Geometrically Nonlinear Random Vibration Responses Of Panels Subjected To Acoustic Excitation

Panel structures are important components of rockets,spacecraft and hypersonic aircraft.These aircrafts frequently suffer extreme environments,which are combined with aeroheating,noise and mechanical loads.Under the strong acoustic loads,the panel structures are prone to undergoing large deflection and nonlinear random vibration.Linear analyses do not account for this effect and consequently may significantly overestimate the response,leading to grossly conservative designs.In this work,the reduced order method-equivalent linearization-finite element method is presented to predict the geometrically nonlinear random vibration of different panel structures subjected to acoustic loadings.The secondary development of commercial finite element software NASTRAN is carried out by means of DMAP(Direct Matrix Abstraction Program),so that geometrically nonlinear random vibration responses of the panel structures are simulated by the equivalent linearization method.This thesis includes the following aspects:(1)A reduced order model of geometrically nonlinear structures for random response analysis is established.A normal modes analysis is performed to obtain the eigenvectors,from which modes with relatively high modal effective mass fraction are selected as main modes to reduce the orders of the equations of motion.The multidegrees-of-freedom physical system is transformed into an easily solved modal system.The nonlinear restoring force components in modal space are replaced by the product of second and third order modal displacements multiplied by unknown nonlinear modal stiffness coefficients.The particular displacement fields are given for a series of inverse linear and nonlinear static analyses to determine the coefficients.As a result,the implicit geometrically nonlinear equations of motion are represented as explicit equivalent nonlinear equations of motion in modal coordinates system.(2)The equivalent linearization method is used to solve the random vibration response of geometrically nonlinear structures.Based on the force error minimization approach,the expression of the equivalent linear stiffness matrix has been derived.The method is presented for generating the spectral density matrix of the loading in physical degrees of freedom,which is then it is transformed to the modal coordinate by using the reduced matrix.The covariance matrix components are calculated from the response spectral density matrix by the Wiener-Khichine formula.The theoretical framework of solving the modal equivalent linear stiffness matrix is thus constructed.(3)The flowchart for equivalent linearization solution procedure is designed and the iterative procedure for determining the modal equivalent linear stiffness matrix is optimized.The existing internal variables in the modal frequency response solution sequence of NASTRAN are called directly by DMAP,and DMAP also implements the iterative procedure for determining the modal equivalent linear stiffness matrix.In this way,the statistical dynamics responses are obtained from a random analysis of linear system which is equivalent to the nonlinear system.The numerical results for a thin simply-supported aluminum plate are in good agreement with the data provided by the NASA research report,which confirms the proposed method has reasonable precision and high efficiency.(4)The proposed method is used to analyze the geometrically nonlinear random responses of thin simply-supported laminated plates.The root mean square and power spectral density of displacement,acceleration and stress responses of the laminated plates are obtained by the linear and equivalent linearization analysis at different sound pressure levels.The change rule of the resonant peak of laminated plates with acoustic load is obtained.The nonlinear characteristics of laminated plates under acoustic excitation are analysed.(5)The proposed method is applied in analyzing the geometrically nonlinear random responses of stiffened metal plates and stiffened laminated plates.The finite element model of the stiffened metal plate includes beam and plate elements with shared nodes.The bottom plate and reinforcement of composite stiffened laminated plates are modeled by shell elements.The stress responses of shell and beam elements of stiffened metal plate model are obtained,respectively.The stress distribution of the stiffened surface and the unstiffened surface are demonstrated.The statistical dynamic response results obtained by linear and nonlinear(equivalent linearization)methods are compared and analyzed.