Study On Dynamics Stabilities Of Two-Dimensional Quasicrystal Structures With The Higher-Order Shear Deformation Theory

Quasicrystal is different from crystalline and amorphous structure in that they are long-range ordering and rotational symmetry.Therefore,quasicrystal exhibits unique physical properties.In the study of quasicrystal structure,not only the generalized elasticity theory,but also phonon field and phase field should be considered.Nowadays,there are many studies on the bending,vibration and buckling of quasicrystal structures.However,no relevant articles on the dynamic buckling of quasicrystal structures are found.Quasicrystal structures are widely used in engineering applications and dynamic stability problems of quasicrystal structures under periodic loading often need to take into consideration.In this thesis,author discusses the dynamic stability problems of two-dimensional quasicrystal plate and shell structures in thermal environment and different foundation effects.The present paper provides a theoretical reference for the practical application of two-dimensional quasicrystal plate and shell structures.The main contents are as follows:(1)Chapter two investigates the dynamic stability of two-dimensional decagonal quasicrystal plate under the action of viscoelastic foundation.The basic equations are derived by using Reddy’s third-order shear deformation theory.After that,the final equations of dynamic stabilities of the two-dimensional decagonal quasicrystal plate are obtained based on the Hamilton’s variational principle.In order to take into account the four-sided simply-supported boundary conditions,double trigonometric formulations are used in this thesis.Bolotin’s approximate method is used to solve for the final dynamic instability boundary.It is pointed out that the viscoelastic foundation strengthens the stiffness of the two-dimensional quasicrystal plate,which makes the stability decrease.(2)The research on the dynamic stabilities of multilayered two-dimensional decagonal quasicrystal shell panel with different foundation supports in chapter four.The equations in displacement field of the two-dimensional decagonal quasicrystal shell panels are based on Pandy’s higher order shear deformation theory.The motion equations are finally obtained by substituting the expressions of external work,potential energy,strain energy and kinetic energy into Hamilton’s principle.The closed-form solutions are given according to simply supported boundary condation,and dynamic stability equations of two-dimensional decagonal quasicrystal shell panel are obtained in the Bolotin’s method.Numerical results show the larger the percentage of quasicrystal material,the higher the stiffness of the structure and the slight decrease in stability in multilayer plates with the same thickness.The clippinglayer parameters has more influence on the stability of multilayered two-dimensional decagonal quasicrystal shell panels than the spring stiffness.(3)Dynamic stability of two-dimensional hexagonal quasicrystal circular cylindrical shell in the thermal environment is discussed in chapter three.The Khdeir’s second-order shear deformation theory is employed to establish displacement field.Dynamic stability equations of two-dimensional hexagonal quasicrystalline cylindrical shell under thermal environment are derived from energy method.The Bolotin’s method is considered for the simply supported boundary conditions at both ends to obtain dynamic stable-unstable region.Dynamic stableunstable region and displacement variation change with considering of diameterthickness ratio,length-diameter ratio,mode number and ambient temperature.The effects of these parameters are discussed in detail.