This paper presents presents a new analytical solution of transverse vibration ofrectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way. The reaction forces ...This paper presents presents a new analytical solution of transverse vibration ofrectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way. The reaction forces of the elastic line supports areregarded as foe unknown external forces acted on the plate. The analytical solution ofthe differential equation of motion of the rectangular plate, which includes theunknown reaction forces. is gained. The frequency' equation is derived by using thelinear relationships between the reaction forces of the elastic line supports and thetransverse displacements of the plale along the elastic line supports. Therepresentations of foe frequency equation and the mode shape functions are differentfrom those obtained by other methods.展开更多
This paper studies the bending of simple-supported rectangular plate on point supports, line supports and elastic foundation. On the basis of three-dimensional elasticity theory, the exact expressions of the displacem...This paper studies the bending of simple-supported rectangular plate on point supports, line supports and elastic foundation. On the basis of three-dimensional elasticity theory, the exact expressions of the displacement functions, which satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the in- termediate supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients are then determined by the boundary conditions on the upper and lower surfaces of the plate. Comparing the numerical results obtained from the proposed method to those obtained from Kirchhoff plate theory, Mindlin plate theory and those obtained from the commer- cial finite element software ANSYS, the high accuracy of the present method has been demonstrated.展开更多
文摘This paper presents presents a new analytical solution of transverse vibration ofrectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way. The reaction forces of the elastic line supports areregarded as foe unknown external forces acted on the plate. The analytical solution ofthe differential equation of motion of the rectangular plate, which includes theunknown reaction forces. is gained. The frequency' equation is derived by using thelinear relationships between the reaction forces of the elastic line supports and thetransverse displacements of the plale along the elastic line supports. Therepresentations of foe frequency equation and the mode shape functions are differentfrom those obtained by other methods.
基金Supported by the Innovation Foundation of Nanjing University of Science and Technology for PhD Graduates
文摘This paper studies the bending of simple-supported rectangular plate on point supports, line supports and elastic foundation. On the basis of three-dimensional elasticity theory, the exact expressions of the displacement functions, which satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the in- termediate supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients are then determined by the boundary conditions on the upper and lower surfaces of the plate. Comparing the numerical results obtained from the proposed method to those obtained from Kirchhoff plate theory, Mindlin plate theory and those obtained from the commer- cial finite element software ANSYS, the high accuracy of the present method has been demonstrated.
