The vibration analysis of the pipe model with Riemann Liouville derivative

This study is a theoretical and practical reference that strengthens the relationship between engineering and mathematics. Particularly, the fluid carrying pipe system modelled with fractional derivatives and analysis presented in the second section provide an important contribution to understanding and modelling the dynamic behavior of pipe systems more accurately. In the first section, basic concepts related to pipe systems are discussed in detail. The history of pipes, their geometric properties and importance in terms of dynamic analysis are explained. In addition, the mathematical background, historical development and application areas of fractional derivatives are evaluated. In this section, critical concepts in engineering such as vibration motion, resonance and viscoelastic behaviour are explained and the behaviour of pipe systems under different support conditions is given. Mathematical modelling techniques and methods, such as the perturbation method, are also detailed in this section. In the second part, a pipe model with Rieamann Liouville fractional derivatives is considered and vibration analysis of this model is performed. The equations of motion of the model are derived and solutions are obtained using the perturbation method. The numerical results clearly reveal the effects of fractional derivatives on the natural frequencies of pipe systems. These findings provide an innovative approach for more accurate analysis in engineering applications. In the last section of the thesis, a general evaluation of the study is made and the findings are summarized. Additionally, the advantages of fractional derivatives are emphasized and suggestions for future studies are presented.