Study On Free Vibration And Buckling Of Quasicrystal Multilayered Beams

Quasicrystal is a new type of structure,which is different from crystal structure and non-crystal structure.Due to its unique physical properties such as low temperature coefficient,low thermal conductivity,high specific heat capacity,high resistivity,etc.,quasicrystals can be used as surface modification materials of composite materials in practical engineering to enhance the strength,stiffness and other mechanical properties of materials.Therefore,it is of great scientific significance to study the layered structure of quasicrystal composites in practical engineering.Firstly,based on the pseudo-Stroh type formula,the free vibration problem of onedimensional hexagonal quasicrystal lamellar beams is studied.By combining with the transfer matrix method,the natural frequency of free vibration of quasicrystal lamellar beams is obtained.Through numerical examples,the natural frequencies of the quasicrystal homogeneous simply supported beams and the sandwich laminates composed of quasicrystal and crystal are obtained.The effects of the laminates,height-span ratio,layer-thickness ratio and layer-number on the natural frequencies and modes of the sandwich laminates composed of two different quasicrystal materials are analyzed.The results show that the lamination sequence,the height-span ratio and the lamination thickness ratio have great influence on the natural frequency of free vibration of one-dimensional hexagonal quasicrystal laminates.The higher the height-span ratio,the higher the natural frequency.The natural frequency of the quasicrystal laminates can be optimized by adjusting the geometric size and lamination sequence of the beams.Secondly,the buckling problem of one-dimensional hexagonal quasicrystal laminate beams is studied.In the buckling analysis,the axial compression load is applied to both ends of the one-dimensional hexagonal quasicrystal beam.By solving the eigenvalue problem of the governing equation,the general solution of the generalized displacement of the onedimensional hexagonal quasicrystal beam is derived.The accurate solution of the critical buckling load of one-dimensional hexagonal quasicrystal laminate beams is obtained by using the transfer matrix.Through numerical examples,the influences of the laminate mode,height-span ratio,layer-thickness ratio and layer-number on the critical buckling load and mode of the quasicrystal beam,the sandwich laminate beam composed of quasicrystal and crystal are analyzed.The results show that the ratio of height to span,the ratio of layer to thickness and the stacking sequence of the beam have great influence on the critical buckling load of the one-dimensional hexagonal quasicrystal laminated beam.When the quasicrystal with high material coefficient is the outermost layer,the quasicrystal beam is more stable.Finally,the free vibration and buckling of two-dimensional decagonal symmetric quasicrystal laminate beams are studied.Three quasi-periodic directions are considered in this paper.The first is the quasi-periodic direction of beam length,the second is the quasiperiodic direction of beam height,and the third is the quasi-periodic direction of beam length direction and beam height direction of vertical beam length direction.According to the corresponding boundary conditions,the general solutions of free vibration and buckling of a two-dimensional decagonal homogeneous simply-supported beam are obtained,and then the exact solutions of the natural frequency of free vibration and the critical buckling load of a two-dimensional decagonal laminated simply-supported beam are obtained by using the transfer matrix method.The effects of height-span ratio,layer-thickness ratio and lamination sequence on the natural frequency of free vibration and critical buckling load of a twodimensional decal symmetric quasicrystal laminated beam are analyzed by numerical examples.