturbation of an Undamped System -- 3.3.6 More Orthogonality Conditions -- 3.3.7 Eigenvalue Degeneracy -- 3.3.8 Unrestrained Systems: Rigid-Body Modes -- 3.4 Damped Systems: Classical and Non-Classical Damping -- 3.4.1 Rayleigh Damping -- 3.4.2 Non-Classical Damping -- 3.5 GEPs and QEPs: Reduction to Standard Form -- 3.5.1 Undamped Systems -- 3.5.2 Viscously Damped Systems -- 3.6 Eigenvalues Sensitivity of Viscously Damped Systems -- 4 Finite-DOFs Systems: Response to External Excitation -- 4.1 Introduction -- 4.2 Response in the Time-, Frequency- and S-Domains: IRF, Duhamel's Integral, FRF and TF -- 4.2.1 Excitation Due to Base Displacement, Velocity or Acceleration -- 4.3 Harmonic and Periodic Excitation -- 4.3.1 A Few Notes on Vibration Isolation -- 4.3.2 Eccentric Excitation -- 4.3.3 Other Forms of FRFs -- 4.3.4 Damping Evaluation -- 4.3.5 Response Spectrum -- 4.4 MDOF Systems: Classical Damping -- 4.4.1 Mode 'Truncation' and the Mode-Acceleration Solution -- 4.4.2 The Presence of Rigid-Body Modes -- 4.5 MDOF Systems: Non-Classical Viscous Damping, a State-Space Approach -- 4.5.1 Another State-Space Formulation -- 4.6 Frequency Response Functions of a 2-DOF System -- 4.7 A Few Further Remarks on FRFs -- 5 Vibrations of Continuous Systems -- 5.1 Introduction -- 5.2 The Flexible String -- 5.2.1 Sinusoidal Waveforms and Standing Waves -- 5.2.2 Finite Strings: The Presence of Boundaries and the Free Vibration -- 5.3 Free Longitudinal and Torsional Vibration of Bars -- 5.4 A Short Mathematical Interlude: Sturm-Liouville Problems -- 5.5 A Two-Dimensional System: Free Vibration of a Flexible Membrane -- 5.5.1 Circular Membrane with Fixed Edge -- 5.6 Flexural (Bending) Vibrations of Beams -- 5.7 Finite Beams With Classical BCs -- 5.7.1 On the Orthogonality of Beam Eigenfunctions -- 5.7.2 Axial Force Effects 5.7.3 Shear Deformation and Rotary Inertia (Timoshenko Beam) -- 5.8 Bending Vibrations of Thin Plates -- 5.8.1 Rectangular Plates -- 5.8.2 Circular Plates -- 5.8.3 On the Orthogonality of Plate Eigenfunctions -- 5.9 A Few Additional Remarks -- 5.9.1 Self-Adjointness and Positive-Definiteness of the Beam and Plate Operators -- 5.9.2 Analogy with Finite-DOFs Systems -- 5.9.3 The Free Vibration Solution -- 5.10 Forced Vibrations: The Modal Approach -- 5.10.1 Alternative Closed-Form for FRFs -- 5.10.2 A Note on Green's Functions -- 6 Random Vibrations -- 6.1 Introduction -- 6.2 The Concept of Random Process, Correlation and Covariance Functions -- 6.2.1 Stationary Processes -- 6.2.2 Main Properties of Correlation and Covariance Functions -- 6.2.3 Ergodic Processes -- 6.3 Some Calculus for Random Processes -- 6.4 Spectral Representation of Stationary Random Processes -- 6.4.1 Main Properties of Spectral Densities -- 6.4.2 Narrowband and Broadband Processes -- 6.5 Response of Linear Systems to Stationary Random Excitation -- 6.5.1 SISO (Single Input-Single Output) Systems -- 6.5.2 SDOF-System Response to Broadband Excitation -- 6.5.3 SDOF Systems: Transient Response -- 6.5.4 A Note on Gaussian (Normal) Processes -- 6.5.5 MIMO (Multiple Inputs-Multiple Outputs) Systems -- 6.5.6 Response of MDOF Systems -- 6.5.7 Response of a Continuous System to Distributed Random Excitation: A Modal Approach -- 6.6 Threshold Crossing Rates and Peaks Distribution of Stationary Narrowband Processes -- Appendix A: On Matrices and Linear Spaces -- Appendix B: Fourier Series, Fourier and Laplace Transforms -- References and Further Reading -- Index Vibration Mechanische Schwingung (DE-588)4138305-9 gnd |
| subject_GND | (DE-588)4138305-9 |
| title | Advanced mechanical vibrations physics, mathematics and applications |
| title_auth | Advanced mechanical vibrations physics, mathematics and applications |
| title_exact_search | Advanced mechanical vibrations physics, mathematics and applications |
| title_exact_search_txtP | Advanced mechanical vibrations physics, mathematics and applications |
| title_full | Advanced mechanical vibrations physics, mathematics and applications Paolo Luciano Gatti |
| title_fullStr | Advanced mechanical vibrations physics, mathematics and applications Paolo Luciano Gatti |
| title_full_unstemmed | Advanced mechanical vibrations physics, mathematics and applications Paolo Luciano Gatti |
| title_short | Advanced mechanical vibrations |
| title_sort | advanced mechanical vibrations physics mathematics and applications |
| title_sub | physics, mathematics and applications |
| topic | Vibration Mechanische Schwingung (DE-588)4138305-9 gnd |
| topic_facet | Vibration Mechanische Schwingung |
| work_keys_str_mv | AT gattipaolol advancedmechanicalvibrationsphysicsmathematicsandapplications |