Vibration Analysis Of Ring-stiffened Elliptic Cylindrical Shells

The study is part of the"Research on the vibration and sound radiation characteristics of submerged non-circular cylindrical shells"in the project of the National Natural Science Foundation of China(Number:51479079).This paper aims to build the theoretical model of the vibration analysis of elliptical shells with ring-stiffeners.Analytical methods are used to investigate the free vibration and forced vibration characteristics of ring-stiffened elliptic cylindrical shells.At the same time,experimental studies are carried out to verify the theoretical results.Through the discussion of the influence of shell's ellipticity parameter,shell length,rib size and other important parameters on the vibration characteristics of the shell,the vibration characteristics of submerged ring-stiffened elliptic cylindrical shells are revealed.The research results can be theoretical guidance for the application of elliptical shells with ring-stiffeners in engineering practice.Firstly,an overview of the research about vibration characteristics of stiffened cylindrical shells and elliptical shells without stiffeners are presented.Methods for the simulation of stiffeners,fluid field,and the variable radius of curvature are summarized.Based on Flügge shell theory and“smeared”stiffener theory,the vibration equations of the ring-stiffened elliptic cylindrical shell coupled with the fluid field is proposed.Assume that the outer fluid is the idea acoustic medium,The sound pressure is described by the Helmholtz Equation.The external excitation load is the circumferential concentrated point load.By transforming the partial differential equations with variable coefficients into linear equations with constant coefficients through trigonometric series transformation method,free vibration and forced vibration theoretical analysis model of the ring-stiffened elliptic cylindrical shell coupled with fluid is established.Based on the vibration theoretical control model,the sound pressure F_L is set to zero.The natural frequency and the forced vibration responses of the ring-stiffened elliptical shell in the vacuum are obtained by solving the vibration equation of the system.The influences of system characteristic parameters such as the ellipticity parameters,the spacing of ring stiffeners,and the size of ring stiffeners on the natural frequency and input power flow of the shell are discussed in detail.Considering that the ring-stiffened elliptical shells will couple with the fluid in engineering practice,the free vibration characteristics and forced vibration responses of the shell—fluid coupling system are systematically studied by solving the theoretical model based on the Fourier series expansion method.The influences of system characteristic parameters on the natural frequency and input power flow of the coupling system are discussed in detail.According to the previous theoretical analysis,the free vibration characteristics of elliptical shells without ribs with simple supports at both ends in the air and fresh water are experimentally studied.A static tensile test is carried out on the processed material of the shell and the actual property parameters of the material are obtained.The experiment strategy is determined by comparing the numerical calculation results of the mode shape and the modal frequency of the shell with/without the sensor mass by the finite element method and theoretical method.Hammer modal experiments are performed on three shell models with two ellipticity and two shell lengths.The vibration modes and corresponding natural frequencies of the shell are obtained by combining the test data.The experiment results and the theoretical solution fits well,which proves that the theoretical vibration model and its solution method are correct.In this paper,the theoretical control model of the vibration of the ring-stiffened elliptic cylindrical shell—fluid coupling system is established.An analytical method for the vibration characteristics of the coupled system is proposed.The free vibration characteristics of elliptical shells without ribs,which is the degenerate model of the theoretical model,is performed by experimental research.The results obtained by the theoretical method and the experimental method show good agreement with those in the literature,which proves that the theoretical model and the solving method is correct.