Dynamic Stiffness Modeling Method And Vibration Behavior Analysis For Plate-shell-coupled Structures With General Boundary Conditions

Quantitative acoustic design is an important factor to promote the quieting process of vessel.Accurate modeling method and analysis of vibration and noise are the foundation and key of quantitative acoustic design.As a huge system,the hull is usually composed of plate and shell elements of different geometric shapes.Existing research methods are usually confined to numerical methods such as finite element method and boundary element method,but there are obvious defects such as long calculation time and large space occupation,which are not convenient for in-depth mechanical research.Therefore,establishing a set of accurate and efficient modeling and analysis methods for coupling structures that are applicable to arbitrary coupling boundary is the key to effectively solve the above contradictions,which has important theoretical value and guide for improving the quantitative acoustic design of vessel.Focusing on the vibration modeling method and dynamic characteristic analysis of complex coupling plate and shell structures with arbitrary boundary conditions,the following work has been carried out:Based on the dynamic stiffness matrix method,the dynamic analysis models for coupling plate and rotating shells under arbitrary boundary conditions are presented.Firstly,the coupling structure is decomposed into several subunits along coupling boundaries.The shape function is exactly derived from the governing equation of the subunit.Then,the stiffness matrix connecting displacement and internal force along boundary lines is constructed.The dynamic stiffness matrix is a function of frequency,and it also contains the inertia,stiffness,damping property of the structure.For a single element with continuous geometry and material properties,only one dynamic stiffness matrix is needed.Finally,the dynamic stiffness matrix of the structure is assembled according to the coupling conditions between the subunits.The accuracy and efficiency of the present method are verified by comparing the results with the existing literatures and simulation software.The free vibration analysis model of in-plane coupled plate structures with arbitrary boundary conditions is established.In the formulation,the idea of Levy solution and the projection method are integrated,which not only reserves the precision of Levy solution but also solves the problem of spatial independence of displacement and internal force.The model is applicable to all kinds of classical boundary conditions.Meanwhile,the virtual spring is introduced to simulate the elastic constraint which realizes the parametric modeling of the boundary conditions.The dynamic stiffness matrix of the plate is constructed according to the boundary line nodes,which can deal with the boundary continuity condition flexibly.Accuracy of the solution is guaranteed by the precise boundary coordination.By several examples,the reliability of the present method is verified.A unified dynamic stiffness matrix modal for dynamic problem of coupling plate structure with arbitrary coupling angle is established,which can effectively illustrate the mechanism of wave transformation.The derivation principles of the shape function and dynamic stiffness matrix for in-plane and transvers vibration are consistent,which provides a theoretical basis for the coupling of the two sets of vibration.The three-dimensional coupling plate is decomposed into sub-plates along the geometric boundary,the whole dynamic stiffness matrix will be assembled by the sub-dynamic stiffness matrixes of the sub-plates.Taking the typical coupling plate structure as numerical example,the effectiveness of the proposed model is verified.Furthermore,the dynamic analysis model of complex periodic plate structure is established thanks to the repeatability of dynamic model of the flexibility of coupling boundary treatment.The band gap behaviors of periodic plate structure are studied in detail,which provides a new idea and reference for ship vibration and noise reduction.The dynamic stiffness matrix method is extended to dynamic modeling of axisymmetric shell.The shape functions of cylindrical shell,circular plate and conical shell are described as exponential function,Bessel function and power series respectively.The virtual spring is introduced to simulate the elastic constraint at the structure boundary to improve the applicability of the boundary conditions.In view of the complicated distribution and large sizeof the interior ribbed plate element,the discretized method is used in this paper and the ribbed plate is described by the annular plate model.Compared with the traditional beam model,the annular plate model is more appropriate to describe the large-size ring-rib structure.A dynamic analysis model of large-size conical shell-ribbed cylindrical shell-conical shell combination system is established.Thanks to the reusability of dynamic stiffness matrix of the substructure and the convenience of coupling boundary processing,the advantages of this method in dealing with complex coupling models are fully demonstrated.On the basis of the coupling shell model,the dynamic stiffness matrix model of the shaft-hull system under the longitudinal excitation from the propeller is further established.In the model,the propeller,shaft and thrust bearing are simulated by mass block,rod element and spring-mass-damping system,respectively.Thrust bearing is used to connect the shaft system and hull structure.The reliability of present model is verified by comparing with the Numerical simulation results.Then,influences of structural parameters on the vibration response of the hull are analyzed.Finally,the experiment rig of the combined shell model is built.The present formulation is verified again by modal test and frequency response test,and the error analysis of the test results is carried out.