| In the field of ship and marine engineering,cylindrical shell is widely used in underwater vehicle structures.Many researchers have studied the vibration and sound radiation characteristics for cylindrical shell,and a relatively perfect theoretical has been formed.However,there are the many types of liquid tanks which exist in cylindrical shell structure.When the liquid in the tank is disturbed,the sloshing effect generated by the free liquid surface of the fluid will couple the cylindrical shell to vibration.And acoustic performance has a significant impact.The study of the coupled vibration problem of the cylindrical shell considering the free liquid sloshing effect has certain reference significance for guiding the acoustic design and acoustic evaluation of underwater vehicles with liquid tanks.In this paper,the physical model of the cylindrical shell with liquid tank is simplified to the partially liquid-filled cylindrical shell considering the sloshing effect of free liquid surface,and the coupled vibration characteristic of the system are studied.The present paper,at first,study the free vibration of the infinite cylindrical shell half-filled with liquid taking into account the linear motion of the free surface,sloshing.Assuming the internal fluid is incompressible and inviscid,and only harmonic motion of the coupling system is considered,the vibrational control equation of the coupled system is been established combination the classical Flügge thin shell theory and the Laplace equation.The circumferential and radial displacements of the shell are expanded in Fourier series,while the velocity potential of the internal fluid is in combinations the Polynomial series and Sine/Cosine series.The analytical formulation of the velocity potential which satisfy the sloshing boundary condition of free surface is obtained.Then the Galerkin integral method is adopted to deal with the velocity continuous condition on the partially coupled interface.The vibration control equations of the coupled system of semi-filled cylindrical shells after considering the sloshing effect are derived.The free vibration solutions of both the inner sloshing fluid and the cylindrical shell are solved simultaneously by solving the characteristic equation values using numerical procedures,The natural frequencies and modal shapes both sloshing liquid and shell are obtained,the sloshing effect of the free surface on the coupled system is discussed,and the results obtained from the present approach are compared with that from the finite element method(FEM)and published literature.A very good agreement is demonstrated,which verify the present method is correct.Then,focus on the general situation,free vibration of the model of the finite cylindrical shell half-contained with internal sloshing liquid are investigated.For the simply supported shell at both ends,the methods of double series expansion which are in terms of Fourier series and triangle series are applied,and according to the Galerkin approach mentioned in previously,and conducting the orthogonal processing.Finally,the coupled vibration control equation of coupled system is obtained.Then the free vibration characteristics both internal sloshing fluid and the shell are solved numerically,and sloshing modal of the fluid and coupled modal of the shell are obtained,the sloshing effect of the free surface on the coupled system is discussed,then the comparison of results between the present method and FEM is carried out,which shows a good agreement.Next,the numerical analysis for the finite cylindrical shell partially filled with fluid considering the sloshing effect of the free surface is carried out.Based on the finite element method(FEM),the finite element model of the cylindrical shell simply supported at both end and the internal sloshing liquid are built,where the shell structure and inner fluid are simulated by the shell element and the acoustic element,respectively.The classical parameters effect such as the shell thickness and liquid depth on the free vibration and forced response of the coupled system are investigated in deeply.Finally,in order to verify the method proposed in this article,two experimental models are designed to measure the sloshing modal characteristics(sloshing frequency and sloshing shape)of internal liquid within the cylindrical shell,and the coupled modal of the shell partially-filled in the air,when the inside liquid is sloshed with small and linear motion,respectively.In this paper,the experiment of sloshing modal characteristics is carried out at present.The sloshing frequencies and modal shapes of the free surface at three different filled depths are measured.The experimental results are in good agreement with the theoretical and finite element results,which proves present approach is correct.This paper takes into account the free surface motion,sloshing,to investigate the vibration characteristics of the partially liquid-filled cylindrical shell by means of three aspects: theoretical method,numerical analysis and experiment.Especially,A new analytical method is proposed for the semi-filled cylindrical shell with internal sloshing fluid,which reveals the mechanism of the sloshing effect on the vibration characteristics of the coupled system in theory.This research can provide a theoretical reference for studying the coupled vibration-acoustic characteristics and noise control of the cylindrical shell with liquid tank. |
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