Element-Free Method For Structures Vibration Analysis

The element-free Galerkin method (EFGM) is used to study the dynamic characteristics of the structure in this paper. The shape function is constructed by moving least-squares (MLS), the penalty method is employed to impose the essential boundary conditions. Based on the moving least-square method and the Hamilton's principle of the elastic system, the corresponding eigen-equation is obtained. The vibrational characteristics of structure are analyzed. The main work is as follows.(1) The basic principle of approximate technique of EFGM-moving least-squares is introduced. Based on the moving least square method and the Hamilton's principle of the elastic system, the differential equation of motion and corresponding eigen-equation of the vibration of structure are obtained. The main parameter of weight function in element-free method is optimized. Then the validity of EFGM in the structure vibration problem is investigated.(2) The free vibration of the tall tube structures with uniform cross-section and non-homogeneous cross-section are analyzed by EFGM. The size of the cross-section is constant along height of the tube, the property of variable cross-section is expressed by the variation of elasticity constant of the material. During dealing with the discontinuousness of the elasticity constant of the material in the non-homogenous interfaces, a jump function term is added in the intrinsic approximate function, and the accurate results are obtained.(3) The dynamic characteristics of cylindrical shell with the different boundary conditions are studied by EFGM. The cylindrical shell of open circumambience with both ends simply supported and the cylindrical shell with clamped ends are analyzed, then the cylindrical shell of close circumambience with simple support and the other end clamped along straight edges are analyzed. The influence of circumferential half wavenumber on natural frequency is studied. The mode diagrams with different boundary conditions are obtained.(4)The computational programme analyzing structure vibration via EFGM is written. The numerical calculation results show that this method has higher precision in...