A simple analytical model for free vibration of orthotropic and functionally graded rectangular plates

Ghashochi-Bargh, H.; Razavi, Soheil

doi:10.1016/j.aej.2017.02.005

Cited by 15 publications

(6 citation statements)

References 50 publications

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“…Table 1 reveals that the present results are comparable to previous results by Fetea [32] who used the Galerkin-Vlasov method to solve the same problem. The present results are also comparable with previous results obtained by Lim et al [30] who used the Finite Element Method (FEM), Eftekhari [27] who used Ritz-DQM, and Ghasochi-Bergh and Ravazi [28].…”

Section: Discussionsupporting

confidence: 92%

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

Oguaghamba¹,

Ike²

2020

International Journal of Engineering Research and Technology

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This work presents the single finite Fourier sine integral transform method for finding the natural frequencies of flexural vibration of rectangular Kirchhoff plates with two opposite simply supported edges (x = 0, x = a) and two clamped edges (y = 0, y = b), where the origin is at a corner. For free harmonic vibrations, the problem is represented mathematically as a fourth order partial differential equation (PDE) over the domain, and boundary conditions along the edges. Application of the transform with respect to the x coordinate variable converts the Boundary Value Problem (BVP) to an integral equation which satisfies all the Dirichlet boundary conditions along x = 0, and x = a, due to the sinusoidal kernel function of the transform used. The integral equation is further simplified to a system of ordinary differential equations (ODEs), which is solved to obtain the unknown deflection in the transform space. Transforms of the boundary conditions are used in the solution of the ODE to generate a system of homogeneous equations in terms of the unknown integration constants. The condition for nontrivial solution is used to obtain the characteristic frequency equation which is solved by iteration methods to obtain the natural frequencies for any given mode of vibration. The results obtained are identical with results obtained by previous researchers who used Galerkin-Vlasov methods, Levy's single trigonometric series method, finite element method, and energy methods.

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Section: Discussionsupporting

confidence: 92%

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

Oguaghamba¹,

Ike²

2020

International Journal of Engineering Research and Technology

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“…Motaghian et al 3 presented an analytical approach for free vibration behavior of rectangular plates on partial elastic foundation based on various mode sequences and they used different boundary conditions. Ghashochi-Bargh and Razavi 4 reported an analytical solution for prediction of the free vibration analysis of rectangular plates made of orthotropic and functionally graded materials, and they used different boundary conditions such as clamped and simply supported. Huang et al 5 studied the natural vibration behavior of rectangular plates with orthotropic structures with different thicknesses, and they used various boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Experimental and statistical free vibration analyses of laminated composite beams with functionally graded fiber orientation angles

Evran

2020

Polymers and Polymer Composites

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In this experimental and statistical study, free vibration behavior of laminated composite beams with functionally graded fiber orientation angles was investigated under clamped-free boundary conditions. The beams were manufactured using E-glass/epoxy. Fiber orientation angles of the beams were analyzed based on Taguchi’s L9 (33) orthogonal array. The effect of fiber orientation angles and beams with optimum levels were assessed using analysis of signal-to-noise ratio. Significant laminates of the beams and their percent contributions on the free vibration responses were obtained using analysis of variance. According to this study, the increase of fiber orientation angle from 0° to 80° causes a decrease in the fundamental frequency behavior of laminated composite beams. The most effective control factors were found to be the first and the second laminates symbolized as L1 with 85.86% contribution, the third and the fourth laminates symbolized as L2 with 12.29% contribution, the fifth and the sixth laminates symbolized as L3 with 1.84% contribution, respectively. This study can be used as a reference for free vibration analysis of cantilever laminated composite beams made of functionally graded fiber orientation angles as experimentally and statistically.

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“…Due to linear scale other parameters are not observed in the graph [21,22]. The only stiffness uncertainty is prominently observed [23].…”

Section: Frf Plot Of the Simply Supported Plate On Linear Scalementioning

confidence: 95%

Harmonic Analysis of Simply Supported Square Plate for Uncertain Parameters

Khan

Zakiuddin

Fulzele

2022

J. Phys.: Conf. Ser.

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Many Mechanical structures are manufacture by using plates. However Harmonic Analysis of plate is growing research subject in today’s era. In the present research paper vibrational response of simply supported square plate with uncertain parameters are studied. In designing any real life mechanical system uncertainty phenomenon plays vital role. Thus it becomes important to study the effect of uncertainty for different frequency domain in mechanical system. In present research work square plate as structural element is selected. On this plate mass, stiffness and both collectively mass and stiffness uncertainty are taken. The plate boundary condition selected is simply supported. For determining the plate dynamic response FEM tool is used. While doing harmonic analysis the behavior of all uncertain parameters plates are compare with bare plate. In the FRF plot of plate with stiffness uncertainty, it is found that it has drastic changes in dynamic response. Thus this shows that uncertain parameters have adverse effects and it changes the dynamic behavior of the structure.

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A simple analytical model for free vibration of orthotropic and functionally graded rectangular plates

Cited by 15 publications

References 50 publications

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

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

Experimental and statistical free vibration analyses of laminated composite beams with functionally graded fiber orientation angles

Harmonic Analysis of Simply Supported Square Plate for Uncertain Parameters

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