A hierarchic high-order Timoshenko beam finite element

• The super-convergent Timoshenko beam element is improved with hierarchic high-order shape functions.
• Fractional error of the 2nd cantilever beam natural frequency with the p-version model is 1% of the h-version counterpart.
• Error in estimating natural frequency split in rotors is also reduced.
• The proposed element is successfully applied to estimate natural frequencies in experiments.

Timoshenko beam theory (TBT) is suitable for vibration studies as it describes beams with small models. The super-convergent Timoshenko beam element is improved by adding hierarchic high-order shape functions using Legendre polynomials, and correction terms were added where necessary. The proposed element is validated in static, dynamic and rotordynamic analyses. With the same model size, the fractional error of the 2nd cantilever beam natural frequency with the p-version beam element is 1/100th of the h-version counterpart, and error in estimating natural frequency split in rotors is reduced. The proposed element is also applied to estimate natural frequencies in experiments.