Analysis Of Vibro-acoustic Response Of Cylindrical And Conical Shell Based On Improved Transfer Matrix Method

In the study of the vibration and sound radiation of submarine,the submarine hull is usually simplified as the ring-stiffened cylindrical shell and stern can be simplified as the ring-stiffened conical shell.It is very difficult to get the derivation of the first order differential equation of the state vector when using the traditional transfer matrix method to solve the vibration characteristics of the shell.In addition,the traditional transfer matrix method by multiplying the transfer matrix of each segment to form a total transfer matrix will produce a relatively large cumulative error.In this paper,an improved transfer matrix method is proposed to analyze the characteristics of free vibration and underwater acoustic radiation of ring-stiffened cylindrical shell and ring-stiffened conical shell due to the shortcomings and limitations of traditional transfer matrix method.Firstly,in this paper,an improved transfer matrix method for solving the free vibration characteristics of a ring-stiffened cylindrical shell is proposed which greatly simplified the derivation process of the transfer matrix by introducing the displacement intermediate vector and the correlation matrix.The point transfer matrix can be derived according to the continuous deformation at the connection of the ring and the shell.The total transfer matrix is obtained by multiplying the transfer matrix and the point transfer matrix,and the natural frequency of the ring-stiffened cylindrical shell is obtained by dichotomy method.The influence of the structural parameters and the boundary conditions on the free vibration characteristics of the cylindrical shell is also discussed.Secondly,considering the excitation of external forces and sound pressure,the improved transfer matrix method is used to construct the response equation of ring-stiffened cylindrical shell.In order to improve the accuracy of the calculation and avoid the error caused by the matrix multiplication in the traditional matrix method,the whole transfer control equation for the acoustic and vibrational characteristics of the ring-stiffened cylindrical shell is assembled by transfer equations of all discrete segments.The Duhamel integral term generated by generalized sound pressure is solved by the precision integral method.The responses under concentrated forces and generalized sound pressure are obtained respectivelythrough the boundary conditions at both ends.Finally,the solution of the sound pressure coefficient is realized according to the continuous motion condition at the interface of the fluid-solid coupling.The influence of structural parameters,boundary conditions,directions of excitation force and fluid medium on underwater acoustic radiation characteristics is discussed.Thirdly,the field transfer matrix and stiffer point transfer matrix of the ring-stiffened conical shell are deduced directly from the cone differential equation by the improved transfer matrix method and the Precision-Gaussian integral method is used to solve the field transfer matrix.In order to improve the accuracy of the calculation,the conical shell is divided into small segments along the shell direction which can narrow the integration step and the whole free vibration equation of the ring-stiffened conical shell is assembled by the control transfer equations of all discrete segments.The natural frequency of the ring-stiffened cylindrical shell is also obtained by dichotomy method.The effects of boundary conditions,ring numbers and height,and the effect of half cone angle on the free vibration of conical shell are studied.Finally,it is the first time to propose an improved transfer matrix method for solving the underwater acoustic radiation of ring-stiffened conical shell and its effectiveness is verified.Compared with the cylindrical shell,this paper solves the nonhomogeneous first order differential equation with variable coefficients in the conical shell.The variable coefficient equation is transformed into a constant coefficient equation by transforming the cone shell into precise segments whose transfer control equations can assemble the whole transfer control equation.According to the boundary conditions of both ends,the displacement responses under concentrated force and sound pressure are obtained from the whole transfer control equation.Finally,according to the continuous motion condition at the interface of the fluid-solid coupling,the sound pressure coefficient can be obtained easily which can be used to get the sound pressure.The effects of cone angle,rings,structural loss factor,medium and boundary conditions on the underwater acoustic radiation characteristics of conical shell are discussed.