Coordinator: Prof. Antonio Vicino
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Linear Dynamics And Vibration Analysis


Monica Malvezzi
University of Siena - Dipartimento di Ingegneria dell'Informazione e Scienze Matematiche
Course Type
Type A/B
April 15-17-21-23-24-28-30 - h. 9.30-12.30
Objective: Provide an introduction to the analysis of dynamics and vibrations of mechanical systems. After the course, students will be able to choose the more suitable representation for the dynamics of a mechanical system (lumped parameter models, continuous models, FEM) and analyze free and forced vibrations of linear multi-degree of freedom models of mechanical systems and matrix eigenvalue problems.

Schedule: Day 1 - Single DOF systems. - Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. - Free and forced vibrations of single DOF systems: main definitions and some examples (accelerometer, seismograph, vehicle suspension). (est. 4h)

Day 2 - Multiple DOF system, analysis. - Multiple DOF systems: main definitions and classification, lumped parameter models, continuous models, Finite Element models. Free and forced vibration of linear damped multi-DOF mechanical systems. (est. 4h)

Day 3 - Building the mathematical model, discrete systems. - Building a lumped parameter model of a mechanical system: Lagrange's equations for systems of particles and rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Inertia, stiffness and damping models. (est. 4h)

Day 5 - Building the mathematical model, continuous systems with FEM model. - Continuous systems, introduction - Vibration analysis with Finite Element Analysis: basic theory and applications with Comsol. (est 4h)

Day 4 - Building the mathematical model, continuous systems, other methods. - From continuous to lumped parameter models: examples (Holtzer model for torsional vibrations and Myklestad - Prohl model for bending vibrations of rotating shafts). (est. 4h )

Exam: application of one of the modeling tools learned in the course for the analysis of a specific mechanical system.



PhD Students/Alumni

Dip. Ingegneria dell'Informazione e Scienze Matematiche - Via Roma, 56 53100 SIENA - Italy