Study On Calculation Methods And Vibro-Acoustic Characteristics Of Single And Double-Walled Shells Of Revolution Coupled With Complex Internal Structures

As the simplified models for submarines,the vibro-acoustic characteristics of single and double-walled shells of revolution have attracted extensive attention.In practical engineering,these shells often contain many types of complex internal structures,such as bases,sector plates floating rafts and equipment.The main characteristic of these internal structures is nonaxisymmetry,which have significant influences on vibro-acoustic behaviors of the shells.Currently,vibro-acoustic models of axisymmetric shells are sufficient,however,methods are still limited to numerical methods and experiments for single and double-walled shells coupled with non-axisymmetric inner structures due to the complexity and diversity of internal structures.In this context,it is of great significance to establish theoretical models for vibro-acoustic analysis of axisymmetric single and double-walled shells coupled with non-axisymmetric interior structures and study influences of complex internal structures on vibro-acoustic characteristics of the shells.Firstly,two kinds of mixed analytical/numerical methods for vibro-acoustic analyses of the single stiffened cylindrical shell and conical-cylindrical-spherical shell with internal structures are proposed.The combined structure is decomposed into stiffened shells of revolution and internal structures,and the shells are further divided into a series of conical,cylindrical shell segments,ring stiffeners and bulkheads.The displacement functions of conical and cylindrical shell segments are described by the wave based method and power series,and the vibrations of ring ribs and bulkheads are expressed by the annular plate theory.The Helmholtz integral equation is used to express the external sound field,and then the sound pressure is introduced into the continuity conditions between the shell segments.For internal structures,the dynamic stiffness matrices are derived by finite element method.In order to fully consider the six degree of freedoms(DOFs)coupling between the shell and internal structures,a moment conversion method is proposed in this paper,which converts the coupling forces containing six components into ones in with four components.Combining the displacement continuity and internal force equilibrium in6 DOFs,rather than just 3 or 4 DOFs,between the shell and internal structures,the governing equations of the combined model are obtained.Numerical examples show that the calculation accuracy when considering 6-DOFs coupling is significantly higher than those when considering only 4-DOFs coupling.Secondly,two analytical substructure methods for vibro-acoustic analyses of the double-walled cylindrical shell and conical-cylindrical-spherical shell interconnected by annular plates are proposed.The Helmholtz integral equation is used to describe the interlayered sound field.Based on the theoretical method for the double-walled cylindrical shells,which makes up the shortage that the traditional analytical method can only deal with the interlayered sound pressure for cylindrical shells.Subsequently,two hybrid analytical/numerical method for vibro-acoustic analyses of the double-walled cylindrical shell with arbitrary interior structures and the one interconnected by arbitrary connections are further proposed.This method breaks through the limitation that the traditional theoretical method can only deal with double-walled cylindrical shells interconnected by annular or sector plates.Compared with the traditional method which just simplifies the sector plates as rods,the accuracy of the proposed approach is significantly higher.Thirdly,the influences of non-axisymmetric internal structures on vibro-acoustic behaviors of cylindrical shells and shells of revolution are studied in wavenumber domain by the developed methods.The results show that there is a one-to-one correspondence between the resonant peak and the vibration mode for axisymmetric shell,while nearly every resonant peak of the shell coupled with non-axisymmetric inner structures is contributed by various modes.Meanwhile,the non-axisymmetric internal structure can induce more high-order circumferential modes participate in the low-frequency vibration and acoustic radiation.Under the transverse excitation,many tiny added peaks emerge in the response curves of the shell with inner structures,resulting in the overall vibroacoustic responses of the shell with internal structures being higher than those of the one without interior structures.When the longitudinal excitation is considered,the nonaxisymmetric internal structure has little influence on the responses of the shell in the middle and low frequency band,while they can lead to the wave pattern conversion of the shell in the high frequency band.Fourthly,the vibro-acoustic characteristics of double-walled cylindrical shells,double-walled cylindrical shells coupled with non-axisymmetric internal and interlayered structures are studied by the present methods.The results imply that the vibro-acoustic behaviors of the shell are dominated by the interlayered solid connections and the annular fluid,respectively.Unlike the single-walled shell,the influences of non-axisymmetric internal structure on the double-walled cylindrical shell connected with annular plates are really small.The radiated sound power and sound pressure of the axisymmetric shell are determined by the circumferential wave number n=1 and n=2,respectively.However,the sound power of the shell coupled with non-axisymmetric internal and interlayered structures obviously contains more higher-order mode components.Finally,the vibro-acoustic responses of the stiffened conical-cylinder-spherical shell with an internal foundation in air and water are tested.The experimental results verify the effectiveness of the proposed method for the single-walled shells of revolution coupled with non-axisymmetric internal structures.