## Maths for acoustics I

### Présentation

13 courses of two hours mixing lectures and exercises divided in 6 chapters: - Introduction: Which problems do we want to solve ? - Finite dof systems: Mass-spring - Continuous systems: Strings, Acoustic cavities; beams, 2D and 3D problems - Strategies (analytical/numerical) to solve these problems - Matrices (Key properties of matrices, Exponential and Transfer Matrices, Key matrix fac- torisation techniques) - n degrees of freedom systems (Exponential Matrix / Transfer matrix, Modes of a finite- degree of freedom system, Resolution ) - Inner Euclidean and Hilbert Spaces (Definition, Inner products and physical systems)

### Objectifs

Expected skills : –    Advanced Matrix calculus –    Main basis of analytical resolutions methods for finite and infinite number of degrees of freedom problems (in 1D, 2D and 3D) –    Techniques of projection (Inner-products, modes) –    Notions on finite difference schemes: truncation error, order of accuracy, spectral ac- curacy, and grid resolution. - Expected knowledge : –    Be able to find the analytical expression of simple and more advanced 1D acoustic problems (strings, beams and cavities of various shapes and boundary conditions) –    Be able to construct standard finite-difference schemes (temporal and spatial). –    Be able to control the accuracy of a finite difference approximation by selecting the scheme and the grid for 1D acoustic problems.

Maths refresher course, especially Matrix manipulation, Calculus and Integration

### Examens

Written exam - 2 hours - Personal notes allowed (except correction of exercises)

### Informations complémentaires

Literature References : G. Strang, Introduction à l’algèbre linéaire, Ecole Polytechnique De Montréal, 2015

### En bref

Crédits ECTS 3.0

Nombre d'heures 30.0

Période de l'année
Automne

• Le Mans

On-line course