Far-field acoustic radiation and vibration of a submerged finite cylindrical shell below the free surface based on energy functional variation principle and stationary phase method

The far-field acoustic radiation and vibration of a submerged finite cylindrical shell below the free surface are studied. Based on the energy functional variation principle, the image method and the Graf's addition theorem, the structureâ–“acoustic coupling vibration equation for the cylindrical shell is established. The far-field sound pressure expressions of the cylindrical shell are obtained by using the Fourier transform and the stationary phase method. The reliability and efficiency of the proposed analytical method are validated by comparison with the finite element method and the boundary element method. It is found that the presence of the free surface increases the natural frequencies of the same orders compared to those without the free surface. When the cylindrical shell is closed to the free surface, the circumferential mode shapes become very different from those in infinite fluid. However, the free vibration and forced vibration characteristics of the cylindrical shell below the free surface become consistent with those in infinite fluid when the submerged depth exceeds severalfold radiuses. The far-field sound pressure of the cylindrical shell below the free surface is very different from that in infinite fluid even though the submerged depth is relatively large. Moreover, the directivity of the far-field sound pressure of the cylindrical shell is similar to that of the acoustical dipole due to the free surface. Based on energy functional variation principle and stationary phase method, the proposed method provides an alternative for vibroacoustic problem of elastic structures bounded by acoustic boundary with good accuracy and applicability.