Overview

ABOUT THE COURSE:Structural dynamics is a course that focuses on the behavior of structures subjected to dynamic loads. The course covers the analysis of Single Degree of Freedom (SDOF), Multiple Degrees of Freedom (MDOF), and Continuous Systems, and provides a fundamental understanding of the dynamic response of structures. Students learn how to analyze the response of structures under various types of dynamic loads, including earthquake, wind etc. The knowledge gained from this course is essential for the design and analysis of any structure that may be subjected to dynamic loads.INTENDED AUDIENCE: B.tech, M.tech, and Ph.D. studentsPREREQUISITES: Structural analysis, Differential equations, Linear algebraINDUSTRY SUPPORT: Any mechanical or civil company working on vibration problem, such as RDSO, RVNL, DRDO, etc

Syllabus

Week 1: SDOF
Module 1:SDOF system intro and undamped system
Module 2:Damped SDOF( underdamped, critical damping, overdamped)
Week 2:
Module 3:Phase portrait, Kinetic and potential energ, time period, damped forced SDOF, DAF
Module 4:DAF, phase angle, transient and steady state vibration, constant force
Week 3:Numerical methods
Module 5:D operator, different types of loading, Duhamel introduction
Module 6: Duhamel cont., problem solved-const. force-duhamel-MATLAB
Week 4:
Module 7: Intro to Base excitation, numerical integration(euler's method, explicit scheme method, state space formulation, central difference, implicit-average acc- linear)
Module 8: Newmark B method, ODE solver basics
Week 5:
Module 9: Runga-Kutta method, comp. of numerical techniques in MATLAB, intro to Fourier series
Module 10:Cont. Fourier series, concept of orthogonal and ortho normal vectors, Fourier transform
Week 6:
Module 11:Cont. of Fourier transformation
MDOF
Module 12:MDOF system (Introduction and formulation), Eigen value analysis, into to modal analysis
Week 7:
Module 13:Modal analysis and MATLAB demonstration on eigen value analysis, mass normalised and displacement normalised eigen vector
Module 14: Modal participation factor, base excitation MDOF, FRF, problem solving and determination of the mode shapes
Week 8:
Module 15: Intro to response spectra, discussion of the codal provissions, calculation of the restoring force, Construction of response spectra using MATLAB
Module 16: Introduction to different damping model(Rayleigh, stiffness proportional, mass proportional)
Week 9:
Module 17:Fundamental of vibration control and H_infinity
Module 18: Base isolation and tune mass damper
Week 10:Continuous system
Module 19: Intro to continous system and derivation of the equation of motion of bar, separation of variables and application of boundary conditions
Module 20:Continous system (Bar problem), Natural frequency, mode shape
Week 11:
Module 21:Derivation of beam Euler-Bernoulli and Timoshenko beam continuous weak form
Module 22: Equation of motion of a beam, modal analysis of a beam, Transfer matrix, natural frequency using transfer, spectral element matrix
Module 23:Cont. to spectral and transfer matrix, beam with tip mass problem
Week 12:
Module 24: Dynamic stiffness matrix from FEM, SEM and MATLAB implementation
Module 25:Spectral and transfer interchange and assembling in spectral (MATLAB)
Module 26:Galerkian and Rayleigh Ritz method, strong form to weak form,
Module 27:Continuous damping