DTIC ADA371868: 1998 Physical Acoustics Summer School (PASS 98). Volume III: Background Materials.

274 Pages·18.8 MB·English

by  Defense Technical Information Center

DISTRIBUTION STATEMENT A
Approved for Public Release
Distribution Unlimited
I
VOLUME HI: BACKGROUND MATERIALS
©TIC QUALITY INSPECTED ft
I
I
1
1
i
1998
PHYSICAL ACOUSTICS
I SUMMER SCHOOL
1
§ iii:
VOLUME BACKGROUND MATERIALS
i
i
i
tnPhis work relates to Department of Navy Grant N00014-98-1-0044
J. issued by the Office of Naval Research. The United States
Government has a royalty-free license throughout the world in all
copyrightable material contained herein.
I
I
DISTRIBUTION STATEMENT A
I
Approved for Public Release
Distribution Unlimited
I
I
Copies of this three-volume proceedings can be obtained by contacting: Libby Furr, NCPA, University of
Mississippi, University, MS 38677; voice: 662-915-5808; fax: [phone]; e-mail: [email protected]
I
i 19991227 101
I
1
I
I
i
TABLE OF CONTENTS
i
ACOUSTICS DEMONSTRATIONS l
i
ACOUSTIC RESONATORS AND THE PROPERTIES OF GASES 2
i CHAOS AND NONLINEAR BUBBLE DYNAMICS 4
NONLINEAR ACOUSTICS 82
i
PERIODIC, RANDOM, AND QUASIPERIODIC MEDIA 135
i
POROUS MEDIA 139
i
QUANTUM MECHANICS MINI-TUTORIAL 140
^ RESONANT ULTRASOUND SPECTROSCOPY AND
| MATERIALS PHYSICS 142
(SCANNING ACOUSTIC MICROSCOPY: LENSES, TIPS AND
SONOELECTRONICS 143
M SENSOR PHYSICS: SIGNALS AND NOISE 238
I SONOLUMINESCENCE 260
THERMOACOUSTICS 262
I
t
I
I
ACOUSTICS DEMONSTRATIONS
Robert M. Keolian
Penn State University Applied Research Laboratory
and Graduate Program in Acoustics
Some of the nonlinear properties of the harmonic oscillator, waves on the surface of water,
and of high amplitude sound will be shown in a series of demonstrations:
■ Bent tuning curves of a rubber band
■ Parametrically driven pendulum
■ Doubly bent tuning curves
■ Parametric stabilization of an inverted pendulum
■ Non-propagating hydrodynamic soliton
■ Shock waves, N waves, and sound eating sound
■ Acoustic Bernoulli effect
■ Acoustic levitation
■ Acoustic match blower
■ Izzy Rudnick's lawn sprinkler
■ Izzy Rudnick's tea party
■ Acoustic log starter
REFERENCES
A.B. Pippard's book, The Physics of Vibration, (Cambridge University Press, Vol. 1, 1st
edition, 1978 or the omnibus edition, 1989), chapters 9-12, is a good reference for nonlinear
oscillators, parametric excitation, and other interesting effects.
Landau and Lifshitz's "Mechanics" (Pergamon Press, 3rd ed., 1976) is also useful.
The soliton is described in: J. Wu, R. Keolian, and I. Rudnick, "Observation of a
Non-Propagating Hydrodynamic Soliton," Phys. Rev. Lett. 52, 1421-1424 (1984) and in J. Wu,
I. Rudnick, "Amplitude-Dependent Properties of a Hydrodynamic Soliton," Phys. Rev. Lett. 55,
204 (1985).
1
1
ACOUSTIC RESONATORS AND THE PROPERTIES OF GASES
I
BY
MICHAEL R. MOLDOVER
1
Objectives I
To identify most of the phenomena that may be encountered in gas-filled acoustic resonators
operating in the linear regime (/> « P ). To motivate the choices made when designing fe
acoustic ambient
measurement systems and when estimating the properties of gases. To exploit the analogies and I
differences between sound waves and electromagnetic waves. Not covered: detailed
calculations, derivations.
