5 Test Problems and Results

In this section some results from the application of subroutine ABSEMGEN to a shielded cube problem are considered. The test problems each consist a 10cm cube (S) of which one face is vibrating uniformly, the other faces of the cube are rigid. A square plate (G) with sides of length 10cm is placed 10cm from the vibrating face. The acoustic medium is air (density = 1.29 kg/m^-3, speed of sound = 331 m/s ). In the initial tests the square plate is assumed rigid. In the final test the square plate assumes the properties of 1mm thick steel (density = 7800 kg/m^-3, Young's modulus = 209 ×10⁹ Pa, Poisson's ratio = 0.3). In each test the acoustic medium is air. The test problem is illustrated in figure 2. In the implementation of the BSEM via subroutine ABSEMGEN, the cube is divided into 96 boundary elements and the shell is divided into 16 shell elements, so that the elements are all of uniform size.

Fig. 2. The Test problem.

The radiation ratios of the system were computed at 10Hz, 20Hz, ..., 5000Hz. The results from this test were compared with the results obtained when the square plate is removed. For these tests the plate is assumed rigid. The results are illustrated in figure 3.

Figure 3 demonstrates that the shield has a major effect on the acoustic properties of the system. Below circa 1300Hz, the unshielded and shielded cube have approximately the same radiation ratio. However, the shield has the effect of significantly reducing the radiation ratio at around 1800Hz, 3000Hz and 4500Hz and significantly increasing it at around 2300Hz and 3700 Hz.

Fig. 3. Radiation ratio curves for both a shielded and unshielded cube.

Let us now go on to study the effect of the shield on the sound pressure field at a set of chosen frequencies. Figures 4, 5, and 6 show the sound pressure level (in this case simply the logarithm of the sound pressure) at points along the line from the centre of the vibrating face to the centre of the plate and beyond at frequencies of 2300Hz, 3050Hz and 3700Hz.

Fig. 4.

Fig. 5.

Fig. 6.

Finally, a case where the plate is non-rigid is considered. It is assumed that the plate is a 1mm thick piece of steel that is hinged on all four sides and it is assumed to have no structural damping. The dynamic properties of the square plate can be found in many textbooks on the analytic vibratory analysis of simple structures, for example reference [19]. The first resonant frequency of the plate is near 490Hz. The shield is not directly forced. Figure 7 compares the sound pressure level for the steel shield with that of the rigid shield at 490Hz.

Fig. 7.