book

Mechanical Vibrations: Theory and Practice

Name: Mechanical Vibrations: Theory and Practice
Author: Shrikant Bhave
ISBN: 9788131732489

by Shrikant Bhave

June 2010

Intermediate to advanced

374 pages

11h 34m

English

Pearson India

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Cover
Title page
Contents
Dedication
Foreword
Preface
Chapter 1. Fundamentals of Vibration Analysis
1.1 Introduction1.1.1 Definition of Vibration of Different Forms1.1.2 Classifications of Vibrations Experienced in Actual Practice1.1.3 Parameters of Vibration Waveform1.1.4 Why do we Need Mathematical Modelling?1.2 Practical Aspects of Vibration Analysis1.2.1 Step 1: Mathematical Modelling1.2.2 Step 2: Derivation of Governing Equations1.2.3 Step 3: Solution of Governing Equations1.2.4 Step 4: Interpretation of ResultsConclusion
Chapter 2. Single Degree-of-Freedom Vibration Systems
2.1 Definition of Degrees-of-Freedom2.2 Single Degree-of-Freedom System2.2.1 Rigid-Body Oscillations2.2.2 Spring–Mass–Damper Systems2.3 Equation of Motion for Single Degree-of-Freedom System (SDOF)2.3.1 Free Vibrations of Single Degree-of-Freedom System—Viscous Damping2.3.2 Free Vibrations of Single Degree-of-Freedom System—Coulomb and Hysteretic Damping2.4 Forced Vibrations of Single Degree-of-Freedom System to Harmonic Excitation Force2.4.1 Response of an Undamped System to Harmonic Excitation Force2.4.2 Response of a Damped System under Harmonic Force2.4.3 Mechanical-Impedance Method2.4.4 Forced Vibrations with Coulomb Damping2.4.5 Forced Vibration with Hysteretic Damping2.4.6 Response of SDOF Systems Subjected to a General Periodic ForceConclusionExercises
Chapter 3. Two Degrees-of-Freedom Systems
3.1 Equations of Motion3.1.1 Analysis of Free Vibrations of an Undamped System3.1.2 Lagrange's Equations3.2 Analysis of Free Vibrations of Damped Systems3.2.1 Orthogonality Principle3.3 Semi-Definite System3.4 Forced Vibration of Two Degrees-of-Freedom System3.4.1 Tuned AbsorberConclusionExercises
Chapter 4. Multi Degrees-of-Freedom Systems
4.1 Introduction4.2 Modelling of Continuous Systems4.3 Equations of Motion for Multi Degrees-of-Freedom Systems4.3.1 Using Newton's Second Law of Motion4.3.2 Influence Coefficients4.4 Generalized Coordinates4.5 Energies in Vibrating Systems4.5.1 Use of Lagrange's Equation4.6 Eigen Value Problem4.7 Orthogonality of Normal Modes4.8 Modal Analysis4.9 Determination of Natural Frequencies and Mode Shapes4.9.1 Method of Matrices and Matrix Iteration4.9.2 Holzer Method4.9.3 Stodola Method4.9.4 Dunkerley's Method4.9.5 Rayleigh's Method4.9.6 Mechanical-Impedance MethodConclusionExercises

Chapter 5. Torsional Vibrations
5.1 Introduction5.2 Torsional Vibration Systems5.2.1 Single Degree-of-Freedom System5.3 Two Degrees-of-Freedom Torsional Systems (Free Unclamped)5.4 Geared Systems5.5 Multi Degrees-of-Freedom Systems5.5.1 Semi-Definite Systems5.5.2 One End Fixed, Other End Free and Both Ends FixedConclusionExercises
Chapter 6. Transverse Vibrations
6.1 Introduction6.2 Lateral Vibrations of Beams6.2.1 Free Vibrations6.2.2 Orthogonality of Normal Functions6.2.3 Forced Vibrations6.3 Rayleigh's Method6.4 Rayleigh–Ritz Method6.5 Whirling of Rotating Shafts6.5.1 Equations of Motion6.5.2 Critical Speeds6.5.3 BalancingConclusionExercises
Chapter 7. Vibration Diagnosis and Control
7.1 Introduction7.2 Sensing and Measurements7.2.1 General Considerations7.2.2 Important Terminologies in Vibration/Noise Measurements and Band-Pass Filter7.2.3 Vibration Pick-Ups7.3 Vibration Nomographs and Vibration Criterion7.4 Vibration Analysis7.4.1 Phase Measurement7.4.2 General-Purpose Vibration Analyser7.4.3 Tape Recorders7.4.4 Real-Time Analysers7.4.5 Remote Sensing7.5 Data Reduction and Processing7.5.1 Vibration Amplitude Versus Frequency Analysis7.5.2 Spectrum Averaging7.5.3 Amplitude Versus Frequency Versus Time Analysis7.5.4 Amplitude/Phase Versus RPM Analysis7.5.5 Time Waveform Analysis7.5.6 Lissajous Pattern (ORBIT) Analysis7.5.7 Mode Shape Analysis7.6 Diagnosis and Corrective Actions7.6.1 Steady-State Operating Regime7.6.2 Detection of Perturbation Forces and Corrective Actions7.7 Modal Analysis7.8 Vibration ControlConclusionExercises
Chapter 8. Finite Element Method
8.1 Introduction8.2 Important Conditions to be Satisfied8.3 Modelling8.4 Shape Functions8.5 Bar Element8.6 Boundary Conditions8.7 Torsion Element8.8 Beam ElementMatlab—Tool for ComputationIntroduction(I) Display Windows(II) Arithmetic Operations(III) Built-in Functions(IV) Matrix(V) Polynomials(VI) System of Linear equationsConclusionExercises
Chapter 9. Fundamentals of Experimental Modal Analysis
9.1 Introduction9.2 Frequency-Response Function9.2.1 Frequency-Response Function—Basic PrinciplesExercises
Chapter 10. Miscellaneous Topics in Vibration Analysis and Introduction to Noise Analysis
10.1 Flow-Induced Vibrations10.2 Acoustics and Analysis of Noise10.2.1 Basics of Sound10.2.2 Amplitude, Frequency, Wavelength, and Velocity10.2.3 Sound Field Definitions10.3 Non-Stationary (Unsteady) Vibrations10.4 Rotor Dynamics and Hydrodynamic BearingsExercises
Appendix - A
Appendix - B
Appendix - C
Appendix - D
Copyright

Content preview from Mechanical Vibrations: Theory and Practice

8 Finite Element Method

8.1 INTRODUCTION

In the previous chapters (Chapters 3, 4, and 6), we explained the method of idealizing/simulating a continuous system as an assemblage of multiple masses, springs, and damper elements to obtain (at least) a first-level evaluation of natural frequencies, mode shapes, and the response of the system to a given system of excitation forces. However, at times, such approximation, which uses lumped masses, springs, and dampers does not yield a reasonably-acceptable/satisfactory result.

While dealing with the analysis of vibrations of beams for various conditions of fixity, we have seen that the solutions are in the form of infinite series, and larger is the number of terms we consider in the series, higher ...

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Mechanical Vibrations: Theory and Practice

by Shrikant Bhave

8