Finite Element method for vibration and Stability analyses


Lecture 1 - Equations of motion using Hamilton’s principle


Lecture 2 - Equations of motion for continuous systems and Rayleigh’s quotient


Lecture 3 - Rayleigh Ritz method and method of weighted residuals


Lecture 4 - FEM: motivations. Analysis of axially vibrating rods and Euler-Bernoulli beams


Lecture 5 - Beam elements. Reference systm. Assembly of matrices. Imposition of BCS. Final equation of motion


Lecture 6 - FE modelling of planar structures


Lecture 7 - FE modelling of planar structures (Continued...)


Lecture 8 - FRF-s and damping models-1


Lecture 9 - FRF-s and damping models-2


Lecture 10 - Material damping models. Dynamic stiffness and transfer matrices


Lecture 11 - Twisting of circular bars and rectangular bars. Analysis of grids


Lecture 12 - 3D frames


Lecture 13 - Mathematical preliminaries and terminologies; Euler’s forward and backward difference methods


Lecture 14 - Forward and backward Euler method. Central difference method


Lecture 15 - Second order implicit methods


Lecture 16 - Energy conservation. Nonlinear systems


Lecture 17 - Model reduction schemes


Lecture 18 - Substructuring schemes


Lecture 19 - Plane stress models


Lecture 20 - Plane stress models (Continued...)


Lecture 21 - 3d Solid element


Lecture 22 - Axisymmetric models. Plate bending elements.


Lecture 23 - Plate bending elements (Continued...)


Lecture 24 - Plate bending elements (Continued...)


Lecture 25 - Plate bending elements (Continued...)


Lecture 26 - Introduction


Lecture 27 - Introduction (Continued...)


Lecture 28 - Nonlinear dynamical systems, fixed points and bifurcations


Lecture 29 - Energy methods in stability analysis


Lecture 30 - FEM for stability analysis. Euler-Bernoulli beam and general formulations


Lecture 31 - 3D beam element; plate element; imperfection sensitive structures; beams on elastic foundations; rings and arches


Lecture 32 - Dynamic analysis of stability and analysis of time varying systems


Lecture 33 - Dynamic analysis of stability and analysis of time varying systems


Lecture 34 - FE modelling of vehicle structure interactions


Lecture 35 - Inverse response sensitivity analysis


Lecture 36 - Inverse response sensitivity analysis (Continued...)


Lecture 37 - Introduction and review of continuum mechanics


Lecture 38 - Review of measures of strain and stress; balance laws


Lecture 39 - Total and updated Lagrangian formulations


Lecture 40 - Closure