Study analyzes structural vibrations and the interactions between them and sound fields. It outlines a conceptual framework to analyze the vibrations of systems and their interactions, incorporating the results of earlier studies and establishing a unified basis for continuing research

Lyon, R. H.

Smith, P. W., Jr.

English

NASA Technical Reports Server

April 1967
	 Brief 67-10068 
NASA TECH BRIEF
	
1 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Study Made of Interaction Between Sound Fields and Structural Vibrations 
"Sound and Structural Vibration," by Preston W. 
Smith, Jr., and Richard H. Lyon, Bolt, Beranek, and 
Newman, Inc., Cambridge, Mass., NASA CR-160, 
March 1965. 
This report is designed to be a systematic develop-
ment of some new techniques for analyzing structural 
vibrations and the interactions between sound fields 
and structural vibrations. In its application to struc-
tural vibration, the approach is quite new, having 
been motivated by the lengthening roster of difficult 
questions concerning vibrations in very complicated 
structures—buildings, missiles, ocean vessels, etc.—
which are caused by a complicated set of forces. 
In the classical approach to a vibration problem, 
one usually asks, "What is the dynamic displacement 
of a particular point at a particular instant?" Now, in 
many practical problems, this is an unreasonable 
question because particular points and particular in-
stants are not really of concern, and a collection of 
data for all points and all instants would be over-
whelming. 
To get a useful answer, some different question 
must be posed: "What is the average dynamic 
response (in a root-mean-square sense) when that 
average is performed both in space and in time?" 
This is better because the answer is one handy 
number. However, too much information has been 
lost in the process. 
The nature of the problem and some idea of the 
answers desired can be brought out by describing a 
typical practical situation. A very large rocket carries a 
moderately large capsule inside of which are mounted, 
in various ways and positions, some packages of deli-
cate electronic instruments. Too much vibration of 
any one of many vacuum tubes, for example, will 
cause the whole rocket to misbehave. It is thought
that the vibration may be caused by sound from the 
rocket engine passing through the capsule and 
reverberating about inside. An estimate of the vibra-
tion generated in this manner is desired so that possi-
ble protective modifications to the structure and the 
instruments can be evaluated in a rational manner. 
The sound inside the capsule is found to be an 
extremely complicated function of time. It is a more 
or less random noise, although the energy is not dis-
tributed uniformly in frequency. Moreover, because of 
the limited space in the capsule, sound does not 
reach the package from any single direction. The 
sound bounces around in the space, and is repeatedly 
reflected from many different angles, which markedly 
affects the spatial distribution of force on the package. 
The vibratory response of the package to sound 
waves can be studied in the laboratory, irradiating it 
with a pure-tone wave incident from a single direction. 
One will then typically find that the response at a 
single point fluctuates tremendously as frequency is 
varied, being very large in small regions of frequency 
near the natural mechanical resonances of the pack-
age. At any one of these natural frequencies, the re-
sponse may vary quite considerably, depending upon 
the angle from which the sound wave arrives. Finally, 
the magnitude of response varies from point to point, 
when frequency and angle of incidence are held fixed. 
Upon inquiry, one discovers that the various elec-
tronic elements are sensitive to vibration in various 
ranges of frequency, and that their exact locations 
either are not known, are subject to change, or are 
distributed widely throughout the package. It is now 
evident that no exact question can be posed; it is 
needless to search for exact answers, of the type we 
called "classical". Only some sort of average, statisti-
cal estimates of response are required. 
Alft (continued overleaf) 
qW
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19670000068 2020-03-11T20:21:26+00:00Z
In this report analytical procedures are developed 
for obtaining estimates of this sort. In crude outline, 
the procedures more or less parallel the experimental 
laboratory study just described. From design draw-
ings, one estimates the average number of resonances 
expected in a moderately broad band of frequency 
and the spatial distribution of response amplitude for 
a "typical" mode of resonance. With this information, 
one estimates the average response of a singie"typi-
cal" mode to sound waves of noise incident from 
many various angles. The product of this average 
response per resonant mode by the average number of 
modes in a frequency band yields an estimate for the 
space-time average response in that frequency band. 
The process is repeated for different bands. 
It is, of course, hopeless to attempt to find the 
exact characteristics of individual modes in the early 
phases of such an analysis. The saving feature of this 
new approach is that many of the average characteris-
tics—number of modes in a frequency band, average 
coupling to sound incident from various angles, etc.—
are insensitive to those details of construction which 
render impossible the exact analysis. 
The aims of the present study are three-fold: (1) 
To outline a conceptual framework for analyzing the 
vibrations of complex distributed systems and the 
interactions of several systems. The approach 
proceeds by (a) a multimodal description of the vibra-
tions of a system; (b) characterization of the modal 
response by the vibratory energy involved, and of the
interactions by energy flux; and (c) formulation of 
statistical average estimates of the dynamic parameters 
of various systems. (2) To incorporate the principal 
results of earlier studies of vibratory interactions 
between sound fields and bending vibration fields in 
panel-like structures. (3) To establish a unified basis 
for continuing research and extensions to new prob-
lems. 
Notes: 
1. Copies of this report are for sale by the Office of 
Technical Services, Department of Commerce, 
Washington, D.C. 20230; price: $6.00 
2. Inquiries concerning this invention may be di-
rected to:
Technology Utilization Officer 
Headquarters 
National Aeronautics and Space 
Administration 
Washington, D.C. 20546. 
Reference: B67-10068 
Patent status: 
Inquiries about obtaining rights for the commercial 
use of this invention may be made to NASA, Code 
GP, Washington, D.C. 20546. 
Source: P. W. Smith, Jr. and R. H. Lyon
of Bolt Beranek, and Newman Inc. 
under contract to
Headquarters, NASA
(HQ-26) 
Brief 67-10068	 Category 02


Study made of interaction between sound fields and structural vibrations

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