Three-dimensional free and transient vibration analysis of composite laminated and sandwich rectangular parallelepipeds: Beams, plates and solids

Qu, Yegao; Wu, Shihao; Li, Hong Guang; Meng, Guang

doi:10.1016/j.compositesb.2014.12.027

Cited by 35 publications

(14 citation statements)

References 22 publications

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“…In what follows, the linear structural model of the plate-cavity system based on Kirchhoff's thin plate bending theory is firstly established within the frame work of the modified variational principle and a least-squares weighted term, which yields the general form of functional as [39,40] …”

Section: Domain Partitioning Of the Platementioning

confidence: 99%

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A variational formulation for vibro-acoustic analysis of a panel backed by an irregularly-bounded cavity

Xie

Zheng

2016

Journal of Sound and Vibration

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Section: Domain Partitioning Of the Platementioning

confidence: 99%

“…This form yielded by the least-squares weighted residual method [39,40,42] is further merged into the stiffness matrix of the cavity. In order to show the convergence and efficiency of the present approach, the weighted parameters κ c should be determined in advance.…”

Section: Domain Partitioning Of the Acoustic Cavitymentioning

confidence: 99%

A variational formulation for vibro-acoustic analysis of a panel backed by an irregularly-bounded cavity

Xie

Zheng

2016

Journal of Sound and Vibration

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“…Zhou et al [ 39 , 40 , 41 , 42 , 43 ] used Chebyshev polynomials and static beam functions as admissible functions in conjunction with Rayleigh-Ritz method to study the three-dimensional vibrations of rectangular, skew, elliptical, and circular annular plates, as well as solid and hollow circular cylinders with different boundary conditions. Qu et al [ 44 ] employed a multilevel partitioning hierarchy, viz., multilayered parallelepiped, individual layer and layer segment, which are based on the exact three-dimensional elasticity theory to analyze the free and transverse vibrations of multilayered laminated composite and sandwich beams, plates, and solids with various boundary conditions. The displacement components of each layer segment are approximated as the product of orthogonal polynomials and/or trigonometric functions.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Vibration Analysis of Laminated Composite Rectangular Plate with Cutouts

2020

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The main purpose of this paper is to establish an analysis model of laminated composite rectangular plate with/without cutouts on the basis of three-dimensional elasticity theory and provide the exact three-dimensional solution. In the present work, the effect of the cutout is considered by subtracting the energies of cutouts from the total energy of the entire plate. The standard three-dimensional trigonometric cosine Fourier series and auxiliary Fourier series are chosen as admissible functions, and the Hamilton’s principle and Rayleigh-Ritz procedure are used to obtain the exact solution. In order to verify the effectiveness and reliability of the proposed method, some numerical results are obtained, and the results are compared with the ones available in the literature or finite element analysis. Finally, the effects of some key parameters which will affect the vibration characteristics are analyzed, and the non-dimensional frequency parameters are obtained, which can serve as benchmark data for the future research.

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“…Yang et al [23] studied the free vibrations of functionally graded sandwich beams by a meshfree boundary-domain integral equation method. Qu et al [24] presented a three-dimensional free vibration analysis of composite structures with parallelepiped shapes including beams, plates and solids. He et al [25] investigated the free vibrations and buckling of composite beams by modifying Reddy's higher-order beam theory.…”

Section: Introductionmentioning

confidence: 99%

A free vibration analysis of three-dimensional sandwich beams using hierarchical one-dimensional finite elements

Hui

Giunta

Belouettar

et al. 2017

Composites Part B: Engineering

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This paper presents a family of beam higher-orders finite elements based on a hierarchical one-dimensional unified formulation for a free vibration analysis of three-dimensional sandwich structures. The element stiffness and mass matrices are derived in a nucleal form that corresponds to a generic term in the displacement field approximation over the cross-section. This fundamental nucleus does not depend upon the approximation order nor the number of nodes per element that are free parameters of the formulation. Higher-order beam theories are, then, obtained straightforwardly. Timoshenko's classical beam theory is obtained as a special case. Short and slender beams are investigated. Simply supported, cantilevered and clamped-clamped boundary conditions are considered. Several natural frequencies as well as the corresponding modes are investigated. Results are validated in terms of accuracy and computational costs towards three-dimensional finite element solutions. The proposed hierarchical models, upon an appropriate choice of approximation order, yield accurate results with a reduced computational cost.

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Three-dimensional free and transient vibration analysis of composite laminated and sandwich rectangular parallelepipeds: Beams, plates and solids

Cited by 35 publications

References 22 publications

A variational formulation for vibro-acoustic analysis of a panel backed by an irregularly-bounded cavity

A variational formulation for vibro-acoustic analysis of a panel backed by an irregularly-bounded cavity

Three-Dimensional Vibration Analysis of Laminated Composite Rectangular Plate with Cutouts

A free vibration analysis of three-dimensional sandwich beams using hierarchical one-dimensional finite elements

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