Learning objectives
The students will develop skills for numerical and experimental modelling of mechanical systems
Prerequisites
Mathematical analysis, physics, geometry, rational mechanics and applied mechanics are recommended.
Course unit content
The course is an advanced course in dynamics of mechanical systems.
The students will be introduced to the process of modelling mechanical systems, developing the governing differential equations associated with dynamic mechanical systems, and studying suitable methods to solve the systems governing equation.
Full programme
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
Rayleigh-Ritz method
Linearisation of the equations of motion
Linear systems: convolution integral and impulse response
Fourier transform and other transforms
Classifications of signals
Time domain analysis
Frequency domain analysis
Frequency response of a dynamic system
Convolution
Auto-spectrum and cross-spectrum
Coherence
Modal analysis
Identification of the modal parameters
Frequency Response Function
Introduction to matlab
Nonlinear problems
Introduction to wave motion in elastic solids
Basic concept of the finite element method
Bibliography
Suggested textbooks
Ottorino Sesini , Meccanica applicata alle macchine, Milano : Casa editrice ambrosiana
L. Meirovitch, Elements of Vibration Analysis, 2nd edition, McGraw Hill, 1986.
D.J. Ewins, Modal Testing:Theory, Practice and Applications - second edition, Research Studioes Press ltd., Brüel & Kjær
K.F. Graff, Wave Motion in Elastic Solids, Dover, 1991.
In-depth textbooks
C. Lanzcos, The Variational Principles of Mechanics, Dover, 1986.
A. Papoulis, The Fourier integral and its applications , McGraw-Hill, 1987.
Teaching methods
Lectures.
Some exercises will be carried out in the lab, where the students will perform some modal analysis and use the software MATLAB
Assessment methods and criteria
The exam consists in the presention of a project and an oral exam at the end of the course.
Other information
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