The Scaled Boundary Finite Element Method For Transient Vibro-acoustic Analysis Of Plates And Shells

Plates and shells,as important components of many mechanical systems such as aerospace vehicles,ships and automobiles,are frequently excited by transient loading and thus radiating sound into the surrounding space.For designing the optimal equipment with a low level of noise,it is essential to develop a powerful computational procedure that can effectively predict the vibro-acoustic behaviors of plates and shells.The scaled boundary finite element method(SBFEM)is a novel technique for solving partial differential equations where the boundary of a problem domain is approximated with finite elements while the solution along the radial direction is analytical.The SBFEM is very suitable for addressing problems involving singularities and unbounded domains and has been applied to predict the bending behaviors of plates and the transient responses of bounded and unbounded acoustic fields.However,the research on the SBFEM for modeling general shell structures and the vibro-acoustic systems of plates and shells has not been reported yet.Aimed at developing a unified SBFEM for transient vibro-acoustic analysis of plates and shells,the following work has been accomplished:First,an SBFEM for static and dynamic analyses of straight beams has been presented.The beam is treated as a plane stress problem and the principle of virtual work involving the inertial force is applied to derive the scaled boundary finite element equation.One-dimensional finite elements are used to discretize the longitudinal dimension of the beam and the solution through the thickness is expressed analytically as a Padé expansion.Finally,the element stiffness and mass matrices are obtained simultaneously.Numerical examples demonstrate that this formulation is able to predict the static and dynamic behaviors of straight beams accurately.Second,an SBFEM for transient analysis of vibro-acoustic systems comprising unidirectional plates and infinite two-dimensional acoustic fields has been presented.The SBFEM for beam analysis is employed to simulate the unidirectional plate which is herein treated as a plane strain problem.An artificial circular boundary is introduced to divide the infinite acoustic field into an interior finite region and an exterior residual region.The former is further split into a number of bounded subdomains which are analyzed using the improved continued-fraction approach while the latter is simulated by the improved high-order doubly asymptotic open boundary.The structural and acoustic domains are discretized independently and the collocation method is applied to perform the data transfer between the non-matching discrete interfaces.The Bathe time integration scheme is employed to solve the coupled system of equations.Numerical examples demonstrate that this formulation is able to analyze two-dimensional vibro-acoustic problems accurately and efficiently.Third,an SBFEM for static and dynamic analyses of general shells has been presented.The shell is treated as a three-dimensional elastic body and the formulation is based on a new scaling idea named“normal scaling strategy”.The principle of virtual work involving inertial force is applied to derive the scaled boundary finite element equation.Two-dimensional finite elements are used to discretize the bottom surface of the shell and the solution through the thickness is expressed analytically as a Padé expansion.Finally,the element stiffness and mass matrices are obtained simultaneously.Numerical examples demonstrate that this formulation is able to model geometrically various shells accurately.Fourth,an SBFEM for transient analysis of vibro-acoustic systems comprising plate and shell structures and infinite three-dimensional acoustic fields has been presented.The SBFEM with normal scaling strategy for shell analysis is employed to simulate the structural part.An artificial spherical surface is introduced to divide the infinite acoustic field into an interior finite region and an exterior residual region.The former is further split into a number of bounded subdomains which are analyzed using the improved continued-fraction approach while the latter is simulated by the improved high-order doubly asymptotic open boundary.The structural and acoustic domains are discretized independently and the collocation method is applied to perform the data transfer between the non-matching discrete interfaces.The Bathe time integration scheme is employed to solve the coupled system of equations.Numerical examples demonstrate that this formulation is able to analyze three-dimensional vibro-acoustic problems accurately and efficiently.Therefore,this research has contributed to the development of the SBFEM by expanding its application and enriching its theory.