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Study on Vibrational Transimission and Control of a Double-beam Structure with Elastic Connecting and Water Inside

Author: LiZeng
Tutor: ZhangZhiYi
School: Shanghai Jiaotong University
Course: Mechanical Design and Theory
Keywords: modal analysis fluid-structure interaction semi-finite double-panel double-beam structure adaptive control
CLC: O327
Type: Master's thesis
Year: 2010
Downloads: 59
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Abstract

Structural vibration and acoustic radiation is an important part of the studies of submarine structures. In the past few decades, lots of investigations were dedicated to these related subjects, and all of them can be divided roughly into two aspects, i.e. mechanisms and control strategies of structural vibration and acoustic radiation. The former focuses on vibration and acoustic characteristics of such structures as beams, plates and cylindrical shells coupled with fluid, and the latter on passive/active control principles as well as realization. On the basis of current researches, this thesis tries to discuss some basic problems and disclose certain phenomena under the background of vibration control of double cylindrical shells filled with water.On the basis of the Euler-Bernoulli theory, modal analysis method is employed to study the characteristics of the coupled vibration of a finite double-beam structure with different elastic connecting and water inside in this thesis, which stems from the simplification of a semi-infinite double-panel structure filled with fluid. Calculation results are derived to exhibit the effects of the fluid layer as well as the stiffness of the elastic connecting on the coupled vibration. Moreover, experiments are conducted to disclose vibration characteristics of an experimental model and demonstrate effectiveness of vibration transmission control. The conducted investigations in this thesis are listed as follows.(1) First of all, a semi-infinite plate model is simplified to a finite beam model. Then, the coupled vibration of a simply-supported double-beam structure with elastic connecting between the middle points of the two beams is investigated on the basis of the free and forced beam vibration equations. Modal analysis method is employed to compute the natural frequencies and frequency response functions (FRFs) of the coupled system, which are verified by the finite element analysis (FEA). Calculation results show that the spring of relatively small stiffness has little influence on resonant vibration frequencies of the system, but as the stiffness of the connecting increases to a certain extent, the natural frequencies of the out-of-phase modes increase with the rising of stiffness while other modes keep unchanged.(2) The coupled vibration of the double-beam system with water inside is investigated by combing the governing equation of transverse vibration, the wave equation and the pertinent boundary conditions. In the modeling, the symmetric and antimetric modes are expanded in terms of finite sine and cosine series, respectively, and FRFs of the coupled system are obtained according to the principle of linear superposition. FEA is used to validate the computation of FRFs, natural frequencies, mode shapes of the beams as well as the acoustic pressure distribution under resonant vibration. Calculation results show that the natural frequencies of the in-phase modes decrease with the reduction of distance between the two beams, but those of the out- of-phase modes are on the contrary.(3) On the basis of the former results, modal analysis method is employed again to describe the coupled vibration of the double-beam system with water and elastic connecting inside. The computation results reveal that the spring affects only the out-of-phase symmetric modes when it connects the middle points of the beams, and the corresponding natural frequencies increase with the stiffening of the spring. Moreover, influence of the fluid layer on vibration modes is different. For antisymmetric modes, frequencies of the in-phase vibration modes increase while those of the out-of-phase vibration modes decrease with the increase in the thickness of the fluid layer, and the symmetric modes are on the contrary. Variation of all natural frequencies decreases as the distance between the two beams approaches the beam length. Compared with the system without fluid, natural frequencies of the fluid-coupled system are reduced. (4) With the established model, adaptive control of vibration transmission in the double-beam system with water and elastic connecting inside has been investigated. Results have demonstrated that the adaptive method based on LMS can be used to reduce the vibration of the point where the actuator is mounted, and the acoustic pressure distribution in the fluid domain is changed accordingly. Furthermore, the in-phase symmetric modes are more difficult to control than the out-of-phase antimetric ones when control force is exerted at the position of connection.(5) An experimental model of finite double-panel is built, and influence of the fluid layer and the connecting between the panels on vibration characteristics as well as vibration transmission under active control are analyzed by vibration measurement and control. Experimental results show that the existence of fluid layer decreases the natural frequencies of the model but strengthens the coupling of vibration of panels as compared to the case without water. Adaptive method can be applied to control vibration transmission in the double-panel system filled with water. Therefore, experimental results have proved the theoretical analyses albeit there are differences between the physical models.

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