Application Of DQ Method Instructure Vibration And Stability Analysis

Differential Quadrature Method (DQM), one of numerical methods of solving boundary problem of differential equation is introduced in this paper. By using DQM, the dynamic stability of pipes conveying fluid and rectangular plates under the action of non-conservative force is studied. The main research work is as follows.The stability of pipes conveying fluid on the elastic foundation with elastic support is analyzed by using DQM. The governing differential equation of pipe conveying fluid on the elastic foundation with one end is fixed and the other end is subjected to elastic support is derived based on D'Alembert's principle. The divergence and flutter instability of the pipe is discussed, and the effect of foundation reaction, foundation shear modulus and elastic constant of the elastic support on shape of instability of elastic pipe conveying fluid are analyzed, and the stability regional graphs (divergence region and flutter region) are plotted.The stability of varying thickness rectangular plate under the action of non-conservative force is analyzed. Because DQM is easy to handle the boundary condition, For three different boundary conditions, variation curves between thickness ratio of plate and vibration frequencies and critical loads are plotted, and the instability shapes of non-conservative varying thickness rectangular plate under different boundary conditions are discussed by DQM.The stability of Functionally Graded Material (FGM) rectangular plate made of metal and ceramic under the action of non-conservative force is analyzed. Based on vibration theory and structure property of FGM, the governing differential equation isderived, and the numerical solution is obtained by DQM. The vibration frequencies and critical loads of FGM plate and the two single-phase material plates (metal plate and ceramic plate) are compared, and the effect of volume fraction on vibration frequencies and critical loads are discussed.