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Figure 12.16 Forces and Velocities for Soft Floor Covering (Ver, 1971)

Figure 12.16 Forces and Velocities for Soft Floor Covering (Ver, 1971)

and arad = 1. If we assume a 15 cm (6 in) dense concrete slab and use the figure, we get about 78 dB, and for a lightweight concrete structure of the same thickness we get about 92 dB with no surface covering. Human heel drops are not this loud, but the numbers are close to the measured levels for a tapping machine test (Fig. 12.18). Since it is usually impractical to increase the slab thickness and density enough to make a significant change, we turn to the floor surface covering for improvement.

Improvement Due to Soft Surfaces

Ver (1971) and Cremer (1973) have analyzed the impact of a carpet or other similar elastic surfaces on tapping machine noise transmitted through a floor. An illustration of Ver's model is given in Fig. 12.16.

The falling weight strikes a surface, whose stiffness is the elasticity of the carpet. In this model damping is ignored and the weight is assumed to strike the surface and recoil elastically once without multiple bounces. The equation of motion of the spring mass system is and d2x m-^ - kx = 0 (12.34)

dt j m0

where the natural frequency ofthe spring mass system is

The spring constant is given by

where Ed = dynamic Young's modulus of elasticity (N/m2) which is about twice the static modulus Sh = area of the striking surface of the hammer = 0.0007 m2 h = thickness of the elastic layer (m) m = mass of the hammer = 0.5 kg When the hammer is dropped it strikes the elastic layer with a velocity u0 at time t = 0 and its subsequent motion can be calculated from Eq. 12.34 to be u (t) = u0 cos (&>nt) for 0 < t <n/rnn (12.38)

and u (t) = 0 for t < 0 and t > (12.39) Figure 12.16 also shows this velocity function. The force is given by

F(t) = m — = uQ œn m sin (œn t) for 0 < t < n/œn (12.40)

Now the Fourier amplitude of the tapping machine pulse train as given in Eq. 12.22

where n = 1, 2, 3,... This yields the force coefficients of the Fourier series

n n4 V a fi in terms of the coefficients given in Eq. 12.43 and

The improvement due to the elastic surface in the impact noise isolation is given in terms of a level

which is shown graphically in Fig. 12.17.

Note that in this model we have ignored the contribution of the floor impedance and have assumed that it is very stiff compared with the elastic covering. At very low frequencies—that is, below the spring mass resonance—the improvement due the covering is zero. Above this frequency the surface covering becomes quite effective, giving a 12 dB per

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