Calculating the Buckling Load and Eigenfrequencies of Regular Frames by Using the Canonical the Cartesian Product of Graphs

With respect to that many structural models can be generated as the graph products of two or three subgraphs known as their generators and Some of them consist ofCartesian, Strong Cartesian, Direct and Lexicographic products then In this paper a special method is presented for calculating the buckling loads and free vibration analysis of symmetric regular frames without sway. In this method the model of structures formed as the Cartesian product of its weighted generators, then by using the canonical forms the critical load and eigenfrequencies are obtained. Examples are provided to illustrate the simplicity and efficiency of the present method

Keywords:

Buckling load , Eigenfrequencies , Decomposing , weighted graph , Symmetry , Regular frames , Cartesian product