Single Finite Fourier Sine Integral Transform Method for the Determination of Natural Frequencies of Flexural Vibration of Kirchhoff Plates

Oguaghamba, Onyedikachi Aloysius; Ike, Charles Chinwuba

doi:10.37624/ijert/13.3.2020.470-476

Cited by 5 publications

(5 citation statements)

References 16 publications

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“…For nontrivial solutions (Cmn  0) Cmn would not vanish and the elastic stability equation was obtained as Equation (50). The solution of the equation gave  2 from which N could be found as Equation (51). Specializations of the solution for biaxial buckling gave the solution for uniaxial buckling as Equation (55).…”

Section: Discussionmentioning

confidence: 99%

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Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Ike¹,

Onyia²,

Rowland-Lato³

2021

Adv. sci. technol. eng. syst. j.

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This paper presents the generalized integral transform method for solving flexural and elastic stability problems of rectangular thin plates clamped along /2 yb = and simply supported along remaining boundaries (x = 0, x = a) (CSCS plate). The considered plate is homogeneous, isotropic and carrying uniformly distributed transversely applied loading causing bending. Also studied, is a plate subject to (i) biaxial (ii) uniaxial uniform compressive load. The method uses the eigenfunctions of vibrating thin beams of equivalent span and support conditions in constructing the basis functions for the plate deflection and the integral kernel function. The transform is applied to the governing domain equation, converting the problem to integral equations for both cases of bending and elastic buckling. The integral equation reduces to algebraic problems for the bending problem, and algebraic eigenvalue problem for the elastic buckling problem. The deflections are obtained as double infinite series with rapidly convergent properties. Bending moments expressions are double series with infinite terms which are rapidly convergent. Maximum deflections and bending moments values occur at the plate centre in agreement with symmetry. The present results gave double series solutions with good convergent properties in closed form for bending problems. The resulting bending solutions were exact. Solving the resulting eigenvalue equation gave closed analytical equation for the buckling loads. Buckling loads are computed for the cases of biaxial and uniaxial uniform compression of square thin plates using one term approximations. The buckling load obtained for one term approximation of the eigenfunction gave results that are 12.23% greater than the exact solution. The use of more terms in the eigenfunction expansion could give more acceptable results for the eigenvalue problem of buckling of CSCS plates.

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Section: Discussionmentioning

confidence: 99%

“…Other contributions to the knowledge of plates are found in such seminal papers as presented by authors in [44][45][46][47][48][49][50][51].…”

Section: Review Of Solution Methods For Plate Problemsmentioning

confidence: 99%

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Ike¹,

Onyia²,

Rowland-Lato³

2021

Adv. sci. technol. eng. syst. j.

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“…Onah et al [19] and Mama et al [20] have obtained closed-form analytical solutions to the buckling problem of moderately thick beams. The governing equation was solved using mathematical methods for solving differential equations, and exact buckling load solutions were obtained for beams with different boundary conditions.…”

Section: Previous Studiesmentioning

confidence: 99%

An Analytical Solution to Buckling of Thick Beams Based on a Cubic Polynomial Shear Deformation Beam Theory

Ike

2023

ETJ

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“…They did not study thick plate buckling. Oguaghamba and Ike [50] used the single finite Fourier sine transform method (SFFSTM) for the natural frequency analysis of flexural vibrations of Kirchhoff plates.…”

Section: Introductionmentioning

confidence: 99%

Single Variable Thick Plate Buckling Problems Using Double Finite Sine Transform Method

Ike

2023

ETJ

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The double finite sine transform method was utilized to obtain exact buckling solutions for thick plate problems • The method simplified the problem to algebraic ones since the sinusoidal function satisfies the boundary conditions • The buckling solutions aligned with exact solutions for thick plates This paper derives buckling solutions for single variable thick plate buckling problems using the double finite sine transform method (DFSTM). The problem governing partial differential equation (GPDE), originally formulated by Shimpi and others, uses a refined plate theory (RPT) and accounts for transverse shear deformations, rendering it applicable to thick plates. The thick plate is simply supported and subjected to (i) uniform uniaxial compressive load in the x direction. (ii) uniform biaxial compressive load in the x and y axes. The DFSTM was applied to the GPDE, and the problem transformed into an algebraic equation, which was simpler in this case due to the Dirichlet boundary conditions satisfied by the sinusoidal kernel of the DFSTM. Analytical buckling solutions were determined for the two considered cases of uniaxial and biaxial compressive loads in terms of the buckling modes, Poisson's ratio (µ), and thickness (h) to least dimension (a) ratio. Critical buckling loads (Pcr) determined at the first buckling modes agreed with previously obtained Navier solutions for Mindlin, Reddy, and Refined plates. Pcr calculated for ratios of h/a equal to 0.01 converged to the solutions obtained using Kirchhoff-Love plate theory (KLPT), illustrating the applicability of the GPDE to thin and thin plate buckling.

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Single Finite Fourier Sine Integral Transform Method for the Determination of Natural Frequencies of Flexural Vibration of Kirchhoff Plates

Cited by 5 publications

References 16 publications

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

An Analytical Solution to Buckling of Thick Beams Based on a Cubic Polynomial Shear Deformation Beam Theory

Single Variable Thick Plate Buckling Problems Using Double Finite Sine Transform Method

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