Mechanical Engineering Commons^™

Eigenvalue Optimization And Its Applications In Buckling And Vibration, Srinivas Gopal Krishna

LSU Doctoral Dissertations

Eigenvalue problems are of immense interest and play a pivotal role not only in many fields of engineering but also in pure and applied mathematics. An in-depth understanding of this class of problems is a pre-requisite for vibration and buckling analyses of structures. Design optimization of structures to prevent failure due to instability (bucking) and vibration introduces the problem of determining optimal physical parameters such that load carrying capacity or the fundamental natural frequency is maximized. A classical example of such problems is the Lagrange problem of determining the shape of the strongest column against buckling. The primary objective of …