Far-field sound radiation of a submerged cylindrical shell at finite depth from the free surface

Abstract

The far-field sound radiation behavior of a circular cylindrical shell submerged at finite depth from the free surface is studied. Based on the Flügge shell theory and the Helmholtz equation, the structure-acoustic coupling equation is established. An image method is applied so that the sound boundary condition of the free surface can be satisfied. Analytical expression of the far-field sound pressure is obtained using the stationary phase method and the Graf's addition theorem. In order to evaluate the effect of the submerged depth on sound radiation, the results of the submerged cylindrical shell at finite depth from the free surface are compared with those of the submerged cylindrical shell in the infinite fluid. The characteristics of the far-field sound pressure with the change of the depth are investigated. It is found that the submerged depth has a significant influence on the far-field sound pressure radiated from the submerged cylindrical shell due to the free surface effects. The work provides more understanding on the sound radiation properties of the submerged circular cylindrical shell without assuming infinite fluid field, which was commonly used in previous studies.

Investigations on the vibrational and acoustic characteristics of a submarine-like system by experiments and simulations

“…The influence of the immersion depth on the radiated sound pressure cannot be neglected when the shell is suspended horizontally. 20 Consequently, the system was hanged vertically in experiment to reduce the reflection effect of the free surface on the acoustics. As depicted in Figure 5(a), the system is attached by a balance weight to maintain neutral buoyant in water and suspended by a steel cable to simulate the free-free boundary condition.…”

On the vibro-acoustic response of a cylindrical shell submerged near a free sea surface

“…The image method has also been implemented to study sound scattering by a rigid cylinder near an impedance boundary, displaying similar patterns of enhanced or reduced scattering depending on the proximity to the planar surface [19][20][21]. More recently, the vibrational characteristics and far-field sound radiation of a cylindrical shell near an impedance plane or a free sea surface has been studied [22][23][24][25][26]. Li and co-authors [24,25] investigated the acoustic responses of cylindrical shells of infinite and finite length submerged at a finite depth from the free surface.…”

“…More recently, the vibrational characteristics and far-field sound radiation of a cylindrical shell near an impedance plane or a free sea surface has been studied [22][23][24][25][26]. Li and co-authors [24,25] investigated the acoustic responses of cylindrical shells of infinite and finite length submerged at a finite depth from the free surface. The far-field sound was approximated using the method of stationary phase.…”

Analysis of Free Vibration Characteristics of Cylindrical Shells with Finite Submerged Depth Based on Energy Variational Principle

“…The above studies are of considerable value, but the numerical method a will require a greater computational cost with considering the free liquid surface. Therefore, Li et al [31][32][33][34] have done a lot of work in this field. Their research results show that when the immersion depth of the structure is greater than or equal to four times the radius of the structure, the vibro-acoustic characteristics of the cylindrical shell tend to be in an infinite domain.…”

“…Different from the previous method used by our research team [31][32][33][34], this article will obtain the shell-liquid coupled vibration equation based on the energy variation principle, which is a new pattern of solution. First, based on the assumption of no rotation of the shell and the Love shell theory, the Euler beam function is used to replace the axial displacement function of the cylindrical shell, then the kinetic energy and potential energy of the shell are obtained.…”