1
Resonators [1]
1. Ideal frequencies I
2. Shape perturbations, degeneracies ™
3. Visco-thermal boundary layers ^
4. Bulk viscosity ■
5. Mechanical compliance, shell resonances, avoided crossings; why resonators are rarely
used to measure the properties of liquids. A
6. Inefficient transducers are useful; waveguides and diaphragms [2] M
7. Mean free path effects: accommodation at the gas-solid boundary et al.
8. Standards Measurements: The gas constant R and the thermodynamic temperature T [1] I
Properties of Gases
I
1. Thermodynamic speed of sound [3];
A. speed of sound measurements for technical applications
1
B. know your impurities
2. Connections between gas properties and intermolecular potentials [3,4]
A. virial coefficients
I
B. viscosity
C. thermal conductivity
D. bulk viscosity [5]
I
E. helium: a standard for gas properties [6]
3. Mixtures; why I wonit measure the speed of sound of air
4. Acoustic measurements of transport properties: status report [7]
Primary Reference P
Moldover, M.R., Mehl, J.B. and Greenspan, M., Gas-filled spherical resonators - Theory and M
experiment, J. Acoustical Soc. of America, Vol. 79, pp. 253-272 (1986) ■
1
I
Other References
[1] Moldover, M.R., Trusler, J.P.M, Edwards, T.J., Mehl, J.B., and Davis, R.S., Measurement of
the universal gas constant R using a spherical acoustic resonator, J. of Res. of NBS, Vol. 93, No.
3, pp. 85-114 (Mar-Apr 1988).
[2] Gillis, K.A., Moldover, M.R., and Goodwin, A.R.H., Accurate acoustic measurements in
gases under difficult conditions, Rev. Sei. Instruments, Vol. 62, No. 9, pp. 2213-2217 (1991).
[3] Gillis, K.A. and Moldover, M.R., Practical determination of gas densities from the speed of
sound using square-well potentials, Int. J. Thermophysics, Vol. 17, No. 6, pp. 1305-1324 (1996)
[4] Joseph O. Hirschfelder, Charles F. Curtiss, and R. Byron Bird, "Molecular Theory of Gases
and Liquids," John Wiley & Sons, Inc., New York (1954) or J. P. M. Trusler, Equation of state
for gaseous propane determined from the speed of sound, Int. J. Thermophysics, Vol 18, pp. 635-
654 or J. P. M. Trusler, W. A. Wakeham, and M. P. Zarari, Molecular Physics, Vol. 90, pp. 695-
703 (1997).
[5] R. Holmes and W. Tempest, The Propagation of sound in monatomic gas mixtures, Proc.
Phys. Soc. London, Vol. 75, pp 898-904 (1960); K. F. Hertzfeld, and T. A. Litovitz, "Absorption
and dispersion of ultrasonic waves," Academic Press, New York (1959).
[6] Aziz, R.A., Janzen, A.R., and Moldover, M.R., Ab initio Calculations for helium: a standard
for transport property measurements, Phys. Rev. Lett., Vol. 74, No. 9, pp. 1586-1589 (1995).
[7] Gillis, K.A., Mehl, J.B., and Moldover, M.R., Greenspan acoustic viscometer for gases, Rev.
Sei. Instrum., Vol. 67, No. 5, pp. 1850-1857 (1996).
