Building Acoustics

Multilayer elements 319

(^) covering h.

ES

s

d

⋅

= (8.51)

The quantities E and d are the E-modulus and thickness of the covering, respectively.
The questions to be raised here are what types of energy loss mechanism are involved
and whether the process is linear or not. Here we shall use some measurement results and
compare these with a simple linear model, a resistance in series with a stiffness given in
Equation (8.51). The model, proposed by Lindblad (1968), was used by Brunskog and
Hammer (1999a) to model the interaction between the tapping machine and lightweight
floors (see section 8.4.2.1).

a)

mh v 0 mh v 0

s

F c

b)

Figure 8.35 a) Floor covering hit by a hammer of speed v 0 ; b) Linear model of covering characterized by a
spring stiffness in series with a resistance.

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

Time (ms)

-50

0

50

100

150

200

F(

t) (N)

s = 3.2. 105 N/m

Figure 8.36 Time history of force pulses using elastic layer model given in Figure 8.35 b). Solid curve –
overdamped case, approximately 20 % more than critical. Dashed curve – approximately 60 % less damped than
critical.

The situation is depicted in Figure 8.35, where the hammer of mass mh and speed v 0
is hitting the covering. We shall assume that the primary floor beneath the covering is
infinitely stiff. Using the model in b) to calculate the improvement, we must, first,