High Frequency Chordwise Bending Vibrations of Rectangular Plates.
WATERVLIET ARSENAL N Y
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Based upon Mindlins theory of flexure of isotropic elastic plates, an approximate theory of flexure for the class of problems associated with rectangular plates that are clamped on one edge and free on the opposite edge is developed. It is assumed that the loads on the faces of the plate vary slowly with the spanwise coordinate and vary arbitrarily with the chordwise coordinate. Certain Timoshenko beam modes and a thickness-twist mode are used to approximate the spanwise behavior of the displacements of the plate, whereas the chordwise components of the displacements are permitted to vary freely in the application of Hamiltons principle. Using the Kantorovich method and Yus generalization of Hamiltons principle, the approximate partial differential equations of motion and the associated boundary conditions are derived. The problem of determining the dispersion relation for straight-crested waves propagating along an infinite cantilevered plate strip is solved, and numerical results are obtained. The numerical values obtained herein are compared with other approximate and exact results developed in previous studies. Author