Chaos and Nonlinear Bubble Dynamics
Werner Lauterborn
Drittes Physikalisches Institut, Universität Göttingen, Bürgerstr. 42-44,
D-37073 Göttingen, Germany, Tel: ++551-39-7713, Fax: ++551-39-7720,
E-mail: [email protected]
Chaos has become a learned word in science as the deterministic companion of a
stochastic process. Nonlinearity lies at its basis and a certain degree of complexity
To enter the realm of chaos a number of concepts have to be looked at for deeper
insight: The state space, trajectories and attractors therein, attractor basins, bifurca-
tions of different kinds, in particular the period-doubling bifurcation and its cascade
bifurcation diagrams, the different routes to chaos, Poincare sections and Poincare'
maps, the connection between maps and differential equations, phase or parameter
space diagrams, embedding of data (time series) into higher dimensional spaces as
the link between experiment and a theoretical description (Fig. 1), fractal dimensions
for chaotic attractors (static description), Lyapunov exponents of attractors as quan-
titative measures of the sensitive dependence of the dynamics on slight deviations
(dynamic description), and even more involved concepts.
measurement
experiment time series trajectory in
state space
Fig. 1: The way from experiment to a trajectory in a state space by embedding.
From chaos theory a new method for characterizing systems has evolved as put
forward graphically in Fig.2. Starting with some system to be investigated or moni-
tored a measurement yields a time series, i. e. a series of samples typically equally
spaced in time. These may be analyzed by the usual linear means as given by Fouri-
er analysis and correlations. These are not discussed here. The new way of nonline-
ar analysis starts with the embedding as visualized in Fig.l yielding a reconstructed
state space. The embedding may be preceded by preprocessing steps (linear filtering
for instance) or by tests on determinism or nonlinearity by constructing surrogate
data from the original data set. Also after embedding the somehow scrambled new
set may be processed, for instance to achieve noise reduction by nonlinear opera-
tions. However, the main aim of embedding is the characterization of the data in a
way that surpasses the usual linear methods. This is done by determining the static
and dynamic properties of the embedding set as they are given by fractal dimensions
and Lyapunov exponents discussed in the lectures. A second way of characterization
may proceed via modelling for describing the system and for prediction of its future
states on the basis of the embedding. The gained insight may also be used for con-
trolling purposes. The final aim, however, is a complete description of the system in
a way of diagnosis of its state at the time of measurement.
System
I
Measurement
♦
JTinieiBerifeä^
Nonlinear
Nöise&eduction
Dimensions
Modelling
Lyapunoy Exponents Prediction
Statistical Analysis, Controlling
Diagnosis
Fig. 2: Nonlinear time series analysis for system characterization via embedding.
Nonlinear oscillators are ideal objects where chaos shows up and where the con-
cepts mentioned above yield considerable new insight as compared to a purely linear
description, i. e. a description working with linearization only and linear transforma-
tions. In the context of acoustics the bubble in a sound field is a nonlinear oscillator
indeed a strongly nonlinear one at higher sound pressure amplitudes. It is even so
peculiar as to emit light upon collapse and to damage any material when coming clo-
se to it. Bubble dynamics will be discussed both from the view of experiments and
ol theoretical descriptions and, of course, the view of chaos theory.
W. Lauterborn and U. Parlitz, Methods of chaos physics and their application to acou-
stics, J. Acoust. Soc. Am. 84 (1988) 1975-1993.
U. Parlitz, Englisch, V., Scheffczyk, C. and Lauterborn, W.: Bifurcation structure of
bubble oscillators, J. Acoust. Soc. Am. 88 (1990) 1061-1077.
W. Lauterborn and J. Holzfuss, Acoustic chaos, Int. J. Bifurcation and Chaos 1 (1991)
13-26.
W. Lauterborn, Nonlinear dynamics in acoustics, Acustica 82 (1996) S-46 - S-55.
Internationa! Journal of Bifurcation and Chaos, Vol. 1, No. I (1991) 13-26
O World Scientific Publishing Company
ACOUSTIC CHAOS
WERNER LAUTERBORN and JOACHIM HOLZFUSS
Institut far Angewandte Physik, Technische Hochschule Darmstadt
Schloßgartenstr. 7, D-6I00 Darmstadt, FR Germany
Received August 7, 1990
The history of chaos pertaining to acoustics is briefly reviewed from the first oeriod^nnhlino
1 nd (vibrated ,iquid hyei) Bd Mcldc
5SÄZ2L? 2 * ■ SÄSÄ
investigations on chaos in thermoacoustics, musical instruments, the hearing process and ultrasoniL
A closer analyse „ gaven of the sound produced in a liquid by standing woJS^S^Si.
