Natural frequencies of thin rectangular plates clamped on contour using the Finite Element Method

Haţiegan, L; Haţiegan, Cornel; Gillich, Gilbert-Rainer; Hamat, Codruta Oana; Vasile, Ovidiu; Stroia, Mihaela Dorica

doi:10.1088/1757-899x/294/1/012033

Cited by 4 publications

(2 citation statements)

References 9 publications

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“…The problem considered is rectangular Kirchhoff plate simply supported along the edges x = 0, and x = a, and clamped along the edges y = 0, and y = b, as shown in Figure 1. The domain PDE is given by Equation (8). The boundary conditions are:…”

Section: Methodsmentioning

confidence: 99%

“…Hatiegan et al [8] determined the natural frequencies of thin rectangular plate with and without damages using the finite element method. Pouladkhan et al [16] presented a finite element model using ABAQUS (v.6.7) software for a simply supported rectangular plate; and obtained solutions for the natural frequencies and mode shapes, which were found to be comparable with the exact solution.…”

Section: Introductionmentioning

confidence: 99%

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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: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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Experimental tests and prediction of insertion loss for cubical sound insulating enclosures with single homogeneous walls

Kosała

2022

Applied Acoustics

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Design of metadevices based on isotropic materials for eigenfrequency recovery in lightened structures

Albanesi,

Álvarez-Hostos,

Fachinotti

et al. 2024

Journal of Vibration and Control

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This work presents a novel approach for the design of metadevices conceived to recover a prescribed set of the natural eigenfrequencies of a structure lightened by machining arbitrary shape holes, using classical topology optimization (TO) techniques. This TO metadevice design (TOMD) is performed by minimizing the error of an eigenfrequency recovery task, using the finite element method (FEM) as an analysis tool, ensuring manufacturability via the solid isotropic material with penalization (SIMP) approach with Heaviside filtering to reduce intermediate-density areas. The spatial variation of mechanical properties derives from the macroscopically distinguishable dual material distribution obtained from the TOMD problem. The methodology was first tested on lightened thin steel plates and then extended to a real-world 3D mechanical component with additional mechanical performance testing. In all cases, the optimized metadevice yielded lower error in recovering eigenfrequencies compared to the lightened component without the metadevice. Furthermore, the metadevice generally achieved further mass reduction, demonstrating its potential for lightweight design while restoring its original eigenfrequencies.

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Natural frequencies of thin rectangular plates clamped on contour using the Finite Element Method

Cited by 4 publications

References 9 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 tests and prediction of insertion loss for cubical sound insulating enclosures with single homogeneous walls

Design of metadevices based on isotropic materials for eigenfrequency recovery in lightened structures

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