Finite Element and Boundary Methods in Structural Acoustics and Vibration  book cover
1st Edition

Finite Element and Boundary Methods in Structural Acoustics and Vibration

ISBN 9781466592872
Published April 17, 2015 by CRC Press
470 Pages 172 B/W Illustrations

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Book Description

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.

Table of Contents

Computational vibroacoustics
Overview of the book
Basic equations of structural acoustics and vibration
Linear acoustics
Linear elastodynamics
Linear poroelasticity
Elasto-acoustic coupling
Poro-elasto-acoustic coupling
Integral formulations of the problem of structural acoustics and vibrations
Basic concepts
Strong integral formulation
Weak integral formulation
Construction of the weak integral formulation
Functional associated with an integral formulation: Stationarity Principle
Principle of virtual work
Principle of minimum potential energy
Hamilton’s principle
A: Methods of integral approximations—Example 41
B: Various integral theorems and vector identities
C: Derivation of Hamilton’s principle from the principle of virtual work
D: Lagrange’s equations (1D)
The finite element method: An introduction
Finite element solution of the one-dimensional acoustic wave propagation problem
A: Direct approach for spring elements
B: Examples of typical 1D problems
C: Application to one-dimensional acoustic wave propagation problem
Solving uncoupled structural acoustics and vibration problems using the finite element method
Three-dimensional wave equation: General considerations
Convergence considerations
Calculation of acoustic and vibratory indicators
Examples of applications
A: Usual shape functions for Lagrange three-dimensional FEs
B: Classic shape functions for two-dimensional elements
C: Numerical integration using Gauss-type quadrature rules
D: Calculation of elementary matrices—three-dimensional wave propagation problem
E: Assembling
Interior structural acoustic coupling
The different types of fluid-structure interaction problems
Classic formulations
Calculation of the forced response: Modal expansion using uncoupled modes
Calculation of the added mass
Calculation of the forced response using coupled modes
Examples of applications
A: Example of a coupled fluid-structure problem—Piston-spring system attached to an acoustic cavity
Solving structural acoustics and vibration problems using the boundary element method
Integral formulation for Helmholtz equation
Direct integral formulation for the interior problem
Direct integral formulation for the exterior problem
Direct integral formulation for the scattering problem
Indirect integral formulations
Numerical implementation: Collocation method
Variational formulation of integral equations
Structures in presence of rigid baffles
Calculation of acoustic and vibratory indicators
Uniqueness problem
Solving multifrequency problems using BEM
Practical considerations
Examples of applications
A: Proof of
B: Convergence of the integral involving the normal derivative of the Green’s function in Equation
C. Expressions of the reduced shape functions
D. Calculation of
E: Calculation of for a structure in contact with an infinite rigid baffle
F: Numerical quadrature of
G: Proof of formula
H: Simple calculation of the radiated acoustic power by a baffled panel based on Rayleigh’s integral
Radiation of a baffled circular piston
Problem of exterior coupling
Equations of the problem of fluid-structure exterior coupling
Variational formulation of the structure equations
FEM-BEM coupling
FEM-VBEM coupling
FEM-VBEM approach for fluid-poroelastic or fluid-fluid exterior coupling
Practical considerations for the numerical implementation
Examples of applications
A: Calculation of the vibroacoustic response of an elastic sphere excited by a plane wave and coupled to internal and external fluids

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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


"…the analyses presented begin with well-known fundamental equations and follow a logical progression to the final solutions. …The book provides a thorough treatment of the theory that underpins FEA and BEA as applied to the solution of vibro-acoustic problems and as such it is a valuable text book for graduate students majoring in acoustics or vibration."
—Colin Hansen, University of Adelaide, Australia

"The approach serves well for researchers of all levels in vibro-acoustics, since the examples provided cover a full spectrum of applications, as well as coupling the examples with the constraints and convergence aspects of FEM that often cause the user to not use the FEM successfully."
Noise Control Engineering Journal, September-October 2015

"This book paves the way for the curious researcher on their often meandering journey. …the authors encourage the reader to think about the various simplifications and assumptions that have been made in the case examples presented; an essential stepping stone for both the junior and senior researcher. This book fills a great need to provide the essential basis for anyone who may be required to use finite element methods and especially boundary element methods in structural acoustics."
—Dr Andrew Peplow, Noise & Vibration Specialist, Atlas Copco Rock Drills AB

"The book aims to introduce the basic concepts of both the FEM and BEM solution approaches, and the first chapters include some basics of acoustics and vibration. This wide scope poses a challenge in terms of depth vs coverage and some details are by necessity not covered in depth. The book has a distinct value as a point of entry to the covered computational methods and the various aspects involved in their application. However, to be really useful, the reader should have, or be prepared to acquire, a quite thorough understanding and background knowledge in engineering mechanics, mathematics, linear algebra, acoustics and elastodynamics."
—Peter Göransson, Nuntius