A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates

Li, Rui; Wang, Pengcheng; Yu, Tian; Wang, Bo; Li, Gang

doi:10.1038/srep17054

Cited by 38 publications

(9 citation statements)

References 38 publications

(45 reference statements)

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“…Figure 2.4 2D Mode Shapes for Plate (Li et al, 2015) The algorithm steps to extract mode shapes for a beam like structure using MCRD is as follow :…”

Section: Mode Shape Extraction From Mcrd Signaturesmentioning

confidence: 99%

Structural health monitoring of two-way slabs based on random decrement technique

Pourrastegar¹

2021

Preprint

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The current research attempts to explore the feasible use of a Structural Health Monitoring method for a two-way slab system through the effective vibration based damage diagnostic technique of Random Decrement (RD). Experimental investigations have been conducted on a total of four reinforced concrete two-way slab specimens. The slabs behaviour was examined under static loading. The results were presented in terms of load-deflection relationship at service and ultimate load, crack pattern and failure modes. At each stage of loading, the ambient vibration excitation test has been performed to investigate the extent of damage at the cracking, yield, and ultimate states through changes in dynamic parameters obtained from RD signatures. Additional applications of RD technique were performed on two-way slabs, first, to explore the location of damage by Multi-Channel Random Decrement using FBG sensor arrays. Secondly, RD technique was utilized to evaluate the extent of damage under successive equal dynamic impacts.

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“…Figure 2.4 2D Mode Shapes for Plate (Li et al, 2015) The algorithm steps to extract mode shapes for a beam like structure using MCRD is as follow :…”

Section: Mode Shape Extraction From Mcrd Signaturesmentioning

confidence: 99%

Structural health monitoring of two-way slabs based on random decrement technique

Pourrastegar¹

2021

Preprint

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“…e symplectic superposition method is developed which is the combination of superposition method as stated above and symplectic elasticity approach [22][23][24][25], and applied systematically to the bending [26,27], buckling [28,29], and free vibration [30,31] problems of plate. is method has attracted wide attention, including plate; it is also applicable to solve shell problems [32].…”

Section: Introductionmentioning

confidence: 99%

Analytical Bending Solutions of Orthotropic Rectangular Thin Plates with Two Adjacent Edges Free and the Others Clamped or Simply Supported Using Finite Integral Transform Method

Zhong

Ullah

et al. 2020

Advances in Civil Engineering

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For the first time, the finite integral transform method is introduced to explore the accurate bending analysis of orthotropic rectangular thin plates with two adjacent edges free and the others clamped or simply supported. Previous solutions mostly focused on plates with simply supported and clamped edges, but the existence of free corner makes the solution procedure much complex to solve by conventional inverse/semi-inverse methods. Compared with the conventional methods, the employed method eliminates the need to preselect the deflection function, which makes it more reasonable and theoretical for calculating the mechanical responses of the plates. Moreover, the approach used can also analyze static problems of moderately thick plates and thick plates with the same boundary conditions investigated in this article. Finally, comprehensive analytical results obtained in this paper illuminate the validity of the proposed approach by comparing with the previous literature and finite element method by using (ABAQUS) software.

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“…16 The symplectic elasticity approach has been applied for exact bending solutions of rectangular thin plates with a variety of boundary conditions. 17–24 Double finite sine integral transform method has been applied to obtain exact bending solutions of clamped rectangular plates, 25 free orthotropic rectangular thin plates supported by an elastic Winkler foundation, 26 and rectangular orthotropic thin plates with rotationally restrained edges. 27 An et al.…”

Section: Introductionmentioning

confidence: 99%

Bending of orthotropic rectangular thin plates with two opposite edges clamped

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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This work presents integral transform solutions of the bending problem of orthotropic rectangular thin plates with constant thickness, subject to five sets of boundary conditions: (a) fully clamped; (b) three edges clamped and one edge simply supported; (c) three edges clamped and one edge free; (d) two opposite edges clamped, one edge simply supported, and one edge free; and (e) two opposite edges clamped and two edges free. By adopting eigenfunctions of Euler–Bernoulli beams with corresponding boundary conditions for each direction of the plate, the governing fourth-order partial differential equation is integral transformed into a system of linear algebraic equations. Boundary conditions at the free edges are treated exactly by carrying out integral transform in the boundary formulations, which are incorporated in the transformed governing equations by integration by parts. The numerical difficulties with the high-order beam functions are overcome by using modified exponential forms, thus limiting the eigenfunctions to the range between −2 and 2. Analytical integration forms are used for the integrals of the coefficients of the transformed equations, further avoiding numerical difficulties with large high-order eigenvalues. The accuracy and convergence of the solutions are shown through numerical examples in comparison with available solutions in the literature and with finite element solutions obtained by using Abaqus program.

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A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates

Cited by 38 publications

References 38 publications

Structural health monitoring of two-way slabs based on random decrement technique

Structural health monitoring of two-way slabs based on random decrement technique

Analytical Bending Solutions of Orthotropic Rectangular Thin Plates with Two Adjacent Edges Free and the Others Clamped or Simply Supported Using Finite Integral Transform Method

Bending of orthotropic rectangular thin plates with two opposite edges clamped

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