Free vibration of rotating and exponentially tapered beams with proof mass
摘要
Rotating non-uniform beams with proof mass are popularly applied in the micro/macro-engineering applications, and to accurately estimate the modal parameters is crucial for the optimal design of the rotating system. In this study, Adomian Decomposition Method (ADM) is employed firstly to calculate natural frequencies and modal shapes for the rotating and exponentially tapered beams with proof mass. The rotating effect, the proof mass, the general boundary constraint, and the rectangular and circular shapes of the beam cross section are all considered during the modeling. The accuracy of the proposed methodology is validated in comparison with the existing work and finite element analyses. This study comprehensively investigates the free vibration dependence of various factors, including the rotational velocity ratio λ, the rotational radius ratio d, spring stiffnesses KT and KR, the exponential factors of non-uniformity, and the tip-mass parameters (the mass ratio μ and the length ratio Q). Results indicate that the dimensionless natural frequency Ω increases monotonically as λ and d increase, with λ exerting a more pronounced effect than d. In contrast, Ω decreases monotonically as the exponential factors of non-uniformity increase and attains the maximum for uniform cross-section beams. Additionally, increasing KT and KR at the constraint end can increase the natural frequencies. Enhancing λ will induce a shift of modal nodes toward the right end attached to the proof mass. Note that the existence of d scarcely affects the characteristics of modal shapes.