1. Introduction
noise is still an area of active research. An example,
Chaotic (i.e., irregular and unpredictable) motion where the properties of acoustic noise could be related
seems to appear in any sufficiently complicated or to chaotic dynamics, is given below for the case of
acoustic cavitation noise.
complex dynamical system. Acoustics, that part of
physics that -describes (and makes use of) the vibra-
2. Historical notes
tions of usually larger ensembles of molecules in gases,
liquids and solids makes no exception. As a main Acoustic chaos and the closely related science of
necessary ingredient of chaotic dynamics is nonlinear- chaotic vibrations are young disciplines [Lauterborn,
ity, acoustic chaos can only be found in the realm of 1989; Lauterborn & Parlitz, 1988; Parker & Chua,'
nonlinear acoustics. Thus, acoustic chaos is closely 1989; Thompson & Stewart, 1986; Moon, 1987]. Yet
related to nonlinear vibrations of and in gases, liquids most experiments conducted today have ancient an-
and solids. It is the science of never-repeating sound cestors. Two classes of oscillatory systems are most
waves. This property it shares with noise, a term susceptible to chaotic motion. These are periodically
having its origin in acoustics and formerly attributed driven (passive) nonlinear systems, which often re-
to every sound signal (and meanwhile other, e.g., spond to an excitation with subharmonics, in particu-
electrical, signals) with a broadband Fourier spectrum.' lar in the form of period doubling, and self-excited
But Fourier analysis is especially adapted to linear systems, which develop sustained oscillations from
seemingly constant exterior conditions. A special sub-
oscillatory systems. There it develops its full power. It
class of the second class forms self-excited systems
is the standard interpretation of the lines in a Fourier
when driven. The simplest model of that class is the
spectrum that each line corresponds to a (linear) mode
driven van der Pol oscillator (see, e.g., Parlitz &
of vibration and a degree of freedom of the system.
Lauterborn [1987]). From real physical systems, the
However, as examples from chaos physics show, a
weather can be put into this category. It is periodically
broadband spectrum can already be obtained with just
driven by the solar radiation with the low period of
three (nonlinear) degrees of freedom (i.e., three depen-
24h. But already a constant heating leads to oscilla-
dent variables). Chaos physics thus develops a totally
tions (Rayleigh-Benard convection), i.e., it is a self-
new view of the noise problem. It is a deterministic
excited system.
view. But it is still an open question how far the new
The first reported subharmonic oscillation of order
approach will reach in explaining still unsolved noise
one half (f/2, /- driving frequency) belongs to the
problems, e.g., the l//noise spectrum encountered so
first class and dates back to Faraday [1831]. Starting
often. The detailed relationship between chaos and
from the investigation of sound-emitting, vibrating
w- Lauterborn & J. Holzjuss
surfaces with the help of Chladni figures, Faraday also
Before going ahead with periodically driven systems,
sprinkled water instead of sand onto his vibrating
which, when nonlinear, almost always seem to develop
plates (vibrating at frequency f), and extended the
chaos in some parameter region, we turn to the second
work to complete layers of fluid to investigate the
class, that of self-sustained vibrations. Among these,
"beautifully crispated appearance" of the liquid layer.
we pick the thermoacoustic oscillations which come in
His aim was the "progress of acoustical philosophy".
two main varieties: Sondhauss oscillations [Sondhauss
To be able to watch the motion of the fluid layer he
1850; Feldmann, 1968a] and Rijke oscillations [Rijke'
enlarged his vibrating plates to lower the frequency of
1859; Feldmann, 1968b], The Sondhauss oscillation
oscillation, and ultimately came up with a board
occurs when the closed end of a gas-filled pipe is
eighteen feet long, upon which a liquid layer of three
heated (externally or internally), or, conversely, when
quarters of an inch in depth and twenty-eight inches by
the open end is cooled (then called Taconis osculations
twenty inches in extent could be vibrated vertically.
