A spectral element for laminated composite beams: theory and application to pyroshock analysis

Ruotolo, Romualdo

doi:10.1016/s0022-460x(03)00488-7

Cited by 34 publications

(18 citation statements)

References 14 publications

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“…If axial tensile force is equal to zero and the distributive loads are equal to zero then equation (6) is reduced to equation of motion used in the works by Chakraborty, 8 Ruotolo 10 and Gopalakrishnon and Mahapatra. 11 If we ignore the axial displacement then…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…To infer dynamic shape function, we consider the general solution of homogenous form of equation (10) in the form as…”

Section: Model Developmentmentioning

confidence: 99%

“…Gopalakrishnan and Mahapatra 1 and Ruotolo 10 developed SEM scheme for the problem of hybrid beam by utilizing the force displacement procedure. In the References 8 and 10, the impacts of damping and axial force on axially loading hybrid beams were not included in SEM stiffness matrix.…”

Section: Introductionmentioning

confidence: 99%

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Development of numerical technique by Galerkin approach of spectral element method for hybrid beam

Bashir

Ahmad

2016

AIP Advances

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This paper introduces a Galerkin spectral element method (GSEM) for hybrid beam. The considered beam model depends upon the first order shear deformation theory (FSDT) is taken into account. The Galerkin strategy is used to formulate the spectral stiffness matrix based on the frequency. The spectral element method (SEM) is assessed by contrasting its solution with the exact analytical results accessible from literature as well as with the results by finite element method (FEM). This technique shows accuracy and computational efficiency with minimum number of element.

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Section: Mathematical Formulationmentioning

confidence: 99%

“…To infer dynamic shape function, we consider the general solution of homogenous form of equation (10) in the form as…”

Section: Model Developmentmentioning

confidence: 99%

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Development of numerical technique by Galerkin approach of spectral element method for hybrid beam

Bashir

Ahmad

2016

AIP Advances

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“…Chakraborty et al 9 presented a locking free finite element model for the analysis of free vibration and wave propagation in asymmetric composite beams. Mahapatra and Gopalakrishnan 10 and Ruotolo 11 provided spectral element models for the composite beams by using the force-displacement approach. In the previous studies, [9][10][11] the effects of axial force and damping were not included in the spectral element (stiffness) matrix for axial-bending-shear coupled composite Timoshenko beam models.…”

Section: Introductionmentioning

confidence: 99%

“…They include analytical approaches, 5,6,8 finite element method, 4,9 and spectral element method. 3,7,10,11 In the literature, the fast Fourier transforms (FFT)-based exact dynamic stiffness method is named spectral element method (SEM). 12 Because the exact dynamic stiffness matrix is formulated from the exact frequency-dependent (dynamic) shape functions, which satisfy the governing equations of motion, it represents the dynamic behavior in a structural element exactly.…”

Section: Introductionmentioning

confidence: 99%

Spectral element analysis of the axial-bending-shear coupled vibrations of composite Timoshenko beams

Jang

Lee

2012

Journal of Composite Materials

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This article presents a spectral element model for the axially loaded axial-bending-shear coupled vibrations of composite laminated beams, which are represented by the Timoshenko beam models based on the first-order shear deformation theory. The variation approach is used to formulate the frequency-dependent spectral element matrix (often called exact dynamic stiffness matrix) for the present spectral element model. As the spectral element matrix is formulated from exact wave solutions satisfying the frequency domain governing equations of motion transformed by the use of discrete Fourier transform theory, the present spectral element model cannot only provide extremely accurate solutions with using only a minimum number of degrees of freedom but also contribute to improving the computation efficiency. The high accuracy of the present spectral element model is numerically verified by comparing its solutions with exact analytical solutions available from references as well as with the solutions obtained by conventional finite element method. The effects of the axial loading and damping are also numerically investigated. For the numerical verification, the finite element model is also provided for the axially loaded axial-bending-shear coupled composite laminated Timoshenko beams.

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Spectral Finite Element for Dynamic Analysis of Piezoelectric Laminated Composite Beams

Nanda

2020

Recent Advances in Theoretical, Applied, Computational and Experimental Mechanics

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A spectral element for laminated composite beams: theory and application to pyroshock analysis

Cited by 34 publications

References 14 publications

Development of numerical technique by Galerkin approach of spectral element method for hybrid beam

Development of numerical technique by Galerkin approach of spectral element method for hybrid beam

Spectral element analysis of the axial-bending-shear coupled vibrations of composite Timoshenko beams

Spectral Finite Element for Dynamic Analysis of Piezoelectric Laminated Composite Beams

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