A.R. Ghaffarian - Civil Engineering, Shiraz University
S. Hashemi - Civil Engineering, Shiraz University
A. Ranjbaran - Civil & Environmental Engineering, Shiraz University

In this paper mathematical formulation for buckling analysis of a column and vibrationanalysis of a beam is presented. The beam and the column is assumed to be non-uniform and cracked.Using calculus of variations, the problem is expressed as an optimization problem. A technique ofoptimization is used for analysis of buckling load. Considering the similarity between the governingequation for buckling and free vibration, the fundamental frequency and mode shape of the beam iscomputed with the same method. Several examples are solved and the results are compared with othermethods, as a result an excellent agreement was obtained.

Buckling, vibration, Cracked, Non, Uniform, Beam, Column