Calculation formulas for natural frequency and critical speed of rotating beam and plate

This paper develops efficient calculation formulas for natural frequencies and buckling instability critical speeds of rotating beam and plate, addressing computational inefficiencies in numerical/finite element methods. By modelling rigid-body rotation effects as distributed inertial forces, the calculation formulas are derived, which require only rotational speed and root offset ratio for calculation of natural frequency without iterative simulations. Moreover, a correction coefficient enhances first-order torsional frequency accuracy for rotating plate. Experimental validation across diverse rotating speeds and comparative analyses with literature data confirm formula accuracy (<7 % error) and universality. Furthermore, dimensionless frequency formulas reveal that stiffening/softening states depend solely on root offset ratio, with critical values derived for state transitions. While the increasing rotational speed will increase the degree of stiffening/softening. The two conditions for buckling instability of rotating beam and plate are: the structure is in a softening state, and the rotational speed reaches the critical speed. The correctness and universality were also verified by Recurdyn simulations. These validated formulas enable rapid prediction of dynamic behavior, significantly enhancing structural optimization efficiency and buckling instability management in rotating machinery.