Free vibration of an extensible rotating inclined Timoshenko beam

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

“…The literature on the free vibration behaviour of rotating beams using only bending theory is surprisingly voluminous and has continued to grow to this day. The authors have compiled a selective sample of recent papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] which provide background information and useful cross-references on the subject.…”

“…Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/jsvi Several of these publications rely on classical methods based on the solution of the governing differential equations and the subsequent imposition of boundary conditions, leading to the frequency equation [5,11]. There are, however, some exceptions where finite element method (FEM) based solutions have also been reported [6,13] along with the application of other methods such as the differential transform method [14,15].…”

“…However, it should be recognised that a handful of researchers [5,11,16] have included the Coriolis terms when investigating the free vibration behaviour of individual beams using the classical method, but without applying the DSM. These earlier studies have highlighted the effect of the Coriolis terms, particularly at high rotational speeds.…”

“…These earlier studies have highlighted the effect of the Coriolis terms, particularly at high rotational speeds. Lin and Hsiao [5] used d'Alembert's principle and the principle of virtual work to formulate the eigenproblem, whereas Lee and Sheu [11] used Hamilton's principle as a precursor to an exact power solution of the same problem. A notable contribution came from Huang et al [16], who investigated the free vibration problem of a rotating Bernoulli-Euler beam inclined at an arbitrary angle to the axis of rotation.…”

A Corotational Finite Element Method Combined with Floating Frame Method for Large Steady‐State Deformation and Free Vibration Analysis of a Rotating‐Inclined Beam

“…However, the vibration analysis of rotating beam with inclination angle, which is considered in the recent computer cooling fan design on the natural frequencies of rotating beams 21 , is rather rare in the literature 10, 19, 21, 22 . In 21,22 , the effect of the steady-state axial deformation and the inclination angle on the natural frequencies of the rotating beam was investigated. However, the lateral steadystate deformation and its effects on the natural frequencies of the rotating beam were not considered in 21,22 .…”