Closed-form approximate solution for natural frequency of axially moving beams

• Closed-form, approximate natural frequencies of axially moving beams are found via the artificial parameter method.
• Different boundary conditions are under consideration.
• The present analytical solution is valid and accurate for both high axial speed and large bending stiffness.

In this study, the artificial parameter method is utilized to find closed-form, approximate natural frequencies of axially moving beam. The method provides efficient approximate natural frequencies for the beam with different boundary conditions. The validity and accuracy of the obtained solution are examined by comparing with numeric values and data found in the literature. It is shown that the present solution is valid and accurate for both high axial speed and large bending stiffness.