Mechanical Vibrations

Indian Institute of Technology Guwahati

Course contents:

• Introduction
Overview of the course, practical applications and research trends. Harmonic and periodic motions, vibration terminology
• Single-DOF Free Vibrations
Vibration model, Equation of motion-Natural Frequency. Energy method, Rayleigh method. Principle of virtual work, Damping models. Viscously damped free vibration. Special cases: oscillatory, non-oscillatory and critically damped motions. Logarithmic decrement, Experimental determination of damping coefficient. Forced harmonic vibration, Magnification factor. Rotor unbalance, Transmissibility. Vibration Isolation. Equivalent viscous damping, Sharpness of resonance.
• Two-DOF Free Vibrations
Generalized and Principal coordinates, derivation of equations of motion. Lagrange’s equation. Coordinate coupling. Forced Harmonic vibration.
• Vibration Absorber
Tuned absorber, determination of mass ratio. Tuned and damped absorber, unturned viscous damper.
• Multi-DOF
Derivation of equations of motion, influence coefficient method. Properties of vibrating systems: flexibility and stiffness matrices, reciprocity theorem. Modal analysis: undamped. Modal analysis: damped.
• Calculation of natural frequencies
Rayleigh method. Stodala method. Matrix iteration method. Holzer method and Dunkerley’s method.
• Torsional vibration
Simple systems with one or two rotor masses. Multi-DOF systems-transfer matrix method. Geared system. Branched system.
• Continuous systems: closed form solutions
Vibration of strings. Longitudinal and torsional vibration of rods. Transverse vibration of beams: equations of motion and boundary conditions. Transverse vibration of beams: natural frequencies and mode shapes.
• Continuous systems: Approximate solutions
Rayleigh’s energy method. Rayleigh-Ritz method. Assumed modes and Galerkin’s method.
• Finite element analysis
Finite element formulation for beams: Galerkin’s method. Beams elemental mass and stiffness matrices, Elemental force vector,
Global finite element assembly and imposition of boundary conditions and solution procedure. Finite element formulation for rods.
• Signature analysis and preventive maintenance
Vibration testing equipments: signal generation, measuring and conditioning instruments. Vibration testing equipments: signal analysis instruments. Vibration signatures and standards. Field balancing of rotors.
• Mod-1 Lec-1 Overview of the Course, Practical and Research Trends
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-1 Lec-2 Harmonic and Periodic Motions, Vibration Terminology
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-2 Lec-1 Vibration Model, Equation of Motion-Natural Frequency
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-2 Lec-2 Energy Method, Principle of Virtual Work
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-3 Lec-1 Viscously Damped Free Vibration Special Cases: Oscillatory
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-3 Lec-2 Logarithmic Decrement Experimental Determination of Damping Coefficient Hysteresis Loop
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-3 Lec-3 Coulomb Damping other Damping Models
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-4 Lec-1 Forced Harmonic Vibration, Magnification Factor
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-4 Lec-2 Laplace Transform, Superposition Theorem
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-4 Lec-3 Rotor Unbalance and Whirling of Shaft, Transmissibility
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-4 Lec-4 Support Motion, Vibration Isolation
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-4 Lec-5 Sharpness of Resonance, Vibration Measuring Instruments
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-5 Lec-1 Generalized and Principle Coordinates, Derivation of Equation of Motion
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-5 Lec-2 Lagranges&#39;s Equation
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-5 Lec-3 Coordinate Coupling
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-5 Lec-4 Forced Harmonic Vibration
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-6 Lec-1 Tuned Absorber, Determination of Mass Ratio
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-6 Lec-2 Tuned and Damped Absorber, Untuned Viscous Damper
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-7 Lec-1 Derivation of Equations of Motion, Influence Coefficient Method
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-7 Lec-2 Properties of Vibrating Systems: Flexibility & Stiffness Matrices, Reciprocity Theorem
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-7 Lec-3 Modal Analysis: Undamped
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-7 Lec-4 Modal Analysis: Damped
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-8 Lec-1 Simple Systems With One Two or Three Discs Geared System
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-8 Lec-2 Multi-Degree of Freedom Systems-Transfer Matrix Method Branched System
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-9 Lec-1 Derivation of Equations of Motion Part 1-Newton&#39;s and Hamilton&#39;s Principle
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-9 Lec-2 Derivation of Equations of Motion Part 2-Newton&#39;s and Hamilton&#39;s Principle
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-9 Lec-3 Vibration of Strings
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-9 Lec-4 Longitudinal and Torsional Vibration of Rods
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-9 Lec-5 Transverse Vibration of Beams, Equations of Motion and Boundary Conditions
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-9 Lec-6 Transverse Vibration of Beams: Natural Frequencies and Mode Shapes
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-10 Lec-1 Rayleigh&#39;s Energy Method
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-10 Lec-2 Matrix Iteration Method
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-10 Lec-3 Durkerley, Rayleigh-Ritz and Galerkin Method
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-11 Lec-1 Finite Element Formulation for Rods, Gear Train and Branched System
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-11 Lec-2 Finite Element Formulation for Beams: Galerkin&#39;s Method
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-11 Lec-3 Global Finite Element Assembly and Imposition of Boundary Conditions
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-12 Lec-1 Vibration Testing Equipments: Signal Measurements
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-12 Lec-2 Vibration Testing Equipments: Signal Analysis
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari
• Mod-12 Lec-3 Field Balancing of Rotors
Prof. S.K. Dwivedy, Prof. Rajiv Tiwari