Vibration analysis of regular structures by graph products: Cable networks

In this paper graph products are utilized for the free vibration analysis of regular structures. A structure is called regular if its model is a product graph. Here, matrices involved in dynamic equilibrium are decomposed into the submatrices of lower dimensions, and in certain cases these are completely digonalized and the natural frequencies are obtained. In order to illustrate the present method, pre-stressed cable networks with different configurations are selected as typical structures suitable for application of the present method.