Functions Derivation Basic derivation theorems. Multivariable functions Introduction to differential equations. Particle and Rigid Bodies Kinematics. Particle and Rigid Bodies Dynamics.

By the end of this subject, students will be able to have: 1. Knowledge and understanding of linear differential equations which are applicable in mechanical vibration problems 2. Knowledge and understanding of key aspects of mechanical vibrations fundamentals; 3. The ability to apply their knowledge and understanding to identify, formulate and solve problems of mechanical vibrations using established methods; 4. The ability to combine theory and practice to solve problems of mechanical vibrations; 5. An understanding of applicable techniques and methods in mechanical vibrations, and of their limitations;

1.- Introduction to differential calculus 1.1.- Functions of a Variable 1.2.- Mathematical Models 1.3.- Classification of Differential Equations 1.4.- Linear Ordinary Differential Equations 1.5.- Solution of Differential Equations 1.6.- Solution of Homogeneous First Order Diff Eq. 1.7.- Solution of Nonhomogeneous Linear First Order Diff Eq. 1.8.- Solution of Second Order Diff. Eq. 1.9.- Integration methods 2.- Numerical methods for solving differential equations 2.1.- Introduction 2.2.- Euler's method 2.3.- Taylor's method 2.4.- Runge-Kutta methods 3.- Introduction to MATLAB 3.1.- Introduction 3.2.- General Rules 3.3.- Basic Operations 3.4.- Output formats 3.5.- Matrices and Vectors 3.6.- Graphics in MATLAB 3.7.- Programming in MATLAB 3.8.- SIMULINK 4.- Solution of Differential Equations using MATLAB 4.1.- Introduction 4.2.- ODE function 4.3.- Example of a first order equation 4.4.- Solution of second order equations 4.5.- Solution of equations by SIMULINK 5.- Introduction to mechanical vibrations: 5.1.- Introduction 5.2.- Classification of vibrations 5.3.- Components of an oscillatory system 5.4.- Simple Harmonic Motion (SHM) 5.5.- Energy of a Simple Harmonic Movement 5.6.- Nonlinear vibrations 6.- Damped mechanical vibrations and forced vibrations 6.1.- Damped harmonic oscillator 6.2.- Differential equation of movement 6.3.- Damping coefficient 6.4.- Solution to the Differential Equation of Motion 6.5.- Logarithmic Decrease 6.6.- Forced vibrations 6.7.- Transmissibility coefficient 6.8.- Resonance 7.- Systems of 2 Degrees of Freedom and N Degrees of Freedom 7.1.- Introduction 7.2.- Undamped free vibrations for 2 DOF 7.3.- Forced undamped vibrations for 2 DOF 7.4.- Damped forced vibrations for 2 DOF 7.5.- N DOF Vibrations systems

Master class Classroom exercises Laboratories exercices Personal work. Team Work