The dynamic analysis of nonuniformly pretwisted Timoshenko beams with elastic boundary conditions

Lin, Shueei-Muh; Wang, Wen Rong; Lee, Sen Yung

doi:10.1016/s0020-7403(01)00018-2

Cited by 41 publications

(18 citation statements)

References 16 publications

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“…The second example is concerned with a cantilever pre-twisted beam treated experimentally by Carnegie [2] and by theoretical means by Lin et al [11] and Subrahmanyam et al [7]. The properties of the beam are given in Table 2.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The properties of the beam are given in Table 2. Although it is well known that shear coefficient depends on the geometry of the cross-section, it is taken the same as in the related references [2,7,11] for comparison purposes. To show efficiency and convergence of the proposed model, the first four frequencies of the second example are calculated.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Chen and Ho [10] introduced the differential transform to solve the free vibration problems of a rotating twisted Timoshenko beam under axial loading. Lin et al [11] derived the coupled governing differential equations and the general elastic boundary conditions for the coupled bending-bending forced vibration of a non-uniform pretwisted Timoshenko beam by Hamilton's principle. They used a modified transfer matrix method to study the dynamic behaviour of a Timoshenko beam with arbitrary pre-twist.…”

Section: Introductionmentioning

confidence: 99%

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

Yardimoglu

Yildirim

2004

Journal of Sound and Vibration

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A new linearly pre-twisted Timoshenko beam finite element, which has two nodes and four-degrees-offreedom per node, is developed and subsequently used for coupled bending-bending vibration analysis of pre-twisted beams with uniform rectangular cross-section. First, displacement functions based on two coupled displacement fields (the polynomial coefficients are coupled through consideration of the differential equations of equilibrium) are derived for pre-twisted beams whose flexural displacements are coupled in two planes. This approach helps to reduce the number of nodal variables. Next, the stiffness and mass matrices of the finite element model are obtained by using the energy expressions. Finally, the natural frequencies of pre-twisted Timoshenko beams are obtained and compared with previously published theoretical and experimental results to confirm the accuracy and efficiency of the present model. Excellent agreement is found with the previous studies. Also, the new pre-twisted Timoshenko beam element has good convergence characteristics. r

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Yardimoglu

Yildirim

2004

Journal of Sound and Vibration

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“…Suppose the numbers of elastic BCs are 0 (0 ≤ 0 ≤ ) and Hamilton's principle is generally used to construct the governing equations of such multibeam system based on Timoshenko's beam theory. Since this approach is widely used [24][25][26], we refine the derivations as follows.…”

Section: Modeling Based On Timoshenko Theorymentioning

confidence: 99%

Dynamic Analysis of Timoshenko Beam with Arbitrary Constraints and a Further Optimization Based on Least Energy Principle

Zhang

Zhu

Zhe

et al. 2018

Mathematical Problems in Engineering

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Based on Timoshenko's beam theory, this paper adopts segmented strategy in establishing the governing equations of a multibeam system subjected to various boundary conditions, in which free, clamped, hinged, and elastic constraints are considered. Meanwhile, Galerkin method is incorporated as a competitive alternative, in which a new set of unified, efficient, and reliable trial functions are proposed. A further optimization in regard to boundary distributions under forces is implemented and established on the least absorbed energy principle. High agreement is observed between the analytical results and the FEM results, verifying the correctness of the derivations. Complete comparisons between the analytical and the numerical results indicate the Galerkin method is beneficial when slender ratio is larger than 30, in which the continuity of the deformation is proved to be a crucial influencing factor. A modified numerical strategy about optimal boundary is employed and the remarks imply the algorithm can be availably used to reduce the energy absorption of the whole system.

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“…Celep and Turhan [25] used the Galerkin method to investigate the in#uence of non-uniform pretwisting on the natural frequencies of uniform cross-sectional cantilever or simply supported beams. Lin et al [26] derived the exact "eld transfer matrix of a non-uniform pretwisted Timoshenko beam with arbitrary pretwist and studied the free vibration of a pretwisted Timoshenko beam with the elastic boundary conditions. No research has been devoted to the forced vibration and the boundary control of the pretwisted Timoshenko beam with time-dependent elastic boundary conditions.…”

Section: Introductionmentioning

confidence: 99%