J. H. Janssen 333 
“normal excitation 
Ve ff 
Fig. 17.9. "Normal" exci- 
tation (i.e., direction of 
force parallel to direction 
of particle displacement of 
beam beam) and “parallel” exci- 
tation (i.e., a bending mo- 
ment is exerted on beam) 
.F “ are compared, It is sup- 
parallel excitation posed that aresilient mount 
is inserted between a beam 
and a source of structure- 
borne sound. The source- 
side contact plane moves 
in a “normal” or in a 
"parallel" direction. The 
height of this plane above 
the neutral layer of the 
beam is H. If the spring 
is mounted at a velocity 
antinode, (a) the "normal" 
excitation causes a veloc- 
| ity v, somewhere on the 
| H beam; or, if it is mounted 
= D i (Le at a node, (b)the “parallel” 
. excitation causes v,. 
"parallel" excitation of the beam. Twocases are compared. The first is "normal" 
excitation acting at a velocity antinode; the resulting velocity at an arbitrary 
point of the beam is v,. The second case shows the same spring at a velocity 
node, the excitation being "parallel." Again, the velocity v, at an arbitrary point 
is observed. 
If the height of the upper contact plane of the spring above the "neutral layer" 
of the beam is H and the stiffnesses are called S, and S,, then the ratio v,/v, is 
given by Ya Shiva (29) 
For an I-beam it must be expected that considerably shorter bending wave - 
lengths may exist in the upper and lower flanges separately, than in the longi- 
tudinal direction of the beam as a whole. It seems wise, therefore, to assume 
that A, in this case equals approximately the value it would have if the flanges 
were free plates of the same thickness. The order of magnitude involved is 
Xg=0.5m and H~0.25 m. The values of the stiffmesses S, and S, are approx- 
imately equal in magnitude. The extreme requirements of many practical appli- 
cations for resilient mounts necessitate a higher degree of isolation for normal 
excitation alone than is often available. A value for yv,/v, in Eq. (29) smaller 
than 1 therefore cannot be tolerated. 
If a foundation is constructed from steel profiles, the resilient mounts should 
be of such design as to render S, sufficiently less than S,, unless very special 
precautions are taken. The same does not apply for wooden beams, because in 
general the bending wavelengths will be greaterthanfor comparable steel struc- 
tures. After the noise has reached the foundation, no appreciable attenuation 
during the propagation through the hull is generally found. 
