Research On Isogeometric Modeling Methods And Vibro-acoustic Characteristics Of Irregular Acoustic Cavity And Plate-cavity Coupling System

Acoustic cavity,elastic structure and their vibro-acoustic coupling system are important research topics in the field of vibration and noise.Traditional finite element method(FFM)is one of the most widely used methods in numerical simulation.However,the mesh generation process of complex model is time and energy consuming,which is not conducive to shorten the cycle of geometric design and numerical analysis.In the context of isogeometric analysis(IGA),the splines basis functions used to exactly model the geometry are also employed for physical field description.Compared with traditional FFM,IGA avoids the tedious meshing step,eliminates the geometry modeling error caused by approximate discretization,and unifies the geometric modeling and numerical analysis.The splines basis functions which inherently hold high-order continuity can easily satisfy the necessary continuities between elements and effectively improve numerical calculation accuracy.In this dissertation,IGA is applied for modeling and characteristics analysis of irregular acoustic cavity,elastic plate and their coupling system,and the following research work has been carried out.For interior two-dimensional acoustic problems,non-uniform rational B-spline(NURBS)or non-uniform rational Lagrange(NURL)basis functions are used to construct acoustic geometric model and analysis model.The performance of NURL-based IGA for interior two-dimensional acoustic modal analysis is investigated for the first time.NURL basis functions can construct exact geometry model like NURBS,and provide a more straightforward way than NURBS to impose boundary conditions.Numerical examples show that IGA has fast convergence rate,high accuracy,and good stability.The influence of geometric parameter on acoustic characteristic of the acoustic domain is studied.A modeling method for three-dimensional acoustic cavity is established based on IGA.For acoustic cavity with continuous cross-section,a single NURBS pacth is used to build its geometric model.For three-dimensional acoustic cavity with abrupt cross-section,multi-patch NURBS model is firstly introduced,and two new modeling ways are proposed.IGA can effectively avoid the time-consuming meshing step existing in traditional FEM.Besides,geometric model and the corresponding analysis model of the acoustic cavity can be changed by changing the location of orginal points and weights,so the present method is not limited for geometric shape.The feasibility and accuracy of the model are verified by numerical examples,and the acoustic performances of L-shaped,U-shaped and various acoustic expansion chambers are studied,which provides a new idea for the analysis and design of acoustic characteristics of complex cavities.Based on the refined plate theory(RPT)and IGA,the modeling method for free vibration of elastic plate is presented.A new shear deformation function is proposed,and the vibration characteristics of in-plane functionally graded plates are investigated.Comparied with the first order shear deformation theory(FSDT),the four-variable RPT requires one fewer unknown,and describes the parabolical distribution of shear stresses through the plate thickness,so RPT is naturally free from shear-locking.A weak form free vibration analysis of elastic plate is derived from Hamilton principle.NURBS basis funtions which are used to bulid the original model are employed to describe the displacement variables,and then the discretized equation for free vibration of flexible plate is obtained.The excellent efficiencyand accuracy of the current method are testified by numrrical examlpes.The effcets of geometric parameter,boundary condition and material parameter on the free vibration of in-plane functionally graded plate are studied,which has important theoretical significance.For an acoustic cavity backed by an elastic plate,formulation of Isogeometric analysis for plate-cavity coupling system is developed.The NURBS basis functions which are utilized to build the original model will also serve the basis of the displacement field and acoustic field.NURBS basis functions have high-order continuous derivatives and easily satisfy the C~1continuity requirement of Kirchhoff-Love plate theory.The stability and accuracy of the current method are testified by comparison with other researchers'solutions.In the context of IGA,inherent characteristic and frequency response function of the plate-cavity coupling system are investigated,and the effects of geometric parameter,acoustic medium and material parameter of elastic plate on vibro-acoustic characteristics are discussed in detail.There is no limit for geometric shape,and IGA is applicable to analyzing vibro-acoustic characteristics of other irregular coupling system.