Paul Filippi

Boundary Integral Equations Method for the Analysis of Acoustic Scattering from Line-2 Elastic Targets

The prediction of the acoustic scattering from elastic structures is a recurrent problem of practical importance as, for example, in underwater detection and target identification. We aim at setting out the diffraction problem of a transient acoustic wave by an axisymmetric shell composed of a cylinder bounded by hemispherical endcaps, called Line-2. Its time-dependent response is expanded in terms of the resonance modes of the fluid-loaded structure. The latter are well suited when the structure is submerged in a heavy fluid: it is an alternative to modal methods whose expansions as series of natural modes of the in vacuo shell are much better for describing the interaction between a structure and a light fluid. The resonance frequencies are defined as solutions of the nonlinear eigenvalue problem described by the set of homogeneous equations governing the structure displacement coupled to the acoustic radiated pressure. The resonance modes of the coupled system are the corresponding eigenvectors.Both hemisphere and cylinder equations are modeled by the approximation of Donnel and Mushtari which governs thin shells oscillations. The modeling of the sound pressure by a hybrid potential integral representation leads to a system of integro-differential equations defined on the surface of the structure only (boundary integral equations). The unknowns, the hybrid potential density as well as the shell displacement vector, are developed into Fourier series with respect to the natural cylindrical coordinate. Each angular component of the unknown functions is then expanded as series of Legendre polynomials, the coefficients of which are calculated thanks to a Galerkin method derived from the energetic form of the equations.The whole method can also be applied to predict the response of the coupled structure to a harmonic or a random excitation.

Acoustics: Basic Physics, Theory, and Methods

Foreword. Preface. Jean-Pierre Lefebvre, Physical Basis of Acoustics. Acoustics of Enclosures. Diffraction of Acoustic Waves and Boundary Integral Equations. Dominique Habault, Outdoor Sound Propagation. Dominique Habault, Analytic Expansions and Approximation Methods. Dominique Habault, Boundary Integral Equation Methods--Numerical Techniques. Aime Bergassoli, Introduction to Guided Waves. Paul J.T. Filippi, Transmission and Radiation of Sound by Thin Plates. Problems. Dominique Habault and Paul J.T. Filippi, Mathematical Appendix: Notations and Definitions. Bibliography. Index.

Chapter 9 – Problems

(15) 1. Redesign the following schema into first normal form. List any functional or multivalued dependencies that you assume. Also list all referential-integrity constraints that should be present in the first-normal-form schema. Answer To put the schema into first normal form, we flatten all the attributes into a single relation schema. We rename the attributes for the sake of clarity. cname is Children.name, and bday, bmonth, byear are the Birthday attributes. stype is Skills.type, and xyear and xcity are the Exams attributes. The FDs and multivalued dependencies we assume are: The FD captures the fact that a child has a unique birthday, under the assumption that one employee cannot have two children of the same name. The MVDs capture the fact there is no relationship between the children of an employee and his or her skills-information. (15) 2. Consider the schemas for the table people, and the tables students and teachers, which were created under people using the following SQL. Give a relational schema in 3NF that represents the same information. Recall the constraints on subtables, and give all constraints that must be imposed on the relational schema so that every database instance of the relational schema can also be represented by an instance of the schema with inheritance. create type P erson (name varchar(20),address varchar(20)) create type Student under P erson (degree varchar(20),department varchar(20)) create type T eacher under P erson (salary integer,department varchar(20)) create table people of P erson

Sound transmission through a thin baffled plate: Comparison of a light fluid approximation with the numerical solution of the exact equations and with experimental results

A thin elastic rectangular plate, with clamped boundaries, extended by an infinite perfectly rigid plane baffle is considered. Both half‐spaces are occupied by a gas. A sound source is located on one side of the plate. One is interested by the sound field transmitted through the plate. The boundary value problem governing the system is solved by two methods: A boundary element method, which gives a numerical solution of the exact equations; and a series representation of the solution in terms of the fluid‐loaded plate resonance modes, an analytical approximation which is obtained by a perturbation technique (the ratio of the gas density to the surface mass of the plate being the small parameter). The discrepency between the two methods does exceed 1 dB or so: This shows that the perturbation method, which is much less time consuming than the BEM, is a very powerful prediction tool. The Laboratoire de Mecanique et d’Acoustique in Marseille has two anechoic rooms, which are connected by an aperture. A steel...