Saeed Soheili - Assistant Professor, Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University,Mashhad, Iran.
Seyyed Esmaeel Hosseini - MSc of Mechanical Engineering, Department of Mechanical Engineering, Imam Hossein University, Tehran,Iran
Abdollah Karimi - MSc of Mechanical Engineering, Department of Mechanical Engineering, Hakim Sabzevari University,Sabzevar, Iran

This paper investigates the longitudinal vibration of rotating shafts using hybrid modeling. The equationof motion for the longitudinal vibration is solved in new analytical method, and modeled as a series ofinterconnected distributed and lumped elements. The natural frequencies of a rotor system with variouselements are calculated based on the distributed lumped modeling technique (DLMT). The resultsobtained by this method are compared and verified with the results of other techniques, such as FEM,using ANSYS software, and the mode shapes are also presented. The method is then employed forcalculating the natural frequencies of a submarine propeller shaft with multiple elements such as differentcouplings. The results are compared and verified with the frequencies obtained by KISSSoft software. Itis shown that the presented method provides highly accurate results, while it can be simply and effectivelyapplied to the complicated systems