Chordwise Bending Deformations of Rectangular Plates.
WATERVLIET ARSENAL N Y
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The Kantorovich method in conjunction with Hamiltons principle is used to develop a simple theory that approximates the classical theory of flexure for thin rectangular elastic plates that are clamped on the edge x 0 and free on the edge x 1. The transverse deflection wx, y, t of the plate is represented in the form fxvy, t, where fx is a chosen function that satisfies the boundary conditions on the clamped edge and vy,t is treated as the independent variation function in Hamiltons principle. The simplified partial differential equation of motion is solved exactly for several free and forced vibration problems a number of results are compared with experimental data and approximate and exact where available theoretical results obtained by other methods. The effect of nonconservative aerodynamic forces is included according to the approximations of piston theory, and two flutter analyses are performed for the edges y 0, H being either simply supported or clamped and perpendicular to the direction of the stream. Plots of the variation of Mach number with thickness-to-length ratio of the plate are presented. Author
- Structural Engineering and Building Technology