On the angle ply higher order beam vibrations

Marur, Sudhakar R.; Kant, Tarun

doi:10.1007/s00466-006-0079-0

Cited by 27 publications

(16 citation statements)

References 15 publications

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“…be noticed that the natural frequencies given in Table 2 are in excellent agreement with the reference solution [7], which were also obtained from the higher-order beam theory, for all boundary conditions.…”

Section: Finite Element Formulationsupporting

confidence: 72%

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Free vibration of axially loaded rectangular composite beams using refined shear deformation theory

Thai

2012

Composite Structures

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Free vibration of axially loaded rectangular composite beams with arbitrary lay-ups using refined shear deformation theory is presented. It accounts for the parabolical variation of shear strains through the depth of beam. Three governing equations of motion are derived from the Hamilton's principle. The resulting coupling is referred to as triply axial-flexural coupled vibration. A displacement-based onedimensional finite element model is developed to solve the problem. Numerical results are obtained for rectangular composite beams to investigate effects of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads and load-frequency curves as well as corresponding mode shapes.

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Section: Finite Element Formulationsupporting

confidence: 72%

“…(21), {∆} is the eigenvector of nodal displacements corresponding to an eigenvalue: Table 2. The material properties of AS4/3501-6 graphite/epoxy composite are assumed to be [7]:…”

Section: Finite Element Formulationmentioning

confidence: 99%

Free vibration of axially loaded rectangular composite beams using refined shear deformation theory

Thai

2012

Composite Structures

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“…Marur et al ([4]- [7]) studied vibration analysis of sandwich and composite beams using the HOBT through proper constitution of elasticity matrix. Shi and Lam [8] presented a FE formulation for the free vibration analysis of composite beams.…”

Section: Soldatos and Elishakoffmentioning

confidence: 99%

Axial-flexural coupled vibration and buckling of composite beams using sinusoidal shear deformation theory

Thai

2012

Arch Appl Mech

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A finite element model based on sinusoidal shear deformation theory is developed to study vibration and buckling analysis of composite beams with arbitrary lay-ups. This theory satisfies the zero traction boundary conditions on the top and bottom surfaces of beam without using shear correction factors.Besides, it has strong similarity with Euler-Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions. By using Hamilton's principle, governing equations of motion are derived. A displacement-based one-dimensional finite element model is developed to solve the problem. Numerical results for cross-ply and angle-ply composite beams are obtained as special cases and are compared with other solutions available in the literature. A variety of parametric studies are conducted to demonstrate the effect of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads and corresponding mode shapes of composite beams.

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“…Adyodgu (2006) presented a pair of shear deformable beam theories by employing parabolic and exponential shape functions respectively in conjunction with the classical beam theory for free vibration analysis of angle ply beams. Marur and Kant (2007) presented a higher order theory for free vibration analysis of angle ply beams.…”

Section: Introductionmentioning

confidence: 99%

Multi-model finite element scheme for static and free vibration analyses of composite laminated beams

Band

Desai

2015

Lat. Am. j. solids struct.

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A transition element is developed for the local global analysis of laminated composite beams. It bridges one part of the domain modelled with a higher order theory and other with a 2D mixed layerwise theory (LWT) used at critical zone of the domain. The use of developed transition element makes the analysis for interlaminar stresses possible with significant accuracy. The mixed 2D model incorporates the transverse normal and shear stresses as nodal degrees of freedom (DOF) which inherently ensures continuity of these stresses. Non critical zones are modelled with higher order equivalent single layer (ESL) theory leading to the global mesh with multiple models applied simultaneously. Use of higher order ESL in non critical zones reduces the total number of elements required to map the domain. A substantial reduction in DOF as compared to a complete 2D mixed model is obvious. This computationally economical multiple modelling scheme using the transition element is applied to static and free vibration analyses of laminated composite beams. Results obtained are in good agreement with benchmarks available in literature.

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On the angle ply higher order beam vibrations

Cited by 27 publications

References 15 publications

Free vibration of axially loaded rectangular composite beams using refined shear deformation theory

Free vibration of axially loaded rectangular composite beams using refined shear deformation theory

Axial-flexural coupled vibration and buckling of composite beams using sinusoidal shear deformation theory

Multi-model finite element scheme for static and free vibration analyses of composite laminated beams

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