Free vibration analysis of rotating Euler beams at high angular velocity

Flapwise bending vibration of rotating tapered Rayleigh cantilever beams

“…For the present study, the solution must satisfy Eqs. (18) and (19), which can be expressed in terms of the aboveintroduced dimensionless variables…”

“…The flapwise bending vibration coupled with lagwise bending and axial vibration was investigated by Huang et al [17]. The coupling between flapwise and chordwise bending vibration was considered by Zhu [18].…”

“…For example, the Frobenius method was suggested in [6,[21][22][23] to formulate the dynamic stiffness matrix to cope with the dynamic analysis of a rotating uniform or tapered beam according to Euler-Bernoulli and Timoshenko theories of beams. The Rayleigh-Ritz method was used to study the vibration characteristics of a rotating beam [7,18]. The Wentzel, Kramers and Brillouin (WKB) approximation was employed by Firouz-Abadi et al [4] to investigate the transverse free vibration of a class of variablecross-section beams.…”

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.…”

Flapwise bending vibration analysis of functionally graded rotating double-tapered beams

“…In this work, the equations of motion were derived in terms of an inertial global coordinate system using d' Alembert principle and principle of virtual work. A method based on the power series solution was proposed by Huang et al (2010) for a slender beam rotating at high angular velocity, in which the beam was divided into equal segments for estimating flapwise vibration and coupled lagwise and axial vibration. New shape functions that include the rotating speed, element position, and centrifugal stiffening effect were considered to derive new finite element to evaluate free vibrations of beams rotating at high speeds by Gunda et al (2009).…”