University of Siena - Dipartimento di Ingegneria dell'Informazione e Scienze Matematiche
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.
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.