1.10.3 Acoustic radiation impedance of a sphere in breathing mode

Products: ABAQUS/Standard  ABAQUS/Explicit  

In this example we calculate the acoustic radiation from a sphere in the “breathing” mode; that is, when the motion consists of uniform radial velocity. The example illustrates the use of a simple absorbing boundary condition in conjunction with acoustic continuum and interface elements and acoustic infinite elements. The results are compared with classical results.

Problem description

Results and discussion

Input files

References

Table

Table 1.10.3–1 Finite element results.

fNBGT POR RatioPWA POR RatioBGT Im RatioPWA Im Ratio
0.050001579.1370.9999914.903790.999990.03438
0.10000789.5680.999997.480000.999990.03477
0.20000394.7840.999993.795700.999990.03574
0.30000263.1890.999992.591220.999990.03744
0.40000197.3920.999992.005550.999990.03985
0.50000157.9140.999991.666260.999990.04292
0.60000131.5950.999991.449140.999990.04666
0.70000112.7950.999991.300960.999990.05110
0.8000098.6960.999991.195150.999990.05619
0.9000087.7300.999991.116990.999980.06199
1.0000078.9570.999991.057720.999980.06843
1.3000060.7360.999990.946780.999980.09174
1.6000049.3480.999990.888680.999980.12096
1.9000041.5560.999990.855870.999980.15591
2.0000039.4780.999990.848340.999990.16879
3.0000026.3190.999970.818320.999980.32989
5.0000015.7910.999630.844430.999890.79138
7.0000011.2800.997990.901951.000781.32394
10.000007.8960.989830.987641.041891.87622
15.000005.2640.967911.024611.862502.01852
20.000003.9481.030011.038995.280964.49785


Figures

Figure 1.10.3–1 Acoustic model finite element mesh used in ABAQUS/Standard.

Figure 1.10.3–2 Pressure magnitude (POR) versus frequency.

Figure 1.10.3–3 Pressure variation on the outer boundary for the transient analysis.