Research On Elastic Wave Propagation Characteristics Of Typical Grillage Structures In Ship Hull

Hull structure is an important pathway of converting vibration of mechanical equipments into underwater radiation noise.Dynamic behaviors of the hull structure are key factors affecting its underwater acoustic radiation characteristics.Excitations from mechanical equipments always transmit through the base to the hull grillage structure and cause its vibration response,which propagates in the hull grillage structures along the longitudinal,transverse and vertical directions of the ship.Such a conversion is essentially a mechanical wave motion phenomenon.Propagation and attenuation characeristics of the dynamic responses caused by mechanical equipments in the hull structure have always been a hot topic in the field of vibration and noise reduction.Research on this topic plays a significant role in dynamic performance evaluation and optimization of ship structures.The main hull structure is a complex three-dimensional beam-plate coupling construction assembled by spatial plate structures composed of decks,bulkheads,side shells and double bottoms,by transverse frame structures consisting of bottom ribs,side ribs and deck beams and by longitudinal frame structures constituted by stringers attached on decks,bulkheads,side shells and bottom plates.Beam and plate are basic components of the hull structure.With respect to these basic components,the theories of Euler-Bernoulli beam and Timoshenko beam and the theories of Kirchhoff plate and Mindlin plate are respectively introduced.Analytical wave solutions of matrix form are presented for the two classical beam theories,and the wave solutions of Kirchhoff thin plate theory and Mindlin plate theory are also derived under general elastic support boundary conditions,which lays a theoretical foundation for analyzing the wave propagation and attenuation characteristics of typical hull grillage structures based on the method of reverberation-ray matrix.According to the wavenumber characteristic equations obtained in the process of solving the dynamic equations of beams and plates,wavenumber spectrum characteristics of the Euler-Bernoulli beam and Timoshenko beam with elastic foundation and an infinite plate are respectively investigated.Wavenumber characteristic curves for the Kirchhoff plate of finite dimension with classical and elastic support boundary conditions are also discussed.In addition,the dynamic equations and their solutions as well as the wavenumber spectrum characteristics of the orthotropic plate,an equivalent model of the typical hull grillage structure in case of rigid plate with weak,orthotropic and closely distributed reinforcements,are also introduced.Ribs and stringers are usually almost periodically distributed along the longitudinal and transverse direction in both of the global and the local structure design of the ship.According to the Bloch theory of the periodic hull grillage structure and the basic idea of the method of reverberation-ray matrix for structural dynamic problems,a numerical formulation for analyzing wave propagation and attenuation characteristics of the beams and plates with periodically variable sections,with periodic couplings,and with doubly periodic couplings is established.Based on the Timoshenko beam theory and the numerical method for calculating the wavenumber spectrum of the above-mentioned periodic models,the wavenumber spectrum characteristics of the typical hull grillage structures are investigated.The effectiveness of the method in analyzing the wavenumber spectrum characteristics of the periodic beam model is verified by comparison of the numerical calculation results with the analytical calculation results of a honogeneous beam.On this basis,the general propagation and attenuation characteristics of the bending wave in beams with periodically variable sections,with periodic couplings,and with doubly periodic couplings are respectively analyzed.Subsequently,the effects of material properties and the geometry parameters on propagation and attenuation characteristics of bending wave in beams with periodically variable sections;the effects of the coupling modes between the beams and the spring oscillators,the mass and moment of inertia of the oscillators,and the translational and rotational stiffness of the spring on propagation and attenuation characteristics of bending wave in beams with periodic coupling oscillators;and the effects of the ratio of mass and moment of inertia of the two sets of oscillators,the ratio of translational and rotational stiffness of the two sets of springs on propagation and attenuation characteristics of bending wave in beams with doubly periodic coupling oscillators are investigated.Besides,in consideration of the difference between the finite periodicity of the typical hull grillage structures and the infinite periodicity of the theoretical model,the influence of spatial periodic extension on the wave propagation and attenuation characteristics of the typical hull grillage structures is also analyzed.In a similar manner,the wavenumber spectrum characteristics of the typical hull grillage structures are studied based on the plate models.The effectiveness of the method in analyzing the wavenumber spectrum characteristics of the periodic plate model is verified by comparison of the numerical calculation results with the analytical calculation results of an isotropic plate of finite width.Based on this study,the general propagation and attenuation characteristics of the in-plane waves,including the longitudinal wave and shear wave,and the out-of-plane waves,including the flexural wave and the near-field response of the plate with periodically variable sections,with unidirectional periodic stiffeners and with doubly periodic stiffeners are analyzed,respectively.Then,the effects of the in-plane stiffness on the propagation and attenuation characteristics of the in-plane waves and the effects of the out-of-plane stiffness and the thickness of the plate on the propagation and attenuation characteristics of the out-of-plane waves of the plate with periodically variable sections;the effects of the height and width of the stiffeners on the propagation and attenuation characteristics of the in-plane and out-of-plane waves of the unidirectionally reinforced plate with periodic stiffeners;and the the effects of the ratio of height and the ratio of width between the two sets of stiffeners on propagation and attenuation characteristics of the out-of-plane waves of the unidirectionally reinforced plate with doubly periodic stiffeners are investigated as well.According to the above-mentioned theoretical and numerical analysis,an experimental study on a truncated typical hull grillage structure has been carried out.Experimental model of the typical hull grillage structure is briefly introduced in the first step,and then the principle and method for equivalence between the typical hull grillage structure and the model of beam coupling with periodic oscillators are discussed.Comparison of the numerical calculation results of the wavenumer spectrum curves of the equivalent model and the experimental results of the spectrum curves of the acceleration admittance of the grillage structure reveals the coincidence of the attenuation bands of the experimental model and its equivalent model,which initially and partially proves the validity and effectiveness of the theoretical model and calculation method proposed in this paper.