Research On Uncertainty Analysis Of Vibration And Noise Of Underwater Structure Based On Isogeometric Boundary Element Method

Acoustic-vibration coupling analysis is very important for high-speed locomotive,naval ship,aviation and other important engineering fields.Most of the current research uses water and air as the sound field medium,but the mechanical impedance of these two mediums is quite different,which results in the distinction of strong and loose coupling.Ignoring this effect can lead to poor analysis accuracy or even errors.To solve this problem,the finite element method（FEM）is used to analyze the vibration response of underwater shell structures,and the boundary element method（BEM）is used to analyze structural vibration acoustically.By combining FEM and BEM,the coupled FEM-BEM method is used for the acoustic-vibration strong coupling analysis of underwater thin shell structures.In order to overcome the problems of discontinuity and low precision in the traditional Lagrangian approximate geometric model and physical field interpolation calculation,the isogeometric method is used to construct the geometric model,and the same spline function is used to perform the high-order interpolation calculation of the physical field,so as to realize the integrated computer aided design / computer aided engineering（CAD）/（CAE）analysis of the underwater acoustic-vibration strong coupling system.In addition,the nonlinear eigenvalue problem generated by the FE/BE method is transformed into a small-scale linear eigenvalue problem by using the contour integral method,and a vibration eigenvalue analysis method for underwater structures is derived.The Burton-Miller method is used to overcome the fictitious eigenfrequency problem in the boundary integral equation,and the scontour integral method used is improved.Uncertainty analysis is devoted to studying the problem of output uncertainty caused by the uncertainty of system input.Monte Carlo simulations（MCs）are a commonly used method for solving system response uncertainty problems with random input variables.However,a large number of samples are required to ensure its accuracy,and the computational cost is high,and it is rarely used directly in practical applications.In order to improve the efficiency of Monte Carlo calculation,it is necessary to combine with other discrete algorithms to reduce the dimension of random variables and reduce the cost and scale of calculation.By using proper orthogonal decomposition（POD）and radial basis function（RBF）,the cost of calculation can be reduced,the efficiency of calculation can be improved,and the fast stochastic analysis based on MCs can be realized.In this paper,the deterministic isogeometric finite element method boundary element modeling method is combined with the accelerated Monte Carlo simulation method to analyze the uncertainty of structures,and the sound scattering problems of underwater spheres and submarines are taken as examples to verify the effectiveness of the algorithm.