Summary:
The purpose of this course is two fold: (1) to introduce the fundamental physics underlying the creation of sound from vibrating structures, and (2) to introduce modern computational methods for predicting and controlling the sound field. The physics of sound generation are presented. The emphasis is on understanding and basic principals, with a modest amount of theoretical development. Important concepts such as coincidence, radiation efficiency, intensity and directivity are discussed and applied to a variety of structures (e.g. planar sources, plates and cylindrical shells). Sound propagation inside pipes is also presented along with methods of attenuating and reflecting acoustic energy.
Numerical techniques for predicting and controlling sound constitute the second half of the course. For planar structures the Rayleigh integral equation is presented and applied to a variety of problems. Transfer and Impedance matrix techniques can be used to calculate plane wave sound propagation in rigid and elastic piping systems ( including fluidelastic coupling) At high frequencies the method of Statistical Energy Analysis is very useful for identifying dominant sound transmission paths from vibrating structures. SEA is also an extremely easy analysis tool for evaluating the effect of design modifications on radiated power. At low frequency where individual modes control radiated sound the Helmholtz integral can be utilized. A recent computational method that utilizes the capabilities of finite elements is an infinite fluid element. This element captures the physics of both the near field and far field. More importantly, the infinite element avoids the traditional inside eigenvalue problem associated with the HIE method and is very computationally efficient since the matrices are well banded. Use of this element in the SARA finite element code is discussed.
Tuition:
Instructor:
Dr. Robert C. Haberman is a Principal Engineer at Bolt Beranek and Newman and
an Adjunct Associate Professor (Mechanical Engineering) for the Renssalaer Polytechnic Institute. He has over 25 years of R& D experience in noise, vibration, acoustics and shock analysis of naval structures. Examples include use of Statistical Energy Analysis to study noise transmission in submarine internal structures, use of Fuzzy Structures to determine submarine hull damping, and application of classical continuum mechanics along with modern computational methods to study problems in acoustic radiation. He is the author of numerous publications, a frequent speaker at noise and vibration conferences, and has written over 100 technical reports.
In 1983, Dr. Haberman and Dr. Henno Allik of BBN presented a paper "On The Use Of Infinite Elements In Structural Acoustics." Since then the element has been incorporated into the SARA computer program that is now used by many government laboratories and universities.
Contact this instructor (please mention course name in the subject line)
Who Should Attend:
The material presented in this course is very well suited for engineers that wish to obtain both a good understanding of the physics of sound generation and knowledge of computational tools for predicting and controlling radiated sound.
Course Outline:
 Fundamentals of Wave Propagation — Flexural, compressional and torsional waves in beams, flexural waves in plates and compressional waves in fluids. Concept of wave number and dispersion curves.
 Acoustic Waves — Intensity, impedance and power in acoustic waves, far field and near field pressure from a sphere, concept of a point source, method of images, directivity.
 Rayleigh's Equation and Applications — Far field pressure and intensity from planar sources such as dipoles, multipoles, arrays, circular and rectangular plates.
 Structural Acoustics of Plates — Radiation from finite and infinite plates, coincidence frequency, Fourier integral transform with applications, methods of stationary phase, concept of radiation efficiency, fluid loading on plates, and sound transmission through plates.
 Structural Acoustics of Shells — Vibration and wave propagation in isotropic and orthotropic cylindrical shells, fluid loading, acoustic radiation and radiation efficiency. Influence of complicating effects on radiation.
 Sound Propagation in Pipes — Plane waves and higher order cuton waves in straight pipes, influence of pipe wall impedance and liners on wave propagation. Methods of analyzing piping systems such transfer and impedance techniques, and methods of reducing noise, such as the use of Helmholtz resonators, side branches and damping.
 Fluid Loading Approximations — Incompressible fluid, rhoc fluid and first and second order doubly asymptotic approximations, DAA with applications. Simple interpretations of DAA in frequency domain.
 Statistical Energy Analysis — Overview of SEA with emphasis on sound transmission and radiation problems. Brief discussion of capabilities of AutoSEA computer program along with several examples.
 Helmholtz Integral Equation — Basic theory of two and three dimensional HIE with coupling to finite elements. Use of HIE in far field pressure calculations using near field analytical or experimental data.
 Infinite Fluid Elements — Basic theory of infinite element with coupling to finite elements. Discussion of SARA (Structural Acoustic Radiation Analyzer) computer program along with several examples, such as calculation of modal radiation efficiency of complex three dimensional structures and radiation from shells.
Tuition:
Tuition for this threeday course is $1740 per person at one of our scheduled public courses. Onsite pricing is available. Please call us at 4109568805 or send an email to ati@aticourses.com.

