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Journal of the Acoustical Society of America

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May 1988

Volume 83, Issue S1, pp. S1-S122

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back to top Session WW. Education in Acoustics IV and Physical Acoustics VIII: Computer‐Based Theoretical Studies in Acoustics
Invited Papers
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MACSYMA automated symbolic mathematics software (A)

Richard Petti

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S106-S106 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Just as computers revolutionized numerical analysis, so symbolic mathematics software is revolutionizing symbolic mathematics computations, yielding major increases in speed accuracy and modeling power in many applications. In addition to automating large and tedious computations, MACSYMA provides automated mathematical expertise in many areas, such as solution of simultaneous equations, integration, Laplace transforms, ordinary differential equations, and simplifications of expressions. The presentations will focus on selected capabilities of MACSYMA that are relevant for acoustics, especially: (1) symbolic vector and tensor calculus, (2) symbolic solution of ordinary differential equations, (3) symbolic approximation methods, (4) use of symbolic math software to generate numerical analysis code, (5) symbolic matrix computations. A partial bibliography of research papers in fluid mechanics reporting on work where MACSYMA was used will also be provided. Also discussed will be the role of symbolic mathematics software in technical education.
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Scratchpad II: A computer algebra language and system (A)

Richard Jenks

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S106-S106 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The Scratchpad II system represents a new generation of systems for doing symbolic mathematics, based on modern algebra and abstract data types. A large number of facilities are provided, for example: symbolic integration, “infinite” power series, differential operators, Cartesian tensors, and solution of nonlinear systems. Scratchpad II has been designed from the outset to be extendible. The system introduces a new data abstraction notion, the “category,” to express intricate interrelationships between data types. The result design permits the compilation of algorithms described in their most natural mathematical setting. The use of categories guarantees user defined types and packages are compatible with each other and with built in facilities. This system provides a single high‐level language with an intepreter and compiler. The language can be used by the naive user for convenient interactive mathematics calculations and by the advanced user for the efficient implementation of algorithms. Scratchpad II is built on Lisp/VM and runs on IBM/370 class mainframes. An implementation of the system on the RT/PC is expected soon.
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A survey of FORTRAN code generation using MACSYMA (A)

Stanly Steinberg and Patrick J. Roache

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S107-S107 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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This paper presents the underlying symbolic manipulation techniques used by the authors to produce FORTRAN code with the artificial intelligence code MACSYMA. The FORTRAN codes produced use finite difference methods to solve the governing equations for numerical grid generation, including elliptic and variational methods, and to solve the hosted equations, including fluid dynamics, heat transfer, and electro‐statics. Consideration will be given to writing the hosted equations in strong conservation form in general nonorthogonal coordinates; high order and conditional differencing schemes; colocated variables versus staggered grids; and code validation procedures.
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Use of symbolic manipulation in physical acoustics (A)

Martin Manley and Vineet Mehta

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S107-S107 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The development of a mathematical theory in acoustics (or in any other field) depends on the insight of the theoretician. However, the formulation of an insight into an equation derived from first principles involves much time spent in activities that fall within the category of a symbolic manipulation. To demonstrate the role symbolic manipulation software can play in the solution process, classical problems in acoustics will be selected. It is known that the solution to the linearized governing equations of an acoustic field can be considered as a superposition of vorticity, thermal, and acoustic modes. However, these modes are coupled. The separation of these modes will be demonstrated. Symbolic manipulation will be used to explore how the higher‐order terms in the perturbation parameters, ϵμ, and ϵκ, affect the modal coupling. The issue of asymptotic degeneracy will also be addressed (the effects of varying the rates at which these parameters approach zero).
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An evaluation of an intelligent computer service assistant (A)

Paul W. Armstrong and Dan LaRue

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S107-S107 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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This presentation will discuss the development issues required for the implementation of an intelligent assistant for Apollo's customer service organization. An overview of the design and requirement goals as well as the integration with current data systems and input will be addressed. Maintenance and future enhancemerits will be reviewed as well as a discussion of the user interface and user profiles.
Contributed Papers
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Application of symbolic computation to singular perturbation problems in physical acoustics (A)

Charles Thompson

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S107-S107 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Problems in fluid mechanics, and in turn in physical acoustics, often incorporate a large number of length scales and parameters. These scales are the result of local fluid interactions with either boundary surfaces or across discontinuities in the physical properties of the fluid. The art of developing a correct description of any physical situation is in discerning the relative importance of each of the parameters of the solution. One might consider solutions to a problem as a restricted range of values of these parameters. In such a case, these solutions would be locally valid in the parameter space and are an asymptotic representation of the global solution. The integration of locally valid solutions into a global description is the essence of singular perturbation methods. In this paper, the method by which computer algebra can be used to solve problems involving a singular perturbation analysis in physical acoustics will be discussed.
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Creation of experiment‐oriented materials to enhance a nonlab acoustics elective (A)

S. A. Elder and M. S. Korman

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S107-S107 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Two acoustics courses are offered by the Naval Academy Physics Department. One is a physics major elective course in physical acoustics with a weekly 2‐h lab; the other, a sonar course, is basically a service course for other departments. On account of the large attendance for the latter, and the limited space available, it has not been possible to make lab work a routine part of the course. Since it is believed that some lab experience is essential to good physics teaching, materials are being created to be used by students outside of class time that will address this need. Among ideas being considered are computer‐graphic homework assignments, special project‐type lab setups, video‐cassette instructional aids, and sonar games. Current materials and experience will be described.
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Farfield criteria for vibrating structures: Numerical simulation on plates and cylinders (A)

Christophe Journeau, Thierry Rohan, and François Pellegrini

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S107-S108 (1988); (2 pages)

Online Publication Date: 13 Aug 2005

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In order to determine practical criteria for the nearfield/farfield transition in the case of underwater vibrating structures, the acoustic field radiated by plates and cylinders is simulated. Various mode shapes of these structures are computed for different frequencies including their resonance frequencies. These calculations are made for radiators of different sizes and are compared with the results of a mechanical simulation for a point‐excited ribbed cylinder. Then the distances at which the pressure field is at ± 1 dB of the farfield value, the wave specific impedance is ρc ± 12% (1 dB), and pressure and velocity have a phase difference of less than ± 15° are tabulated as a function of frequency. The envelope of these points is compared with the standard criterion (R ≫ λ and R ≫ L2/λ). Finally, various criteria are proposed depending on which property of the farfield is required.
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