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

Abstract

In this study, two approaches having different characteristics, one being TransferMatrix Method (TMM) that reduces computational effort and time by reducingthe dimension of the considered matrix to four for all problems and the otherbeing The Adaptive Network based Fuzzy Inference System (ANFIS) used in TheFuzzy Logic Toolbox of Matlab software that again needs less computationaleffort and time are compared in the free vibration analysis of Timoshenkocolumns with attached masses having rotary inertia. The governing equation ofthe column elements is solved by applying the separation of variables method inthe TMM algorithm. The same problems are solved, also, by fuzzy-neuralapproach in which ANFIS model is used by establishing Neuro Fuzzy FrequencyEstimation (NFFE) models. Natural frequencies for the first three modes of anelastically supported Timoshenko column with 1, 5 and 10 attached masses arecomputed using NFFE models, and the results are compared with the ones ofTMM. The comparison graphs are presented in numerical analysis to show theeffectiveness of the considered methods, and it is resulted that neuro-fuzzyapproach may give encouraging results for these kinds of models having greatnumber of attached masses.