Warminski J. Numerical modelling of mechanical systems 2015 torrent

Textbook in PDF format

Modelling of dynamical systems — introduction and basic definitions.
Physical model.
Mathematical model.
Numerical model.
Model validation.
Calculation results and their presentation.
Bibliography.
Ordinary differential equations — methods of analysis.
Basic concepts in dynamics of mechanical systems.
Stability of singular points.
Singular points classification — phase plane.
Node.
Focus.
Centre.
Saddle.
Singular points in case of mathematical pendulum.
Numerical methods.
Representation of numbers, conditioning of the numerical problem and stability of algorithms.
Numerical methods for ordinary differential equations — initial problem.
Euler method.
Runge-Kutta method.
Self-training problems.
Bibliography.
Partial differential equations. Finite-difference method.
Partial differential equations.
Finite-difference method.
Example — string vibrations.
Bibliography.
Analysis of non-linear signals.
Introduction.
Fourier’s Transform.
Proposal of an exercise.
Method of delayed coordinates and recurrence diagrams.
Proposal of an exercise.
Method of multi-scale entropy MSE and CMSE.
Bibliography.
Foundations of finite element method.
Overview.
Linear static analysis of a truss structure.
Assumptions and limitations of linear analysis.
Uniaxial bar element.
Global stiffness matrix of the structure.
Boundary conditions and reduced global stiffness matrix of the structure.
Truss equilibrium equation.
Element strain and stress; axial force.
Flexure elements. Linear analysis of beams.
Assumptions.
Shape functions of the beam element.
Stiffness matrix of the beam element.
Distributed load.
Bibliography