Dynamic Modeling And Vibration Characteristic Analysis Of Functionally Graded Structures

Functionally graded materials(FGMs)are classified as novel composite materials which possess continuous and smooth spatial variations of material properties along desired directions.Such materials can eliminate the high stress concentration in conventional laminated composite structures.Moreover,designers may obtain the desirable material properties by changing the volume fraction of constituents appropriately.Due to the superior properties,functionally graded materials have wide and bright prospect of application in many fields especially in marine,aircraft,aerospace and nuclear power.With the wide use of FGM structures in modern engineering,the vibration problems of FGM plates and shells have received intensive concern.Consequently,establishment of reliable and efficient analysis model to predict vibration behavior of FGM plate and shell structures can provide a theoretic foundation and technique support for design of FGM structures which will be of great applied value.Surrounding the problems of the dynamic modeling for FGM plate and shell structures,the main work in the thesis includes:A three-dimensional vibration analysis model is established in order to study the vibration mechanism of functionally graded structures essentially.Since no hypotheses are assumed for the distribution field of the deformations and stresses,this model successfully used to deal with arbitrarily thick FGM plate and shell structures not only provides realistic results but also brings out physical insights.Consequently,the results obtained from the present model can serve as validation benchmark to assess the adequacy of different plate and shell theories and other approximate solutions.In addition,due to geometrical boundary conditions are enforced through the penalty function method,the analysis model and obtained algorithm possess versatility in handling general boundary conditions.In actual applications,the dynamic prediction of engineering structures needs to satisfy the requirements of accuracy of calculation and speed of computing.Therefore,a fast dynamic prediction model for functionally graded structures on the basis of the shear deformation theory is developed.Besides the advantage in treating boundary conditions,this model has good calculation accuracy and efficiency due to the introduction of shear deformation theory.Although it is initially applied in single-layer FGM structures,this method has good adaptability to laminated FGM structures.Moreover,the spatial variation of the material properties leads to the failure in simulation on FGM structures using finite element software.Consequently,the model can be as an alternative method and has significant applied value.A so-called Fourier spectral element method is proposed for vibration analysis of FGM coupled shells.A substantial reduction of the time consumption in creating computational models results from repeat utilization of models of the substructures.The big elements used to deal with the coupled shell structures lead to decrease the degree of freedom and improve the calculation efficiency.In addition,due to adding boundary nodal displacement information into the admissible functions,the interface continuity and boundary conditions are easily handled in the presented method.From the large amount of the literature survey,this work appears to be the first time to study the vibration behaviors of FGM coupled shells,and is of important theoretical significance.As one of expansions of FGMs,functionally graded piezoelectric materials(FGPMs)have been proposed by introducing the concept of FGMs to piezoelect:ric materials which have the advantages of both.The complexity of material properties and multi-field coupling provide a challenge to establishment of precise dynamic prediction model.Therefore,a unified formulation for vibration analysis of FGPM structures with general boundary conditions is developed.The penalty function method is used for first time to deal with the electronic boundary conditions which make this model have a wide range of applications.This work enriches and develops the analysis method for FGPM structures.