Buckling Analysis And Free Vibration Of Quasicrystal Beam And Plate

The research on vibration and buckling of plate and beam structures is one of the most important research fields in applied mechanics,which has attracted the attention of many researchers.The free vibration and buckling of beams and plates have been applied in mechanical,civil,aeronautical,electronic,oceanic,atomic and structural engineering.Various analytical and numerical methods have been developed to study them extensively.Quasicrystals are a new type of condensed matter,and their structural characteristics are different from traditional crystals.There are phonon field and phason field in the quasicrystals,so the buckling analysis and free vibration equation of the quasicrystals are much more complex.In this paper,the buckling and vibration problems of two-dimensional decagonal and one-dimensional hexagonal quasicrystals are studied.The buckling coefficients of two-dimensional decagonal and the free vibration of one-dimensional hexagonal quasicrystals are solved respectively by using differential quadrature method.The first chapter is the introduction,introduces the research status of thin plate buckling analysis and beam free vibration,and introduces the development and application of differential quadrature method in plate and beam.The second chapter introduces the basic principle and solving steps of differential quadrature method,and explains the processing of boundary conditions of differential equations in detail.The differential quadrature method is used to solve the stress distribution of rectangular thin plate under the cosine distribution compression load,and the applicability of the method is verified.In the third chapter,several common beam theories are introduced and applied to one-dimensional hexagonal quasicrystals.Axial displacement,cross section Angle and transverse displacement are used to describe the displacement field of quasicrystals.Based on the Hamiltonian principle,the free vibration control differential equations and boundary conditions of a hexagonal quasicrystal beam are derived.The differential quadrature method is used to solve the free vibration of a one-dimensional hexagonal quasicrystal simply supported beam,and the results obtained by ignoring the phason field are compared with the existing solutions to verify the validity of the solution results.Finally,the effect of material size on the natural frequency of one-dimensional hexagonal quasicrystals is studied.In the fourth chapter,the differential quadrature method is first used to solve the numerical solution of the stress distribution of two-dimensional decagonal quasicrystal rectangular thin plate under cosine compression.Secondly,based on the thin plate theory,the deflection equation and boundary conditions of two-dimensional decagonal quasicrystal thin plate are obtained based on Kirchhoff thin plate hypothesis.Finally,the numerical stress distribution and differential quadrature method are used to solve the buckling deflection equation.In the numerical analysis part,the buckling analysis under arbitrary combination boundary conditions of fixed support and simple support is discussed.The fifth chapter summarizes the work done and prospects the future research direction.