THE EIGENVALUE PROBLEM FOR BEAMS AND RECTANGULAR PLATES WITH LINEARLY VARYING IN-PLANE AND AXIAL LOAD

摘要

The equation of motion and boundary conditions for uniform beams carrying constant end thrust and linearly varying axial load are derived from Hamilton's principle. Previous studies on the determination of natural fre-quencies of beams with varying axial loads are reviewed. The eigenvalue problem is formulated in a variational form to facilitate approximate solutions.nThe equation of motion of uniform plates carrying in-plane loads is derived from Hamilton's principle. The eigenvalue problem for a rectangular plate carrying a linearly varying in-plane load parallel to one side is trans¬formed into that of a uniform beam subjected to a uniformly distributed axial load whenever the sides of the plate parallel to the loading are simply sup¬ported. The eigenvalues for the beam are presently being computed and will be tabulated in a later report.