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Scientific area of pertinence: ING-INF/13

This course addresses the modeling of vibrations in all kinds of structures from its fundamentals to its applications. This is an essential course for addressing a wide range of problems, from noise modeling and control, to the characterization of vibrations in resonating structures (such as musical instruments).

Module 1: “Fundamentals of vibration analysis” (5 CFU)

  • Free vibration of single-DOF linear systems. Procedure for deriving the differential equation of motion. The harmonic oscillator. Undamped and damped free vibration.
  • Forced vibration of single-dof linear systems. Frequency response. The superposition principle.
  • Two and multi-dof vibrating systems. Procedure for deriving the equations of motion. Matrix formulation. Free vibration of undamped systems: natural modes. Free damped vibration. Eigenvalue problem. Frequency response.
  • Modal superposition. Orthogonality of modal vectors. Coordinate transformation from physical to principal coordinates.

Module 2: Vibroacoustics of Musical Instruments (5 CFU)

  • Vibration and wave propagation in one-dimensional and two-dimensioanl structural elements. Transversal vibration of stretched strings, quasi-longitudinal vibration of bars, bending vibration of slender beams and thin plates.
  • Sound waves. The homogeneous acoustic wave equation. Sound pressure and particle velocity. Propagation of plane and spherical sound waves. Sound intensity and sound power. Fundamental acoustic source models.
  • Sound radiation from vibrating structures. General formulation of the vibroacoustic problem. Sound radiation from an infinite plate. Wave/boundary matching. Critical frequency. Sound radiation from finite plates. Radiation efficiency.
  • Experimental techniques in vibroacoustics. Fundamentals of experimental modal analysis. Sound intensity and sound power measurement. Sound source mapping through microphone arrays. Examples of application to stringed musical instruments.
  • Numerical methods in vibroacoustics. Introduction to finite-element and boundary-element methods. Examples of application to the simulation of the vibroacoustic behaviour of stringed musical instruments.