The noise contamination in the cities is an important problem nowadays as the cities become more populated and there are more vehicles on the streets. One part of the problem is the noise in studying and working areas as well as in the residential areas.

In the University of Panamericana in Guadalajara, Mexico, there is an electrical emergency plant which supplies electricity for the campus during the electricity cut-offs in the summer during the rainy season. The plant has a diesel engine and electric generator which are installed inside a small building. This engine was producing a very loud noise which was heard all over the university campus and was the cause of many complaints by students and professors.

The results of the noise measurements inside and outside of the plant are shown in Figure 1. The noise level inside the plant is very high (112 dBA). It decreases 13 dBA passing the open door of the plant. Then it decreases slowly till 72 dBA at 25 m from the source being still high. The measurements in the offices and the class rooms of the building nearer to the plant showed noise levels from 59 dBA to 69 dBA which are all beyond the permissible noise level.

The noise spectrum inside the plant shows (Figure 2) that the majority of noise’s components are in low fre-

quency range near 200 Hz; meanwhile there are also high level components in the middle frequency range up to 1200 Hz and in higher frequencies.

The principle ways of noise propagation must be studied to reduce effectively the noise level. The noise radiated by the machine towards the internal acoustical space inside the plant goes out to the external acoustical space by three ways: 1) through the entrance door and the exhaust hole in the ceiling, 2) through the walls, 3) through the foundation. The third way can be considered insignificant because the machine is properly vibroisolated from the foundation.

To realize the acoustical analysis of the plant by the SEA method an acoustical model in Figure 3 can be used.

Where E1—acoustical energy of the internal acoustical space, J E2—acoustical energy of the external acoustical space, J W in—acoustical power introduced by the machine, W

—acoustical power dissipated in the element i of the model, which can be determined using the following equation [1]

Where

η_i—loss factor of element iω = 2πf—angular frequency, rad/s f—frequency, Hz.

—acoustical power transmitted through the walls and ceiling, W

—acoustical power transmitted through the door and the air duct in the ceiling, W According to [1] [2] the equation of energy balance can be written as follows

Here

Where

η_ij—transmission loss factor between elements i and j.

Substituting Equation (3) into Equation (2) and then into Equation (1) and considering that acoustical energy transmission is insignificant in the inverse direction, as, the equation of energy balance can be obtained in the following form

.

Now, dividing the first equation of (4) by the second, we have

The acoustical energy transmitted through the holes must be proportional to the relation

, where

—the total area of the holes,

—the total area of the walls and the ceiling.

So the coefficient can be found from the equation

When, Equation (6) can be transformed into the equation

Substituting Equation (7) in Equation (5), we have

The attenuation of machine noise by the walls and the ceiling can be found as

where

η₁—loss factor of the absorption of the noise by the walls, the ceiling and the floor, it can be accepted equal to absorption coefficients of materials [3] .

According to [1]

where c—sound velocity in airτ = 10^−TL/10—Transmission loss factorTL—transmission lossV1—volume of the internal acoustical space, m³

f—sound frequency, Hz.

The transmission loss depends on the sound frequency and the critical frequency f_c of the walls [2] ,

Where c_L—velocity of longitudinal waves in the barrier (walls, ceiling), m/s t—barrier width, m.

For the walls and ceiling of bricks with t = 0.15 m and f_c = 129 Hz, c_L = 3400 m/s, c = 344 m/s.

When f < f_c the mass law actuates and

when

when (12)

where ρ—air density, kg/m³

ρ_S—unit area density, kg/m²

η_W—walls dissipation coefficient ( for bricks η_W = 0.01).

The total area of the walls and ceiling of the plant is A = 110.5 m², the volume V₁ = 110.05 m³. The area of the holes was estimated as A = 3 m².

The attenuation of sound is calculated using Equations (10) - (14). The results of these calculations are presented in Figure 4. The curve 1 corresponds to the initial conditions. It gives only 15 dB except the zone of critical frequency where the attenuation falls till 5 dB. This almost coincides with the results of noise measurements (Figure 1). The reduction of the area of holes up to 1 m increases the attenuation by 5 dB except in the critical frequency (curve 2). For further increase of the attenuation, two silencers for the suction and exhaust holes were designed and fabricated. The silencers are of absorbing type and were designed using fiberglass and perforated steel sheets.

The attenuation of sound in silencers can be estimated [4] [5] using this equation:

where l—longitude of silencer, m

α—absorption coefficientP—interior perimeter of the duct, m S—interior transverse area of the duct, m².

The absolute value of this sound absorption is

Taking into account the silencers attenuation, Equation (9) will transform in the following

Using Equation (17) curve 3 and 4 in Figure 4 is calculated. As we see from Figure 4 the introduction of silencers reduces the noise very much except in the critical frequency. For reducing the noise in the critical frequency and overall, the walls and the ceiling are covered with fiberglass of 2 inch thick (curve 4 in Figure 4).

In Figure 1 the effect of this vibroacoustical design in the reduction of noise level of the plant is presented. It can be seen that the noise level is reduced by 23 dBA at the distance of 15 m away from the source. Now the noise of the plant in the working area is so low that it is practically not heard.

1) The noise measurements of the plant in the university campus show that the noise level exceeds the permissible levels in the offices and classrooms.

2) An analysis of the acoustical system of the plant using the SEA method shows that the walls and the ceiling don’t have enough transmission loss because of vast holes at the suction of air and at the exhaust.

3) The reduction of the hole areas from 3 m² to 1 m² does not give a sufficient reduction of the noise.

4) By using fiberglass coatings for the walls and ceiling and especially designed silencers, a sufficient reduction of noise level (23 dBA at the distance of 15 m from the source) is achieved.