Jacobi-Ritz Method And Application For Vibration And Sound Radiation Of Composite Shells Of Revolution

With the development of vibration and noise reduction technology for ship,the light weight,high strength,low vibration,low noise and designability have gradually become the design requirements of new ships and submarines.However,the material and mechanical properties of steel are difficult to meet new requirements of vibration and noise reduction for the ship.On the one hand,composite materials have advantages of light weight,high strength,corrosion resistance,etc..On the other hand,due to the difference in impedance between composite materials and steel structure,the transmission of vibration energy in ship can be reduced,which makes its application more prominent in ships and submarines.The research on vibration and acoustic radiation of composite materials involves the interdisciplinary fields of structural mechanics,fluid mechanics and material mechanics.There are some difficulties in theoretical modeling,complex derivation process and insufficient solving methods.Domestic and foreign scholars have carried out a lot of fruitful research on the vibration and acoustic radiation of composite materials,including analytical method,domain decomposition method,improved Fourier method,differential quadrature method,finite element method,etc.for vibration analysis and analytical method,boundary element method,infinite element method,wave method,etc.for acoustic radiation analysis.However,there are still some problems in research of vibration and acoustic radiation characteristics of composite shells of revolution,such as the unified vibration analysis formula of composite shells of revolution has not been effectively established,the simulation of complex boundary conditions and elastic coupling continuity conditions of substructures is difficult,the acoustic radiation analysis method of composite shells of revolution needs to be improved,and the influence mechanism of structural parameters on vibration and acoustic radiation for composite shells of revolution still needs to be further revealed.For this reason,the paper focusing on the method and applications of vibration and sound radiation for fiber reinforced composite and functionally graded composite,this paper has carried out the following research work:Based on three-dimensional elastic theory,the motion differential equation of composite structure is derived by using energy variational method,and the simulation of complex boundary condition of composite structure is realized by introducing penalty method.On basis of domain decomposition method,the construction form of displacement functions for revolution shells based on Jacobi polynomial is proposed,which expands the selection and construction of displacement functions.In this paper,the energy functional of composite shells is constructed,and the Jacobi-Ritz method is proposed,which is suitable for general shells of revolution and integrates various semi analytical methods.On this basis,three-dimensional elastic theory is reduced to thin shell theory.Taking cylindrical and spherical shells as examples,the convergence analysis of Jacobi-Ritz method is carried out,and the stable convergence range of Jacobi parameters and shell segments is given.The results of this paper are compared with approximate exact solution and finite element method,and the effectiveness of the method is preliminarily verified.Based on the research of Jacobi-Ritz principle for vibration analysis of composite shells,three-dimensional elastic theory is reduced to first-order shear deformation theory(FSDT),and the vibration characteristics of composite shells with moderately thickness are studied.Firstly,the composite shells with general geometric shape is decomposed into several shell segments along the circumferential direction based on micro element method.The displacement admissible functions of the shell are expressed by Fourier series in circumferential direction and Jacobi polynomial in axial direction.The energy variation method is used to derive the motion differential equation of composite shells,and the energy functional of general shells under complex boundary conditions is constructed.In addition,the unified formula for vibration analysis of composite shells is proposed.On this basis,the composite shells are divided into single shells and doubly curved shells.The convergence analysis and effectiveness verification are carried out for different curved shells,and the stable convergence range of Jacobi parameters,number of segments,truncation number of displacement admissible functions are defined,and the validity of unified formula is verified from many aspects.On basis of the above research,the parametric study on vibration characteristics of the mentioned shells is carried out from two dimensions of fiber reinforced composite and functionally graded composite,and the influence rules of structural parameters,material parameters and laying scheme on the vibration characteristics of composite shells are explored.In order to solve the problems such as the lack of revealing the vibration mechanism of combined composite shells and the difficulty for simulate the elastic coupling of substructure,the vibration characteristics of combined composite shells with moderate thickness are studied based on Jacobi-Ritz method and FSDT.Firstly,the combined composite shells are decomposed into several substructures at interface by using differential element method,and the substructure is further decomposed into several shell segments.The complex elastic boundary conditions and elastic coupling simulation of substructure interface are realized by introducing penalty method.The energy equations such as kinetic energy,strain energy,substructure elastic potential energy,boundary elastic potential energy and shell elastic potential energy of combined composite shells are given.The energy functional of combined composite shells is constructed,and the unified formula for vibration analysis of combined composite shells is formed.On this basis,the vibration characteristics of combined composite laminated shells and functionally graded shells are studied respectively,which verifies the fast convergence and effectiveness of unified formula for vibration analysis of combined composite shells,and the mechanism of influence of material parameters,structural parameters,exciting force position and fiber laying angle on vibration of combined composite shells of revolution are revealed.Based on the study of Jacobi-Ritz method for vibration analysis of composite shells,the idea of spectral method is introduced to improve the traditional boundary element method,and a Jacobi-Ritz-modified boundary element method(MBEM)for acoustic radiation analysis of composite shells of revolution is proposed.Specifically,the composite shells are firstly decomposed into several shell segments,and then the Helmholtz integral equation is transformed into the boundary integral equation.Referring to treatment of displacement admissible functions,the acoustic variables and Green's functions are expanded into the form of Fourier series and orthogonal Jacobi polynomials.The theoretical model for acoustic radiation analysis of composite shells is established based on one-dimensional Helmholtz boundary integral equation.For non-unique solution of characteristic frequency points and singular integral problems,the chief point method and elliptic integral method are used to deal with the problem.Considering the far-field radiation condition of Sommerfeld at infinity and the impedance difference between light and weight fluids,a unified acoustic-vibration coupling equation of composite shells is established based on principle of virtual work.The convergence and effectiveness of Jacobi-Ritz-MBEM are investigated through a series of numerical calculations and comparative verification.The influence mechanisms of structural parameters,material parameters,boundary conditions,excitation location and laying scheme,etc.on acoustic radiation characteristics of composite and combined composite shells are explored.Based on the above research,taking cylindrical-conical-spherical(CCS)shell as an example,the vibration and sound radiation transfer characteristics of the composite shell in light and heavy fluid environment were tested.According to the test content and environment,the test scheme is designed.The effects of model processing error,sensor added mass,fluid density and hydrostatic pressure on the vibration characteristics of CCS shell are studied.The vibration and acoustic radiation transfer characteristics of CCS shell under the excitation of exciter in anechoic chamber and anechoic pool environment are tested,and the experimental results are compared with those obtained by present method.Finally,based on Jacobi-RitzMBEM method,the circumferential sound pressure distribution characteristics for typical cross section of CCS shell are present,which provides the method and numerical reference for the acoustic radiation characteristics of the CCS shell.