TY - JOUR
T1 - Natural vibration of pre-twisted shear deformable beam systems subject to multiple kinds of initial stresses
AU - Leung, A. Y T
AU - Fan, J.
PY - 2010
Y1 - 2010
N2 - Free vibration and buckling of pre-twisted beams exhibit interesting coupling phenomena between compression, moments and torque and have been the subject of extensive research due to their importance as models of wind turbines and helicopter rotor blades. The paper investigates the influence of multiple kinds of initial stresses due to compression, shears, moments and torque on the natural vibration of pre-twisted straight beam based on the Timoshenko theory. The derivation begins with the threedimensional Green strain tensor. The nonlinear part of the strain tensor is expressed as a product of displacement gradient to derive the strain energy due to initial stresses. The Frenet formulae in differential geometry are employed to treat the pre-twist. The strain energy due to elasticity and the linear kinetic energy are obtained in classical sense. From the variational principle, the governing equations and the associated natural boundary conditions are derived. It is noted that the first mode increases together with the pre-twisted angle but the second decreases seeming to close the first two modes together for natural frequencies and compressions. The gaps close monotonically as the angle of twist increases for natural frequencies and buckling compressions. However, unlike natural frequencies and compressions, the closeness is not monotonic for buckling shears, moments and torques. © 2009 Elsevier Ltd. All rights reserved.
AB - Free vibration and buckling of pre-twisted beams exhibit interesting coupling phenomena between compression, moments and torque and have been the subject of extensive research due to their importance as models of wind turbines and helicopter rotor blades. The paper investigates the influence of multiple kinds of initial stresses due to compression, shears, moments and torque on the natural vibration of pre-twisted straight beam based on the Timoshenko theory. The derivation begins with the threedimensional Green strain tensor. The nonlinear part of the strain tensor is expressed as a product of displacement gradient to derive the strain energy due to initial stresses. The Frenet formulae in differential geometry are employed to treat the pre-twist. The strain energy due to elasticity and the linear kinetic energy are obtained in classical sense. From the variational principle, the governing equations and the associated natural boundary conditions are derived. It is noted that the first mode increases together with the pre-twisted angle but the second decreases seeming to close the first two modes together for natural frequencies and compressions. The gaps close monotonically as the angle of twist increases for natural frequencies and buckling compressions. However, unlike natural frequencies and compressions, the closeness is not monotonic for buckling shears, moments and torques. © 2009 Elsevier Ltd. All rights reserved.
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U2 - 10.1016/j.jsv.2009.12.002
DO - 10.1016/j.jsv.2009.12.002
M3 - RGC 21 - Publication in refereed journal
SN - 0022-460X
VL - 329
SP - 1901
EP - 1923
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
IS - 10
ER -
