cod. 05974

Academic year 2011/12
2° year of course - Second semester
Academic discipline
Meccanica applicata alle macchine (ING-IND/13)
A scelta dello studente
Type of training activity
Student's choice
72 hours
of face-to-face activities
9 credits
course unit
in - - -

Learning objectives

The course gives the basics for the theoretical and experimental vibration analysis of mechanical systems


- - -

Course unit content

1. Vibrations of single-degree-of-freedom systems. Free and forced vibrations. Base excitation.
2. Linear systems, convolution integral and impulsive response. Integral transforms (Fourier and Laplace). Transfer function. Fourier series. Response of a damped single-degree-of-freedom system to generic excitation.
3. Discrete Fourier transform. Shannon theorem. Introduction to FFT. Aliasing, leakage and time windows.
4. Power spectral energy. Autopower spectrum and autocorrelation function. Cross-power spectrum and cross-correlation function. Averaging. Frequency response function (H1, H2 and HV). Coherence. Introduction to nonlinear systems: hardening and softening systems.
5. Condition monitoring of machines by vibration measurement. Application to rotating machines: imbalance, misalignment, runout, looseness, resonances. Damage of gearboxes and rolling-element bearings.
6. Vibrations of multi-degree-of-freedom systems. Equations of motion in matrix form. Free vibrations of conservative systems; reduction to a standard eigenvalue problem. Dynamic vibration absorber. Definite and semidefinite matrices. Properties of natural frequencies and modes. Normalization, orthogonality, expansion theorem. Linear transformation of coordinates; natural coordinates. Forced vibrations of conservative systems. Proportional damping. General damping and solution by transition matrix. Complex modes. Applications.
7. Experimental measurement of vibrations in laboratory. Measurement of time-varying signals, autopower spectrum, FRF, coherence. Experimental set-up. Instrumentations: accelerometers, force transducers, hammer for modal tests, electrodynamic exciter (shaker), power and charge amplifiers, front-end.

Vibrations of continuous systems: local and global discretization (Rayleigh-Ritz, Galerkin, FEM); vibrations of beams and thin-walled structures.
Introduction to large-amplitude vibrations and nonlinear phenomena.
Stability problems of systems with fluid-structure interaction: flutter and divergence of aeronautical and aerospace structures.
Applications to actual problems.
Experimental modal analysis on structures with high modal density.

Full programme

- - -


L. MEIROVITCH, 1986, Elements of Vibration Analysis, 2nd edition, McGraw Hill.
S. S Rao, Mechanical Vibrations (4th edition), Prentice Hall, 2004

Teaching methods

Classes, tutorials and laboratory experiences.

Assessment methods and criteria

Written exam on the program that can be integrated with assignments and reports of laboratory experiences or specific projects

Other information

- - -