Comparing transfer matrix method and ANFIS in free vibration analysis of Timoshenko columns with attachments

In this study, two approaches having different characteristics, one being Transfer Matrix Method (TMM) that reduces computational effort and time by reducing the dimension of the considered matrix to four for all problems and the other being The Adaptive Network based Fuzzy Inference System (ANFIS) used in The Fuzzy Logic Toolbox of Matlab software that again needs less computational effort and time are compared in the free vibration analysis of Timoshenko columns with attached masses having rotary inertia. The governing equation of the column elements is solved by applying the separation of variables method in the TMM algorithm. The same problems are solved, also, by fuzzy-neural approach in which ANFIS model is used by establishing Neuro Fuzzy Frequency Estimation (NFFE) models. Natural frequencies for the first three modes of an elastically supported Timoshenko column with 1, 5 and 10 attached masses are computed using NFFE models, and the results are compared with the ones of TMM. The comparison graphs are presented in numerical analysis to show the effectiveness of the considered methods, and it is resulted that neuro-fuzzy approach may give encouraging results for these kinds of models having great number of attached masses.