Finite Element and Boundary Methods in Structural Acoustics and Vibration: 1st Edition (Paperback) book cover

Finite Element and Boundary Methods in Structural Acoustics and Vibration

1st Edition

By Noureddine Atalla, Franck Sgard

CRC Press

470 pages | 172 B/W Illus.

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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.


"…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

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


About the Authors

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

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