In this study, the frequency equations for calculating the natural frequencies of the beams with generally restrained boundary conditions by both translational and rotational springs are derived in matrix form using Fourier sine series. In order to show the validation of the solution, numerical results for two degenerate cases are compared with existing results for natural frequency obtained by the conventional analysis. And as a specific application, the natural frequencies of fuel rod for KSNP (Korean Standard Nuclear Plant) fuel assembly are calculated and compared with the external excitations. As a result, the frequency equation derived by present paper seems to be very useful to evaluate the natural frequencies of the double span beams with various boundary conditions. Especially, when some parametric analyses are needed to modify fuel design, the equation can be applied very easily.

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