Finite element model for vibration analysis of pre-twisted Timoshenko beam

Anderson, 1953, Flexural vibrations in uniform beams according to the Timoshenko theory, Journal of Applied Mechanics, 20, 504, 10.1115/1.4010755 Carnegie, 1959, Vibration of pre-twisted cantilever blading, Proceedings of the Institution of Mechanical Engineers, 173, 343, 10.1243/PIME_PROC_1959_173_038_02 Carnegie, 1964, Vibration of pre-twisted cantilever blading allowing for rotary inertia and shear deflection, Journal of Mechanical Engineering Science, 6, 105, 10.1243/JMES_JOUR_1964_006_019_02 Dawson, 1971, Effect of slenderness ratio on the natural frequencies of pre-twisted cantilever beams of uniform rectangular cross-section, Journal of Mechanical Engineering Science, 13, 51, 10.1243/JMES_JOUR_1971_013_008_02 Carnegie, 1972, The effects of shear deformation and rotary inertia on the lateral frequencies of cantilever beams in bending, Journal of Engineering for Industry Transactions of the American Society of Mechanical Engineers, 94, 267 Gupta, 1978, Finite element eigenvalue analysis of tapered and twisted Timoshenko beams, Journal of Sound and Vibration, 56, 187, 10.1016/S0022-460X(78)80014-5 Subrahmanyam, 1981, Coupled bending–bending vibration of pre-twisted cantilever blading allowing for shear deflection and rotary inertia by the Reissner method, International Journal of Mechanical Sciences, 23, 517, 10.1016/0020-7403(81)90058-8 Rosen, 1991, Structural and dynamic behavior of pre-twisted rods and beams, Applied Mechanics Reviews, 44, 483, 10.1115/1.3119490 Chen, 1993, Transverse vibrations of a rotating twisted Timoshenko beam under axial loading, Journal of Vibrations and Acoustics, 115, 285, 10.1115/1.2930347 Chen, 1999, Transverse vibration of a rotating twisted Timoshenko beams under axial loading using differential transform, International Journal of Mechanical Science, 41, 1339, 10.1016/S0020-7403(98)00095-2 Lin, 2001, The dynamic analysis of nonuniformly pre-twisted Timoshenko beams with elastic boundary conditions, International Journal of Mechanical Science, 43, 2385, 10.1016/S0020-7403(01)00018-2 Banerjee, 2001, Free vibration analysis of a twisted beam using the dynamic stiffness method, International Journal of Solids and Structures, 38, 6703, 10.1016/S0020-7683(01)00119-6 Rao, 2001, Finite element vibration analysis of rotating Timoshenko beams, Journal of Sound and Vibration, 242, 103, 10.1006/jsvi.2000.3362 Narayanaswami, 1974, Inclusion of transverse shear deformation in finite element displacement formulations, American Institute of Aeronautics and Astronautics Journal, 12, 1613, 10.2514/3.49563 Dawe, 1978, A finite element for the vibration analysis of Timoshenko beams, Journal of Sound and Vibration, 60, 11, 10.1016/0022-460X(78)90397-8 Petyt, 1990 Przemieniecki, 1968 Reddy, 1993 Bathe, 1996