Research On Vibration Band Gap Analysis Methods And Its Characteristics Of Ship Hull Periodic Grillage Structures

The noise control of hull structures has always been an important content of ship design.Not only military ships pay attention to the negative impact of the low-frequency line spectrum characteristics of the hull on its acoustic stealth ability,but also civil ships put forward higher requirements for the comfort of personnel’s work and life.With good vibration and noise reduction performance,it poses a more arduous challenge to the design of modern ship structures.The vibration in the ship hull is often transmitted through the grillage structures.With the development and maturity of equipment vibration isolation technology,the low-noise structure design for the ship hull is facing great development demands.In recent years,the research on the vibration band gap characteristics of periodic structures is more in-depth.Therefore,the vibration band gap theory of periodic structures is considered to be applied to the design of low-noise structure of ship hull grillages in this thesis.The vibration band gaps of the ship hull periodic grillage structures can be used to adjust the transmission characteristics of elastic waves and improve the noise performance of the ship hull structures.Focusing on the research goal of vibration band gap characteristics of ship hull periodic grillage structures,the numerical analysis models of periodic grillage structures suitable for spectral element method and wave finite element method are puted forward,the vibration band gap calculation methods of periodic grillage structures are summarized,the vibration band gap characteristics and influencing factors of infinite and finite-width periodic grillage structures are studied,the similarities and differences of different methods in dealing with vibration band gaps of grillage structures are discussed,and finally the numerical analysis method and influence parameters of vibration band gap are verified through model tests in this thesis.Firstly,the vibration band gap research status of periodic structures is introduced,the advantages and disadvantages of different research methods are summarized,and then the spectral element method and wave finite element method are selected to calculate and analyze the vibration band gap characteristics of ship hull periodic grillage structures.On this basis,the research thinking of introducing the numerical methods into the vibration band gap analysis of periodic grillage structures is elaborated,and the main research contents of this thesis are summarized.In order to calculate the vibration band gap characteristics of periodic grillages,the equivalent and corresponding relationships between periodic grillages and grid structures are defined.Then the main basic theories of periodic structures are summarized and research on the vibration band gap characteristics is carried out on this basis.The two numerical methods correspond to different numerical models,so the motion control equations of the periodic structures should be derived respectively.For the periodic grid model used in the spectral element method,the spectral stiffness matrix of Timoshenko beam element is firstly established,and then the complete stiffness matrix of the periodic grid unit can be obtained through coordinate transformation and unit assembly.Combined with the Bloch periodic boundary,the control equation for vibration band gap analysis can be obtained;For the wave finite element method,the geometric model of grillage structures is firstly established according to the lattice and energy band theory,and then the characteristic equation of periodic unit under the given wave vector is deduced combined with the Bloch theorem.Then,the vibration band gap characteristics of periodic grillage structures based on spectral element method are analyzed.For the periodic grid structures,the spectral element method is used to calculate the vibration band gap characteristics,and then the outplane and inplane vibration of the structure are decoupled.The band gap numerical results are verified by calculating the vibration transmission of the finite-length periodic grid structures.After that,the influences of periodic grid unit layout,the material and structural parameters of the longitudinal and transverse members on the distribution of vibration band gaps are analyzed.Based on the periodic grid structures,the periodic oscillator coupled grid structure model is proposed,and the coupling effect of the vibrator mass system is analyzed.The basic process of the periodic grillage structures equivalent to the numerical analysis model is summarized,and the dynamic equivalence of the grillage structures is realized.Then the vibration band gap calculation method based on the spectral element is verified by band gap characteristics calculation and analysis of the periodic grillage structures and the finite-length grillage model test.Then,the vibration band gap characteristics of periodic grillage structures based on wave finite element method are analyzed.Firstly,the vibration band gap characteristics of periodic plate structures obtained by finite element method is verified by plane wave expansion method,and then wave finite element is applied to analysis of vibration band gap characteristics of periodic grillage structures,in which the effectiveness and accuracy are verified by model test.After that,the influences of the component material differences,the single or double wall grillages and the longitudinal or transverse frame types of grillage structures on the vibration band gaps are discussed,which provides a reference for the vibration and noise reduction design of engineering structures.Based on the above numerical models,the vibration band gaps of infinite periodic grillage structures is calculated,and the consistency of the numerical methods is verified.Furtherly,the numerical analysis model of ship hull periodic grillage structures vibration band gap calculation is proposed,and then the band gap characteristics of ship hull finite-width periodic grillages under the fixed support boundary condition on both width sides are calculated.The similarities and differences between ship hull periodic grillage structures and infinite periodic grillages are analyzed.At the same time,the advantages and disadvantages of two numerical methods in calculating the vibration band gaps of periodic grillages are compared,and the selection suggestions of numerical methods are provided.Afterwards the vibration band gap influencing factors of typical ship hull periodic grillage structures are studied,which will provide guidance for the design and application of vibration band gap characteristics of ship hull periodic grillages.Finally,the experimental study on the vibration band gap characteristics verification of the reduced scale model of ship hull periodic grillages is carried out.The vibration band gap characteristics obtained by the numerical method are verified through the test results of vibration transmission of the manufactured periodic grillage structures.And the variation law of vibration band gap characteristics is verified by changing the design parameters of the grillage structures.Meanwhile,the vibration transmission spectra of grillages under the loads of liquid tank and added water mass are obtained,which prove the influence of additional mass on the vibration transfer characteristics and provide a reference for the practical engineering structure design.The research content of this thesis can be applied to many related fields,such as structural acoustic design,vibration and noise reduction.