Study On Semi-analytic Methods And Vibro-acoustic Characteristics Of Coupled Propeller-shaft-hull Structures Subjected To Longitudinal Excitations

At low cruising speed,longitudinal forces of propellers are one of main excitations generating vibrations and radiated noises of submarines,and the excitations have terrible effects on the stealth performance of submarines.In the opened literature,investigations about vibrations of shell structures mainly focus on individual cylindrical shells,conical shells and spherical shells,but practical submarine hulls are generally composed of ring-stiffened conical shell,ring-stiffened cylindrical shell with multi-compartments and opened spherical shell.In addition,as submarines are excited by the longitudinal component of propeller forces,vibrations of the hull are the whole longitudinal and bending vibrations.As a result,considering separate submarine compartment cannot predict accurate vibro-acoustic results.Maybe the finite element method and boundary element method are powerful tools to deal with the problems,and commercial software,e.g.ANSYS and Virtual.Lab,can be utilized on hand.However,these numerical methods have inherent disadvantages in efficiency,storage space and mechanism analysis.Under the circumstance,developing a theoretical approach to accurately and effectively predict vibro-acoustic responses of coupled propeller-shaft-hull structures subjected to longitudinal excitations is of important academic value and military significance.First of all,a semi-analytic method is proposed for vibro-acoustic analysis of ring-stiffened shells of revolution,and the only limitation of the proposed method is the axial symmetry of shells.The method is involved in dividing the shell into several shell segments and annular plate substructures,and narrow shell segments are approximately treated as conical or cylindrical segments,which depends on the semi-vertex angle.As analyzing substructures,displacements of conical segments,cylindrical segments and annular plates are expanded as power series,wave functions and Bessel functions,respectively.After all substructures analyzed,they can be assembled together through continuity conditions,and the corresponding governing equation about vibration responses can be established by additionally taking into account boundary conditions.In addition,for the rings with rectangular seciton,T-seciton or L-seciton,a new approach which utilizes the combination of annular plates and cylindrical shell segments to model rings is proposed,and the influences of rings on the shell can be considered by the approach.As the shell is submerged in fluid,the fast boundary element method of axisymmetric structures is extended to analyze the fluid-structure interaction.By expanding the surface pressure and velocity as Fourier Series and utilizing the relations between the surface velocity of shell and displacement functions of shell segments,surface Helmholtz integral equation is simplified to the line integral along one generating line,and the relationship between the surface pressure and displacements can be easily obtained by dividing the generating line to several 3-node elements.The vibro-acoustic governing equation of submerged shells of revolution can be established by introducing acoustic radiation pressure to continuity conditions of adjacent shell segments.Since only axial symmetry is utilized to deduce the governing equation,the application of proposed method is wide,and it is no need to solve complex wavenumbers in fluid,which obviuosly improves the efficiency.More importantly,vibro-acoustic results of three kinds of shells of revolution,including stiffened conical shells,stiffened cylindrical shells and opened spherical shells,indicate that the proposed method is of fast convergence speed and high accuracy.Based on the established governing equation of ring-stiffened shells of revolution,three kinds of combined conical-cylindrical shells,such as stepped cylindrical shells,stepped conical shells and combined conical-cylindrical shells with ring stiffeners,are firstly employed to discuss the accuracy of present method,and effects of boundary conditions and discontinuities are further studied.In addition,influences of stiffeners,bulkheads,excitations and contributions of different modes on vibro-acoustic characteristics of submerged combined conical-cylindrical-spherical shells are emphatically investigated,and the results are useful for vibro-acoustic analysis of coupled propeller-shaft-hull structures in the following analysis.To investigate vibro-acoustic characteristics of coupled propeller-shaft-hull structures subjected to longitudinal excitations,a fast semi-analytic method is proposed.The method overcomes the shortage of general analytic methods that only cylindrical shells are employed to model the hull,and a more practical model,ring-stiffened combined conical-cylindrical-spherical shell,is adopted.To analyze the propeller-shaft system,the propeller,shaft,thrust bearing and foundation are modeled as lumped mass,rod,spring-damping-mass and Timoshenko beams,respectively.Through the governing equation of shells of revolution and continuity conditions between the hull and propeller-shaft system,the governing equation for vibro-acoustic analysis of coupled propeller-shaft-hull structures can be easily established.By comparing results of present method and FEM/BEM,validity of the proposed method is demonstrated,and influences of the model truncation and coupling effects between the hull and propeller-shaft system are investigated in detail.To reduce vibro-acoustic responses of the hull subjected to propeller longigudinal excitations,one effective way is to control the transmission path of longitudinal excitations.On the basis of the proposed method,three kinds of measures,namely changing the foundation and inserting longitudinal isolator and resonance changer between the foundation and thrust bearing,are considered to attenuate vibro-acoustic responses of the hull,and effects of some parameters about the three measures are further discussed.Finally,vibro-acoustic experiments about two stiffened shells of revolution,such as conical and cylindrical shells,are carried out,and the two models are closed by two end plates.By comparing vibro-acoustic results of present method and experiments,the validity of proposed method for vibro-acoustic analysis of ring-stiffened shells of revolution is demonstrated once again.Furthermore,based on the experiment results,the differences of the two ring-stiffened shells of revolution under vertical and longitudinal excitations are analyzed,and relative tendencies of the shells under different excitations are consistent with the ones obtained by the proposed semi-analytic method in vibro-acoustic analysis about the combined conical-cylindrical-spherical shell.