Portale di Ateneo - En.Unibs.it

Introduction to the study of the vibrations
Degrees of freedom of a vibrating system, vibration classification, springs and their combinations, dampers, use of the complex algebra for harmonic motion analysis, definitions and terminology, methods for writing the motion equations of a mechanical system (dynamic equilibrium of forces, energy methods, Lagrangian approach).

Free vibrations of systems with one degree of freedom
Undamped free vibration, natural frequency, free vibrations with viscous damping, underdamped and overdamped systems, critical damping, root locus in the complex plane, estimation of the damping factor using the logarithmic decrement method.

Vibration of single degree of freedom systems with harmonic excitation
Vibrations due to a sinusoidal force applied to the mass, vibrations produced by an eccentric mass rotating at constant speed, vibrations generated by the harmonic motion of the base, resonance, frequency response and its graphical representation, vector diagrams, energy considerations, force and displacement transmissibility, critical speed of a rotating shaft.

Vibration of single degree of freedom systems with periodic and non-periodic arbitrary excitation
Response to a periodic non-harmonic force, practical applications for cam mechanisms, response to typical excitations (impulse, step, ramp), convolution integral, study of the transient, integration the motion equation by numerical methods.

Free and forced vibrations of multi-degree of freedom
Motion equations for systems with many degrees of freedom, matrix approach, static and dynamic coupling, natural frequencies and mode shapes, solution of the eigenvalue-eigenvector problem, free motion of undamped systems, semidefinite systems and their properties, free vibrations of damped systems, steady state vibrations with harmonic excitation (undamped and damped case), resonance, dynamic vibration absorbers, modal approach, orthogonality of modal vectors with respect to mass and stiffness matrices, principal coordinates solution for undamped cases, Rayleigh hypotesis for damped cases, transient vibrations for generic forcing conditions, numerical solution of the motion equations.

Vibrations of mono-dimensional continuous systems
Vibrations of strings, axial vibrations of rods, torsional vibrations of shafts, flexural vibrations of beams, calculations of natural frequencies and mode shapes for various constraint conditions.