[Taconis et al., 1949]). The Rijke osculation occurs
Then, by ordinary inspection, he could observe that
when an internal grid located in the lower half of a
the heaps of liquid making up the crispations where
vertical pipe is heated. Both ends must be open to
oscillating in a sloshing motion to and fro between
allow for a flow of gas (self-generated or enforced)
neighboring heaps of liquid. He states: "Each heap
through the pipe. Sound is also produced when the
(identified by its locality) recurs or is re-formed in two
grid, this time being located in the upper half of the
complete vibrations of the sustaining surface" and
vertical pipe, is cooled [Riess, 1859].
adds in a footnote "A vibration is here considered as
Taconis oscillations with steep temperature gradients
the motion of the plate, from the time that it leaves its
and large temperature difference show complex behav-
extreme position until it returns to it, and not the time
ior [Yazaki et al., 1987]. The oscillation may period
of its return to the intermediate position". This result
double, develop quasiperiodic oscillations through the
was confirmed by Rayleigh [1883a].
appearance of a second incommensurate frequency and
Today, the powerful methods of nonlinear dynamics
also chaotic oscillations. This behavior is attributed to
and computerized experimental instrumentation are
mode competition similar to the Faraday experiment of
applied to this problem, and the nonlinear and chaotic
Ciliberto and Gollub [1985]. When Taconis oscillations
oscillations are investigated in some detail [Keolian
are confronted with periodic, externally imposed acous-
et al. 1981; Miles, 1984; Ciliberto & Gollub, 1985-
tic osciUations, the whole set of nonlinear dynamical
Meron & Procaccia, 1986; Gu & Sethna, 1987]. Sub-
phenomena seems to occur [Yazaki et al., 1990], as
harmonic oscillations as low as f/35 (/= driving fre-
encountered, when self-excited systems are additionally
quency), quasiperiodic and chaotic oscillations have
driven (see, e.g., the driven van der Pol oscillator [Par-
been observed in an essentially one-dimensional variant
litz & Lauterborn, 1987]). These acoustic oscillations
of the Faraday experiment [Keolian et al., 1981]. Period
are not just of scientific interest, but have a potential as
doubling, quasiperiodicity and chaos have been ob-
"natural engines" [Wheatley & Cox, 1985].
served for the original two-dimensional case with a
Coming back to driven systems of the passive (i.e.,
cylindrical fluid layer of 1 cm in depth and radius
not self-excited) type, period doubling has been ob-
6.35 cm [Ciliberto & Gollub, 1985]. Mode competition
served in connection with loudspeakers. Conical loud-
is singled out as the mechanism underlying the complex
speakers, when strongly driven, start to period double
dynamics. This experiment may naturally occur on the
[Pedersen, 1935]. Subharmonics have later been ob-
curved surface of bubbles set into motion in a sound
served when a liquid is irradiated with a pure tone of
field (see Sec. 3.4 below).
high intensity [Esche, 1952]. This work, where fre-
A second topic, where subharmonics were observed
quencies f/2, f/4, and f/3 of the driving acoustic
early, is the Melde experiment [Rayleigh, 1883b, 1887]
sound wave of frequency /were found in the output
In this experiment, the tension of a string is modulated
sound from the liquid (Fig. 1), stimulated the discus-
periodically by.fastening it to the prong of a tuning fork.
sion as to the physical mechanism producing these
Under suitable conditions, the string will vibrate at half
subharmonic frequencies. This topic will be investi-
the driving frequency. Rayleigh developed a theory for
gated in more detail below.
parametrically driven systems of this kind. String vibra-
Nonlinear dynamics also appears in musical instru-
tions play an important role in musical instruments
ments, where oscillations are produced to generate
and the investigation of nonlinear string vibrations
sound. These systems are therefore a priori apt to
form a large, separate part in nonlinear dynamics (see
generate chaotic sound waves. But there are not
Tufillaro [1989] to enter the field).
many investigations in this area. A first account can be