Pradeep Mahadevan and Anindya Chatterjee
ABSTRACT: We reexamine some classical buckling problems using a prestress based three dimensional modal projection approach. The approach was recently developed for finding the critical speeds of arbitrary axisymmetric rotors. Both buckling and rotor whirl are problems of nonlinear elasticity, and the primary contribution of the approach is to intuitively identify key terms among all the nonlinear terms present that essentially determine the critical parameter of interest (load, for buckling; and speed, for whirl). Here, we briefly state the reduced formulation (that retains only key terms), and use modal projections to find the buckling loads for four systems. The primary contribution of the present paper lies in that the treatment of these classical and simple problems, though based on a continuum formulation, is analytical. The match obtained with known solutions to these problems suggests that the approach may be useful for a variety of other problems as well.
KEYWORDS: Buckling, Prestress, Modal Projection