Vibration analysis of tapered composite beams using a higher-order finite element. Part I: Formulation

Ganesan, Rajamohan; Zabihollah, Abolghassem

doi:10.1016/j.compstruct.2005.07.018

Cited by 52 publications

(22 citation statements)

References 25 publications

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“…Moreover, in [32], the investigation of the free undamped vibration response of tapered composite beams, using a higher-order finite element formulation, was carried out. Şimşek and Kocatürk [33] studied the free vibration of beams with different boundary conditions within the framework of the third-order shear deformation theory.…”

Section: Introductionmentioning

confidence: 99%

Dynamic response of aerospace structures by means of refined beam theories

Pagani

Petrolo

Colonna

et al. 2015

Aerospace Science and Technology

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Please cite this article in press as: A. Pagani et al., Dynamic response of aerospace structures by means of refined beam theories, Aerosp. Sci. Technol. (2015), http://dx. AbstractThe present paper is devoted to the investigation of the dynamic response of typical aerospace structures subjected to different time-dependent loads. These analyses have been performed using the mode superposition method combined with refined one-dimensional models, which have been developed in the framework of the Carrera Unified Formulation (CUF). The Finite Element Method (FEM) and the principle of virtual displacements are used to compute the stiffness and mass matrices of these models. Using CUF, one has the great advantage to obtain these matrices in terms of fundamental nuclei, which depend neither on the adopted class of beam theory nor on the FEM approximation along the beam axis. In this paper, Taylor-like expan- sions (TE), Chebyshev expansion (CE) and Lagrange expansion (LE) have been employed inthe framework of CUF. In particular, the latter class of polynomials has been used to develop pure translational displacementbased refined beam models, which are referred to as Component Wise (CW). This approach allows to model each structural component as a 1D element. The dynamic response analysis has been carried out for several aerospace structures, including thin-walled, open section and reinforced thin-shells. The capabilities of the proposed models are demonstrated, since this formulation allows to detect shell-like behaviour with enhanced performances in terms of computational efforts.

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Section: Introductionmentioning

confidence: 99%

Dynamic response of aerospace structures by means of refined beam theories

Pagani

Petrolo

Colonna

et al. 2015

Aerospace Science and Technology

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“…(28). The positions held by each 2.316 (7,8) 3.617 (9,10) TBM 0.145 (1,2) 0.579 (3,4) 1.302 (5,6) 2.310 (7,8) 3.602 (9,10) N = 1 0.145 (1,2) 0.579 (3,4) 1.302 (5,6) 2.310 (7,8) 3.602 (9,10) N = 2 0.145 (1,2) 0.579 (3,4) 1.302 (5,6) 2.310 (7,8) 3.603 (9,10) N = 3 0.145 (1,2) 0.579 (3,4) 1.300 (5,6) 2.306 (7,8) 3.592 (9,10) N = 4 0.145 (2,3) 0.579 (4,5) 1.300 (6,7) 2.306 (8,9) 3.592 (10,11) (1,2) 56.602 (3,4) 123.825 (6,7) 212.170 …”

Section: Annular Cross-section Beammentioning

confidence: 99%

“…14.019 (2,3) 51.470 (10,11) 103.369 (21,22) 162.382 (29,30) 223.927 (39,40) ( * ): between brackets the positions of the frequencies in the eigenvalues vector are reported. frequency in the eigenvalues vector are reported as well.…”

Section: Annular Cross-section Beammentioning

confidence: 99%

“…( * ): "b" stands for bending mode, "l" stands for longitudinal mode, "t" stands for torsional mode, c stands for circumferential mode. (1) 36.692 (3) 102.511 (4) 200.236 (6) 329.634 (8) TBM 5.859 (1) 36.536 (3) 101.491 (4) 196.639 (6) 320.461 (8) N = 1 5.859 (1) 36.536 (3) 101.491 (4) 196.639 (8) 320.461 (9) N = 2 5.963 (1) 37.071 (3) 103.047 (5) 199.759 (8) 325.149 (11) N = 3 5.913 (1) 36.312 (3) 98.705 (5) 185.376 (8) 290.665 (11) N = 4 5.903 (1) 36.142 (3) 97.876 (5) 182.813 (8) 284.400 (11) …”

Section: Annular Cross-section Beammentioning

confidence: 99%

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Unified Formulation Applied to Free Vibrations Finite Element Analysis of Beams with Arbitrary Section

Carrera

Petrolo

Nali

2011

Shock and Vibration

105

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Abstract. This paper presents hierarchical finite elements on the basis of the Carrera Unified Formulation for free vibrations analysis of beam with arbitrary section geometries. The displacement components are expanded in terms of the section coordinates, (x, y), using a set of 1-D generalized displacement variables. N-order Taylor type expansions are employed. N is a free parameter of the formulation, it is supposed to be as high as 4. Linear (2 nodes), quadratic (3 nodes) and cubic (4 nodes) approximations along the beam axis, (z), are introduced to develop finite element matrices. These are obtained in terms of a few fundamental nuclei whose form is independent of both N and the number of element nodes. Natural frequencies and vibration modes are computed. Convergence and assessment with available results is first made considering different type of beam elements and expansion orders. Additional analyses consider different beam sections (square, annular and airfoil shaped) as well as boundary conditions (simply supported and cantilever beams). It has mainly been concluded that the proposed model is capable of detecting 3-D effects on the vibration modes as well as predicting shell-type vibration modes in case of thin walled beam sections.

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“…The formulation of two higher-order shear deformation theories by Subramanian [29] satisfied the traction-free surface conditions at the top and bottom beam surfaces. A higher-order FE model based on classical laminated theory presented higherfrequencies analysis capabilities for the vibration response of laminated tapered beams [14,15]. Recently, Ş imşek and Kocatürk [26] highlighted that a third-order shear deformation theory gives significantly better results than classical theories in the case of short beams and high mode numbers.…”

Section: Introductionmentioning

confidence: 99%

Static and Dynamic Analysis of a Thin-Walled Layered Cylinder by Refined 1d Theories

Varello¹,

Carrera²

2014

Proceedings of 10th World Congress on Computational Mechanics

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Abstract. This paper presents an application of refined one-dimensional (1D) models to the static and free vibration analysis of thin-walled layered structures. Carrera Unified Formulation (CUF) is employed to easily introduce higher-order 1D models with a variable order of expansion for the displacement unknowns over the beam cross-section. Classical Euler-Bernoulli beam theory is obtained as a particular case of these variable kinematic models while a higher-order expansion permits the detection of the in-plane cross-section deformation. Finite element (FE) method is used to provide numerical results. In particular, the case of a deformable clamped-clamped thin-walled layered cylinder loaded by a non-uniform internal pressure is discussed. The static analysis reveals the model capabilities in accurately describing the three-dimensional deformation of the cylinder. The free vibration analysis provides results not detectable by typical 1D models in excellent agreement with a solid (3D) FE solution. The present models do not introduce additional numerical problems with respect to classical beam theories. Moreover, the results clearly show that finite elements which are formulated in the CUF framework offer shell-type capabilities in analyzing thin-walled structures with a remarkable reduction in the computational cost required.

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Vibration analysis of tapered composite beams using a higher-order finite element. Part I: Formulation

Cited by 52 publications

References 25 publications

Dynamic response of aerospace structures by means of refined beam theories

Dynamic response of aerospace structures by means of refined beam theories

Unified Formulation Applied to Free Vibrations Finite Element Analysis of Beams with Arbitrary Section

Static and Dynamic Analysis of a Thin-Walled Layered Cylinder by Refined 1d Theories

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