Mechanical Systems Dynamics

Synthetic program:

DINAMICA DEI SISTEMI MECCANICI
Il corso fornisce nozioni avanzate relative alle vibrazioni dei sistemi meccanici, con particolare riferimento alle vibrazioni dei sistemi discreti a più gradi di libertà e dei sistemi continui, rendendo disponibili per l'allievo strumenti di analisi e modellazione di sistemi complessi a corpi rigidi (con le moderne tecniche multicorpo) e deformabili (con l'approccio ad elementi finiti). Alcune nozioni essenziali inerenti la dinamica di sistemi non lineari ed esempi applicativi inerenti la dinamica di macchine e strutture soggette a campi di forze non conservativi vengono fornite a completamento del percorso formativo avanzato sulla dinamica dei sistemi.

Vibration analysis of discrete systems
Free and forced vibration of single-dof and multi-dof systems. Modal superposition approach and principal coordinates formulation of the equations of motion.

Vibration analysis of one-dimensional continuous systems
Transverse vibration of strings. Axial vibration of bars. Torsional vibration of circular shafts. Bending vibration of slender beams (Euler-Bernoulli formulation). Wave propagation and standing wave solutions. Free vibration: natural frequencies and vibration modes for different boundary conditions, transient response to assigned initial conditions. Forced vibration: steady-state response to harmonic input. Modal superposition approach and principal coordinates formulation of the equations of motion.

Experimental modal analysis
Overview of test procedures and Frequency Response Function (FRF) estimation. Mathematical formulation of the FRF based on modal superposition. Algorithms for frequency-domain modal parameters identification (multi-mode curve fitting method and simplified single-mode identification procedure).

The finite element method in structural dynamics
General introduction to the finite element discretization of continuous systems. Detailed formulation of the 6-dof beam element for in-plane analysis: shape functions for axial and bending deformation, mass and stiffness matrices. Procedure for developing the finite element model of a structure: global and local reference systems, work-equivalent nodal forces, matrix assembling, structural damping model, boundary conditions and matrix partition. Classical dynamic analysis: natural frequencies and vibration modes, frequency response.

Three-dimensional dynamics of a rigid body
Kinetic energy and inertia tensor. 3D kinematics: rotation matrix and body angular speed. Dynamics of a rigid body rotating about a fixed axis.

Rotordynamics
Overview of the dynamic problems in rotating machinery. Balancing conditions and balancing procedures for a rigid rotor. Bending critical speeds and balancing procedures for a flexible rotor.