Dagli B.Y.Ergut A.Turan M.E.2024-07-222024-07-22202316785878http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/12069This paper focuses on determination of the natural frequencies in slenderness pipe flows by considering fluid–structure interaction approach. Rayleigh beam theory is used to model the pipe. The fluid in the pipe is assumed as ideal, steady and uniform. Hamilton’s variation principle is demonstrated to obtain the equation of motion of pipe–fluid system. The dimensionless partial differential equations of motion are converted into matrix equations, and the values of natural frequencies of first three modes are archived with the analytical method. The results are arranged to be a data set for hybrid meta-heuristic artificial neural network (ANN) method. Three different meta-heuristic algorithms are used to train the ANN: particle swarm optimization (PSO) and artificial bee colony (ABC) and grey wolf optimizer (GWO). The comparison is presented to find a suitable algorithm based on accuracy for determining the natural frequency of the Rayleigh pipe conveying fluid. The results show that the PSO algorithm outperforms the other meta-heuristics in terms of performance indicators in prediction analysis. However, all algorithms and models can predict the natural frequencies with rate with satisfactory accuracy. © 2023, The Author(s), under exclusive licence to The Brazilian Society of Mechanical Sciences and Engineering.EnglishEquations of motionForecastingHeuristic algorithmsHeuristic methodsMatrix algebraNeural networksParticle swarm optimization (PSO)Artificial bee colonyArtificial beesBeam theoriesGray wolf optimizerGray wolvesHybrid metaheuristicsOptimizersParticle swarmParticle swarm optimizationRayleigh beam theoryRayleigh beamsSwarm optimizationNatural frequenciesArticle10.1007/s40430-023-04156-3