A unified three-dimensional method for vibration analysis of the frequency-dependent sandwich shallow shells with general boundary conditions

Functionally graded materials (FGMs) structures are increasingly used in engineering due to their superior mechanical and material properties, and the FGMs plate with cutouts is a common structural form, but research on the vibration characteristics of FGMs plate with cutouts is relatively limited. In this paper, the three-dimensional exact solution for the vibration analysis of FGMs rectangular plate with circular cutouts subjected to general boundary conditions is presented based on the three-dimensional elasticity theory. The displacement field functions are expressed as standard cosine Fourier series plus auxiliary cosine series terms satisfying the boundary conditions in the global coordinate system. The plate with circular cutout is discretized into four curve quadrilateral sub-domains using the p-version method, and then the blending function method is applied to map the closed quadrilateral region to the computational space. The characteristic equation is obtained based on the Lagrangian energy principle and Rayleigh–Ritz method. The efficiency and reliability of proposed method are verified by comparing the present results with those available in the literature and FEM methods. Finally, a parametric study is investigated including the cutout sizes, the cutout positions, and the cutout numbers from the free vibration characteristic analysis and the harmonic analysis. The results can serve as benchmark data for other research on the vibration of FGMs plates with cutouts.

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Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method

International Journal of Mechanical Sciences ◽

10.1016/j.ijmecsci.2005.06.010 ◽

2005 ◽

Vol 47 (11) ◽

pp. 1740-1755 ◽

Cited By ~ 78

Author(s):

Metin Aydogdu

Keyword(s):

Boundary Conditions ◽

Vibration Analysis ◽

Ritz Method ◽

General Boundary ◽

General Boundary Conditions ◽

Laminated Beams

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Vibration Analysis of Laminated Composite Rectangular Plates With General Boundary Conditions

ASME 2018 Noise Control and Acoustics Division Session presented at INTERNOISE 2018 ◽

10.1115/ncad2018-6106 ◽

2018 ◽

Cited By ~ 1

Author(s):

Yu Fu ◽

Jianjun Yao ◽

Zhenshuai Wan ◽

Gang Zhao

Keyword(s):

Boundary Conditions ◽

Vibration Analysis ◽

Ritz Method ◽

Laminated Composite ◽

Free Vibration Analysis ◽

Geometric Parameters ◽

General Boundary ◽

Rectangular Plates ◽

General Boundary Conditions ◽

Benchmark Solutions

In this investigation, the free vibration analysis of laminated composite rectangular plates with general boundary conditions is performed with a modified Fourier series method. Vibration characteristics of the plates have been obtained via an energy function represented in the general coordinates, in which the displacement and rotation in each direction is described as an improved form of double Fourier cosine series and several closed-form auxiliary functions to eliminate any possible jumps and boundary discontinuities. All the expansion coefficients are then treated as the generalized coordinates and determined by Rayleigh-Ritz method. The convergence and reliability of the current method are verified by comparing with the results in the literature and those of Finite Element Analysis. The effects of boundary conditions and geometric parameters on the frequencies are discussed as well. Finally, numerous new results for laminated composite rectangular plates with different geometric parameters are presented for various boundary conditions, which may serve as benchmark solutions for future research.

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