• 052841 - VIBROACOUSTICS

The aim of the course is to introduce students to engineering methods for vibration and sound radiation analysis of continuous structures. Both analytical/numerical models and experimental techniques are covered and particular attention is given to examples and applications, especially in the field of string musical instruments. Each topic is treated theoretically and practically, through traditional lectures and experimental/computer labs.

The course will provide students with:

1. a knowledge of the modelling approaches to vibration analysis of continuous systems (DD1);
2. an understanding of the basic physical principles of sound radiation from a vibrating structure (DD1);
3. the ability to apply theoretical knowledge to the handling of complex vibroacoustic problems in real structures (DD2, DD3);
4. the ability to perform standard vibration and sound measurements and to critically apply data processing techniques for modal parameters extraction or sound analysis (DD2, DD3);
5. an opportunity to develop skills in summarizing and presenting the results achieved during the lab activities (DD4).

Vibration and waves in one-dimensional continuous systems

The partial differential equation governing transverse vibration of stretched strings and axial vibration of bars (one-dimensional wave equation). Traveling waves and standing waves. Wave propagation speed, wavenumber, mechanical impedance. Transmission and reflection at an impedance change. Natural frequencies and vibration modes for different boundary conditions. The partial differential equation governing bending vibration of slender beams (Euler-Bernoulli beam). Dispersion and evanescent waves. Vibration modes, principal coordinates and modal superposition approach.

Vibration and waves in two-dimensional continuous systems

The partial differential equation governing bending vibration of thin plates (Kirchhoff plate). Bending waves propagation, the wavenumber vector, point mobility. Bending vibration of finite plates. Vibration modes of plates with different geometry and boundary conditions. Theoretical soundboard models for stringed instruments. Introduction to finite element method and examples of application to musical instruments.

Sound radiation from vibrating structures

General formulation of the problem. Sound radiation from an infinite plate. Wave/boundary matching. Critical frequency. Sound radiation from finite plates. Radiation efficiency. Introduction to the boundary element method and examples of application to the simulation of the vibroacoustic behaviour of musical instruments.

Experimental techniques

Fundamentals of experimental modal analysis: test equipment and test procedure, data processing and identification algorithms. Sound intensity and sound power measurement techniques. Practical examples relevant to stringed musical instruments.

The topics covered by the first module (Fundamentals of Vibration Analysis) are prerequisites to the second one (Vibroacoustics).

In addition to traditional lectures, the course includes experimental and computer labs, focused on specific methodologies, case studies or practical applications. Students are requested to prepare short reports on the assignments given during the labs, to be delivered at the final exam. The exam consists of an oral test, which includes a discussion on lab reports.

With reference to the expected learning outcomes: the oral exam is intended to verify items 1, 2 and 3, while items 4 and 5 will be checked during the discussion on lab reports.