DYNAMICS OF MECHANICAL SYSTEMS
Learning outcomes of the course unit
The course is an advanced course in dynamics of mechanical systems.
The students will be introduced to the processes of modelling mechanical system, to the development of the governing differential equations associated with dynamic mechanical systems and to the definition of possible methods of solution to the systems governing equation.
Mathematical analysis, physics, geometry, rational mechanics and applied mechanics are recommended.
Course contents summary
Introduction and definitions
Examples of mechanical systems
Different approaches to the dynamical study of mechanical systems
Principles of dynamics: general considerations.
Principle of virtual work, D’Alambert’s principle, Hamilton’s principle
Lagrange equations for lumped and continuous systems
Linearisation of the equations of motion
Linear systems: convolution integral and impulse response
Fourier transform and other transforms
Introduction to frequency analysis
Wave motion in elastic solids
Wave and vibration in strings, bars and plates
Group velocity and energy flow
Reflection and transmission of elastic waves
Wave motion in periodic structures
Basic concept of the finite element method
Ottorino Sesini , Meccanica applicata alle macchine, Milano : Casa editrice ambrosiana
L. Meirovitch, Elements of Vibration Analysis, 2nd edition, McGraw Hill, 1986.
K.F. Graff, Wave Motion in Elastic Solids, Dover, 1991.
C. Lanzcos, The Variational Principles of Mechanics, Dover, 1986.
A. Papoulis, The Fourier integral and its applications , McGraw-Hill, 1987.
Some exercises will be carried out in the lab, where the students will perform some numerical exercises using the software MATLAB
The exam consists in a written exam during the course and an oral exam at the end of the course.