Fundamentals of harmonic analysis.
Main problems in A/D conversion.
Study of linear time-invariant SDOF and MDOF systems.
Isolation and efficiency of mechanical suspensions.
Modeling with transfer matrices methods.
The finite element method.
Reduction techniques.
Fundamentals of dynamics of nonlinear systems.
Multibody systems: modelling, kinematics and dynamic analysis.
Representation of 2D and 3D mechanical systems in Multibody systems.
Recommended books:
E. Funaioli ed altri, "Meccanica applicata alle macchine", vol. II, Ed. Patron Bologna
D.J. Ewins, "Modal Testing - Theory, Practice and Application", Second Edition, Research Studies Press LTD.
G. Genta, "Vibration of Structures and Machines - Practical Aspects", Second Edition, Springer-Verlag
Cyril M. Harris, "Shock and Vibration Handbook", Fourth Edition, Mc.GRAW-HILL
Handouts provided by the Teacher available at the e-learning website of the University of Florence:
http://e-l.unifi.it/
(section "Corso Magistrale in Ingegneria Meccanica")
Learning Objectives
The purpose of the course is to provide the knowledge needed to understand the main dynamic modeling techniques and theoretical and experimental modal analysis. Another purpose is to provide the student with the ability to understand and analyze any problem concerning the vibrations reduction techniques, also introducing the issues concerning non-linear systems. It also dealt with modeling of mechanical systems through Multibody technique.
Prerequisites
Knowledge of Physics (mechanics), analytical mechanics, geometry (vectors), Linear Algebra (Matrix Calculus)
Teaching Methods
Lectures in the classroom
Further information
EXAMINATIONS CALENDAR
2014-2015
(I) session
Friday, January 9, 2015 (registration from 10/12/2014 to 5/01/2015)
(II) session
Tuesday, January 27, 2015 (registration from 10/12/2014 to 23/01/2015)
(III) session
Tuesday, February 17, 2015 (registration from 10/12/2014 to 13/02/2015)
(IV) session
Monday, June 22, 2015 (registration from 15/05/2015 to 17/06/2015)
(V) session
Friday, July 3, 2015 (registration from 15/05/2015 to 29/06/2015)
(VI) session
Friday, July 17, 2015 (registration from 15/05/2015 to 12/07/2015)
(VII) session
Friday, September 4, 2015 (registration from 10/08/2015 to 29/08/2015)
Online exam registration is required through University of Florence online registration service. Alternatively (only in case of problems) you can send an e-mail to the Teacher the request within the deadline(e-mail address mirko.rinchi@unifi.it).
Before registering, please read the rules (including the detailed examinations calendar). The document (“Regolamento”) can be found among the files in “Materiale didattico” section of the Course in the e-learing website of the University of Florence.
An e-mail communication to the Teacher is however welcome.
The dates of the summer sessions (IV-VII) may have light slips.
Any change in examinations calendar will be promptly made known through changes in University of Florence online registration service.
The students eventually rejected are not encouraged to join the very adjacent examination session (at least one month between two exams).
Type of Assessment
Oral examination
Course program
Topics covered in the Course are:
Fundamentals of harmonic analysis: periodic, harmonic and transient analog signals.
Introduction to signal frequency spectrum and spectral analysis concepts. Series and Fourier Transform. Meanings and problems regarding A/D conversion. The Discrete Fourier Transform. Aliasing and Leakage.
Introduction to physical models, mathematical models, modal and FRF models.
Dynamics of linear SDOF systems (Single Degree of Freedom) by using the simplest dynamic model characterized by time-invariant parameters.
Solution of the equation of motion: study of free and forced behavior of SDOF systems. Viscous damping. Logarithmic decrement and half-power method. Frequency response functions (FRFs): calculation and representation through the Bode diagrams and on Nyquist's plan.
Natural frequency, and resonance. Dynamic models of accelerometers and seismometers as SDOF systems. Piezoelectric accelerometer. Vibration isolation through elastic suspension.
Linear MDOF systems (Multi Degrees Of Freedom) with viscous and structural damping. Free and forced behavior. Natural frequencies and vibration modes of the system. Modal matrix decoupling. Principal and normal coordinates. Resonances and anti-resonances.
Overview on experimental modal analysis: transducers and measuring chains. Transducers for structural excitation signals (transients and random). Main setup for modal test analysis. Parametric identification techniques.
Modeling techniques through transfer matrices: Holzer's method for torsional vibrations, Myklestad method for bending vibrations.
Vibrations of distributed parameters systems: vibrating string, rotary, longitudinal and bending oscillations of a beam with constant cross section.
Finite element method (FEM): single finite element equations. Rotation and assembly of the various elements equations in order to obtain the complete dynamical model of the system. Introduction of mechanical constraints.
Nodal and modal reduction techniques.
Vibrations in nonlinear systems: non-linear elastic behavior of a spring and friction. Exact and approximate techniques to solve nonlinear dynamic equations.
Definition of multibody system: kinematics and dynamic analysis.
Fundamentals of kinematics: reference frames, arrays, orientation by means of Euler angles and/or Euler parameters in order to model 3D multibody systems.
Kinematic analysis of 2D multibody systems: constraint equations for the main kinematic joints. Solution of velocity and acceleration problems.
Kinematic analysis of 3D multibody systems: joint reference system and definition of constraint equations for the main kinematic joints.
Analytical Dynamics: virtual work principle, D'Alambert principle, Hamilton's principle, Lagrange equations.
Identification of multibody systems dynamic equations through Lagrange multipliers technique. Lagrange multipliers and joint reaction forces.
Basics on numerical solution techniques for differential equations.