Analysis Of Vibro-Acoustic Characteristics Of Double Cylindrical Shell Underwater Based On Precise Transfer Matrix Method

In the study of vibro-acoustic characteristics of underwater vehicle,the middle cabin of underwater vehicle is usually simplified as the double cylindrical shell underwater.The equations of inner shell and outer shell should be calculated simultaneously with considering the effect of connecting structure and flow field between shells when using precise transfer matrix method to solve the vibration and sound radiation of the double cylindrical shell underwater.The solving process is more complicated than the solving process of single-layer shell.At present,precise transfer matrix method is generally used to solve the problems with free,simply supported and clamped boundary conditions.The method has its limitation when solving the elastic boundary problem,especially in underwater acoustic radiation.In this paper,precise transfer matrix method is extended to the study of free vibration and underwater acoustic radiation of double-layer cylindrical shell with elastic boundary.Firstly,precise transfer matrix method of single-layer cylindrical shell for analyzing vibro-acoustic characteristics is introduced.The first order homogeneous partial differential equation of displacement and internal force vector is derived from the basic equation of cylindrical shell.The general transfer equation is assembled with the field transfer matrix of cylindrical shell obtained by precise integration.The natural frequency of cylindrical shell is calculated according to the boundary condition.On this basis,considering the effect of point force and sound pressure,the responses under point force and generalized sound pressure are obtained respectively,and the sound pressure coefficient is calculated according to the continuous motion condition at the interface of the fluid-solid coupling.Thus the calculation results of vibration and sound radiation of cylindrical shell are obtained.Through comparing the results of precise transfer matrix method with the results of finite element and boundary element method,the accuracy and efficiency of the proposed method is verified.Secondly,the transformation matrix of boundary is proposed to obtain the total transfer equation of cylindrical shell with elastic boundary.By this,the natural frequency of cylindrical shell with elastic boundary is calculated.The field transfer matrix of cylindrical shell with variable thickness is derived from the basic equation of cylindrical shell.The natural frequency of cylindrical shell with variable thickness is calculated with the Pade function replacing Taylor expansion in precise integration.The influence of boundary restraint stiffness,thickness variation and ratio of length to radius on free vibration characteristics is studied.Thirdly,based on the transformation matrix of boundary proposed in Chapter 3,the responses under point force and generalized sound pressure are calculated respectively with taking into account the action of point force and sound pressure,thus the general transfer equation for solving underwater acoustic radiation of cylindrical shell with elastic boundary is obtained.The sound pressure coefficient is calculated according to the continuous motion condition at the interface of the fluid-solid coupling,and the calculation results of underwater sound radiation of cylindrical shell are obtained.The effect of structural parameters,structural loss factor,and fluid medium on underwater acoustic radiation characteristics with elastic boundary is studied.The effect of boundary restraint stiffness and damping on acoustic radiation characteristics under elastic boundary is also discussed.Finally,precise transfer matrix method is extended to the study of free vibration and underwater acoustic radiation of double cylindrical shell with elastic boundary.By calculating the transfer equations of inner shell and outer shell simultaneously,using two considerations to calculate the point transfer matrix of ring ribbed plate between shells and introducing the transformation matrix of elastic boundary,then the general transfer equation of double cylindrical shell with elastic boundary is obtained.The natural frequency of double shell is solved,and the underwater radiated sound pressure of double shell is calculated with considering the action of point force and sound pressure.The numerical results of two thinking ways are compared and analyzed,and the effect of boundary restraint stiffness,damping and restraint position on natural frequencies and radiated sound pressure is discussed.