ABOUT THE COURSE: The course introduces the basic concept of dynamic equilibrium, Degrees of freedom, and equation of motion at the beginning. Then the learners are introduced to the free vibration of the SDOF system with Viscous and Coulomb damping followed by forced vibration of the SDOF system. Then the half-power bandwidth technique, energy dissipation due to damping, and equivalent / rate-independent damping are introduced. It is followed by different methods of the numerical response evaluation, the response spectrum, and the preparation of the elastic design spectrum with the examples solved using MATLAB. Then the MDOF system is introduced with eigen solution based decoupling for modal superposition, time history analysis, and response spectrum analysis for the multistoried buildings are explained with examples in MATLAB. The free and forced vibration of a continuous system are also covered. At last, the dynamic analysis of a building using Finite Element software is demonstrated.INTENDED AUDIENCE: UG Final Year Students, PG Students, and Research Scholars.
Overview
Syllabus
Week 1:
Lecture 1 : Newton’s Law, D’Alembert Principle, Degree of Freedom
Lecture 2 : Equation of Motion, Simple Harmonic Motion. Week 2:
Lecture 3 : Undamped Free Vibration, Solution, Natural Frequencies
Lecture 4 : Damped Free Vibration, Solution, Under Damped, Critical Damped, Overdamped system
Lecture 5 : Energy in Free Vibration, Viscous, and Coulomb Damping models, Logarithmic Decrement, Week 3:
Lecture 6 : Vibration due to constant force and harmonic force, Numerical examples
Lecture 7 : Half power Bandwidth Technique, Response due to Support Motion, Force Transmission
Lecture 8 : Energy Dissipation, Equivalent Viscous Damping, Rate Independent Damping.Week 4:
Lecture 9 : Impulse Response function, Duhamel’s Integral, Example using MATLAB
Lecture 10 : Response due to Step and Ramp force.
Lecture 11 : Response due to Rectangle and Half Sinusoidal pulse force
Lecture 12 : Response due to Arbitrary support motionWeek 5:
Lecture 13 : Numerical techniques, Implicit and Explicit methods, Central Difference, Example with MATLAB Coding
Lecture 14 : Newmark - ß algorithm, Example with MATLAB Coding
Lecture 15 : Wilson - ? algorithm, Example with MATLAB CodingWeek 6:
Lecture 16 : Concept on Response Spectrum, Tripartite Response Spectrum, Important Features.
Lecture 17 : Elastic Design Spectrum, spectrum-compatible earthquake
Lecture 18 : Numerical Example in MATLAB.Week 7:
Lecture 19 : Hamilton Principle, Lagrange Equation
Lecture 20 : Coupled Equation of Motion
Lecture 21 : Rayleigh Damping, Caughey Damping, Non-Classical Damping.Week 8:
Lecture 22 : Natural Frequencies and Mode shapes of MDOF system
Lecture 23 : Orthogonality of Modes, Normalization of Modes, Modal Expansion of displacement.
Lecture 24 : Free Vibration of a Damped MDOF system. Week 9:
Lecture 25 : Response Analysis in the Time domain by modal superposition, Numerical Example in MATLAB
Lecture 26 : Response Analysis in the frequency domain, Numerical ExampleWeek 10:
Lecture 27 : Equation of Motions, Solution Strategy, example in MATLAB
Lecture 28 : Peak modal response, Modal combination rules - SRSS, CQC methods
Lecture 29 : Model reduction Technique: Static Condensation, Theory, and Example
Lecture 30 : Model reduction Technique: Dynamic Condensation, Theory, and Example in MATLABWeek 11:
Lecture 31 : Free Vibration – Eigen value problem
Lecture 32 : The vibration of a beam under different support conditions
Lecture 33 : Rayleigh’s Quotient, Approximate Method - Rayleigh’s Energy Method
Lecture 34 : Forced Vibration of a beamWeek 12:
Lecture 35 : Introduction to FE software
Lecture 36 : Response Spectrum Analysis of a multistoried building using FE software
Lecture 37 : Time History Analysis of a Multistoried building using FE software
Lecture 1 : Newton’s Law, D’Alembert Principle, Degree of Freedom
Lecture 2 : Equation of Motion, Simple Harmonic Motion. Week 2:
Lecture 3 : Undamped Free Vibration, Solution, Natural Frequencies
Lecture 4 : Damped Free Vibration, Solution, Under Damped, Critical Damped, Overdamped system
Lecture 5 : Energy in Free Vibration, Viscous, and Coulomb Damping models, Logarithmic Decrement, Week 3:
Lecture 6 : Vibration due to constant force and harmonic force, Numerical examples
Lecture 7 : Half power Bandwidth Technique, Response due to Support Motion, Force Transmission
Lecture 8 : Energy Dissipation, Equivalent Viscous Damping, Rate Independent Damping.Week 4:
Lecture 9 : Impulse Response function, Duhamel’s Integral, Example using MATLAB
Lecture 10 : Response due to Step and Ramp force.
Lecture 11 : Response due to Rectangle and Half Sinusoidal pulse force
Lecture 12 : Response due to Arbitrary support motionWeek 5:
Lecture 13 : Numerical techniques, Implicit and Explicit methods, Central Difference, Example with MATLAB Coding
Lecture 14 : Newmark - ß algorithm, Example with MATLAB Coding
Lecture 15 : Wilson - ? algorithm, Example with MATLAB CodingWeek 6:
Lecture 16 : Concept on Response Spectrum, Tripartite Response Spectrum, Important Features.
Lecture 17 : Elastic Design Spectrum, spectrum-compatible earthquake
Lecture 18 : Numerical Example in MATLAB.Week 7:
Lecture 19 : Hamilton Principle, Lagrange Equation
Lecture 20 : Coupled Equation of Motion
Lecture 21 : Rayleigh Damping, Caughey Damping, Non-Classical Damping.Week 8:
Lecture 22 : Natural Frequencies and Mode shapes of MDOF system
Lecture 23 : Orthogonality of Modes, Normalization of Modes, Modal Expansion of displacement.
Lecture 24 : Free Vibration of a Damped MDOF system. Week 9:
Lecture 25 : Response Analysis in the Time domain by modal superposition, Numerical Example in MATLAB
Lecture 26 : Response Analysis in the frequency domain, Numerical ExampleWeek 10:
Lecture 27 : Equation of Motions, Solution Strategy, example in MATLAB
Lecture 28 : Peak modal response, Modal combination rules - SRSS, CQC methods
Lecture 29 : Model reduction Technique: Static Condensation, Theory, and Example
Lecture 30 : Model reduction Technique: Dynamic Condensation, Theory, and Example in MATLABWeek 11:
Lecture 31 : Free Vibration – Eigen value problem
Lecture 32 : The vibration of a beam under different support conditions
Lecture 33 : Rayleigh’s Quotient, Approximate Method - Rayleigh’s Energy Method
Lecture 34 : Forced Vibration of a beamWeek 12:
Lecture 35 : Introduction to FE software
Lecture 36 : Response Spectrum Analysis of a multistoried building using FE software
Lecture 37 : Time History Analysis of a Multistoried building using FE software
Taught by
Prof. Arunasis Chakraborty
