The Whipping Response Of Ship Under Underwater Explosion Loading And Total Longitudinal Strength Check

The stiffened cylindrical shell is the main form of submarine which has been studied extensively.The whipping response is a unique form motion of the slender body structure under non-linear load,which has a great influence on the ship’s total longitudinal strength.Therefore,the research on the whipping response of the stiffened cylindrical shell is particularly important.The experimental research method and numerical research method are applied more,and the research on analytical solution is less studied.Compared with the experimental research method and numerical research method,the analytical solution consumes less manpower and material resources,and it does not need to establish a large-scale three-dimensional finite element model,which saves time and cost.Therefore,the research on analytical solution has positive significance.In this paper,a whipping response analytical method of ship girder under underwater explosion loading is proposed,and its validity is verified by numerical method and experimental data.Finally,based on the analytical solution,the influence of different parameters on the whipping response is discussed and the software for calculating whipping response is written.Firstly,in the introduction,the research status of underwater explosion shock wave load,bubble load and dynamic response of cylindrical shell under underwater explosion is reviewed,and their advantages and disadvantages are compared to provide theoretical guidance for subsequent research.Whipping response analytical solution of hull girder under underwater explosion load is described in detail.According to the motion characteristics,the hull is simplified into a one-dimensional beam element using Timoshenko beam model and Rayleigh damping,and Cole’s semi-empirical and semi-analytical formula of underwater explosion load is selected as the underwater explosion shock wave load model.Based on the Taylor plate theory,the hydrodynamic force of the shock wave stage is calculated,the advantages and disadvantages of Vernon bubble model and G-H bubble model are compared and analyzed,and the bubble model type used in the analytical solution is determined.Based on potential flow theory and Morison’s relative velocity formula,the hydrodynamic force in the bubble load stage is calculated.Finally,the Newmark method was used to solve the dynamic response of hull girder.The design process of the experimental stiffened cylindrical shell model is discussed based on the similarity theory.The main reason of the whipping response is the low-order mode resonance,and the experimental conditions are designed based on this theory.The least square method is used to process the strain data,and the data removed trend term is compared with the original experimental data.The acceleration signal is decomposed by EMD method,the noise signal and trend terms are removed.The modal parameters are identified by LSCE method,and the false modal parameters are removed based on the stability diagram.The processed strain data,acceleration data and the identified modal parameters based on the acceleration data provide the data basis for the subsequent numerical simulation research and the validity verification of the analytical solution.Using ABAQUS numerical simulation software,a finite element model of a stiffened cylindrical shell is established based on the acoustic-solid coupling method and the validity of the finite element model is verified.The total longitudinal strength of stiffened cylindrical shell is calculated and analyzed from the perspective of the ultimate bending moment.Finally,based on the whipping response analytical method,the strain data of the stiffened cylindrical shell used in the test is calculated.The experimental method,numerical simulation method and analytical method are compared and analyzed from the maximum strain amplitude and the peak time of the first whipping response.Based on the analytical method,the influence of charge depth,explosive distance and charge longitudinal position on whipping response is discussed.The strain increases and then decreases,the whipping response is the most intense when the ratio is 1.34.The strain decreases with the explosive distance.The strain response increases and then decreases with longitudinal charge position.The whipping response is the most intense when longitudinal charge position is the middle of ship.