Dynamic characteristics analysis of rotating variable thickness thin plates with setting angles including accurate centrifugal force via NCFFR

Abstract

Two novel dynamic models using nodal coordinate based floating frame of reference formulation (NCFFR) are proposed to investigate dynamic characteristics of rotating variable thickness thin plates with setting angles. Based on Lagrange's equations of the second kind and NCFFR, the dynamic equations of the rotating plates are derived, directly incorporating accurate centrifugal force and Coriolis force terms. Thereby avoiding the omission of such terms that may occur in absolute nodal coordinate formulation (ANCF) based modal calculations. Compared to the conventional floating frame of reference (FFR) method, NCFFR leverages the advantages of ANCF by accounting for the effects of steady-state deformation on modal properties. The convergence and validation analyses are compared with existing literature. The vibration characteristics of the blade during smooth operation are revealed through fast Fourier transform (FFT). The results show that the first-order mode of the rotating thin plate is excited under steady-state uniform rotation, leading to deformation dominated by this mode. And the increased rotational angular velocity shifts the system's frequency response resonance region (the ratio excitation frequency to first-order natural frequency) to higher. The torsional deformation of the rotating plate is triggered by the setting angles. Variable thickness plates enhance out-of-plane bending stiffness and reduce in-plane torsional stiffness, resulting in higher natural frequencies for out-of-plane modes compared to uniform plates.