Finite Element and Boundary Methods in Structural Acoustics and Vibration

Effectively Construct Integral Formulations Suitable for Numerical Implementation Finite Element and Boundary Methods in Structural Acoustics and Vibration provides a unique and in-depth presentation of the finite element method (FEM) and the boundary element method (BEM) in structural acoustics and vibrations. It illustrates the principles using a logical and progressive methodology which leads to a thorough understanding of their physical and mathematical principles and their implementation to solve a wide range of problems in structural acoustics and vibration. Addresses Typical Acoustics, Electrodynamics, and Poroelasticity Problems It is written for final-year undergraduate and graduate students, and also for engineers and scientists in research and practice who want to understand the principles and use of the FEM and the BEM in structural acoustics and vibrations. It is also useful for researchers and software engineers developing FEM/BEM tools in structural acoustics and vibration. This text: Reviews current computational methods in acoustics and vibrations with an emphasis on their frequency domains of applications, limitations, and advantages Presents the basic equations governing linear acoustics, vibrations, and poroelasticity Introduces the fundamental concepts of the FEM and the BEM in acoustics Covers direct, indirect, and variational formulations in depth and their implementation and use are illustrated using various acoustic radiation and scattering problems Addresses the exterior coupled structural–acoustics problem and presents several practical examples to demonstrate the use of coupled FEM/BEM tools, and more Finite Element and Boundary Methods in Structural Acoustics and Vibration utilizes authors with extensive experience in developing FEM- and BEM-based formulations and codes and can assist you in effectively solving structural acoustics and vibration problems. The content and methodology have been thoroughly class tested with graduate students at University of Sherbrooke for over ten years.

IntroductionComputational vibroacousticsOverview of the bookReferencesBasic equations of structural acoustics and vibrationIntroductionLinear acousticsLinear elastodynamicsLinear poroelasticityElasto-acoustic couplingPoro-elasto-acoustic couplingConclusionReferencesIntegral formulations of the problem of structural acoustics and vibrationsIntroductionBasic conceptsStrong integral formulationWeak integral formulationConstruction of the weak integral formulationFunctional associated with an integral formulation: Stationarity PrinciplePrinciple of virtual workPrinciple of minimum potential energyHamilton’s principleConclusionA: Methods of integral approximations—Example 41B: Various integral theorems and vector identitiesC: Derivation of Hamilton’s principle from the principle of virtual workD: Lagrange’s equations (1D)ReferencesThe finite element method: An introductionIntroductionFinite element solution of the one-dimensional acoustic wave propagation problemConclusionA: Direct approach for spring elementsB: Examples of typical 1D problemsC: Application to one-dimensional acoustic wave propagation problemSolving uncoupled structural acoustics and vibration problems using the finite element methodIntroductionThree-dimensional wave equation: General considerationsConvergence considerationsCalculation of acoustic and vibratory indicatorsExamples of applicationsConclusionA: Usual shape functions for Lagrange three-dimensional FEsB: Classic shape functions for two-dimensional elements C: Numerical integration using Gauss-type quadrature rulesD: Calculation of elementary matrices—three-dimensional wave propagation problemE: AssemblingReferencesInterior structural acoustic couplingIntroductionThe different types of fluid-structure interaction problemsClassic formulationsCalculation of the forced response: Modal expansion using uncoupled modesCalculation of the added massCalculation of the forced response using coupled modesExamples of applicationsConclusionA: Example of a coupled fluid-structure problem—Piston-spring system attached to an acoustic cavityReferencesSolving structural acoustics and vibration problems using the boundary element methodIntegral formulation for Helmholtz equationDirect integral formulation for the interior problemDirect integral formulation for the exterior problemDirect integral formulation for the scattering problemIndirect integral formulationsNumerical implementation: Collocation methodVariational formulation of integral equationsStructures in presence of rigid bafflesCalculation of acoustic and vibratory indicatorsUniqueness problemSolving multifrequency problems using BEMPractical considerationsExamples of applicationsConclusionA: Proof of B: Convergence of the integral involving the normal derivative of the Green’s function in EquationC. Expressions of the reduced shape functionsD. Calculation of E: Calculation of for a structure in contact with an infinite rigid baffleF: Numerical quadrature of G: Proof of formulaH: Simple calculation of the radiated acoustic power by a baffled panel based on Rayleigh’s integralRadiation of a baffled circular pistonReferencesProblem of exterior couplingIntroductionEquations of the problem of fluid-structure exterior couplingVariational formulation of the structure equationsFEM-BEM couplingFEM-VBEM couplingFEM-VBEM approach for fluid-poroelastic or fluid-fluid exterior couplingPractical considerations for the numerical implementationExamples of applicationsConclusionA: Calculation of the vibroacoustic response of an elastic sphere excited by a plane wave and coupled to internal and external fluidsReferences

Noureddine Atalla is a professor in the Department of Mechanical Engineering (Université de Sherbrooke). He is also a member and past director of GAUS (Group d’Acoustique et de vibration de l’Universite de Sherbrooke). Professor Atalla received an MSC in 1988 from the Université de Technologie de Compiègne (France) and a PhD in 1991 in ocean engineering from Florida Atlantic University (USA). His core expertise is in computational vibroacoustics and modeling and characterization of acoustic materials. He has published more than 100 papers and is also the co-author of a book on the modeling of sound porous materials. Franck Sgard is team leader of the mechanical and physical risk prevention group at the Institut Robert Sauvé en Santé et Sécurité du Travail (IRSST) in Montreal (Canada). He graduated from Ecole Nationale des Travaux Publics de l’Etat (ENTPE) in Vaulx en Velin (France) as a civil engineer in 1990. He obtained his master’s degree in mechanical engineering from the University of Washington (Seattle) in 1991. In 1992 and 1993, he worked as a research assistant in the acoustic group of the University of Sherbrooke (GAUS). He then started a joint PhD (University of Sherbrooke/Institut National des Sciences Appliquées in Lyon, France) in mechanical engineering (acoustics), which he completed in 1995. From 1995 till 2006, he worked as a professor at ENTPE, teaching acoustics