Finite element free flexural vibration analysis of arbitrary plates

Barik, Manoranjan; Mukhopadhyay, Madhujit

doi:10.1016/s0168-874x(98)00023-7

Cited by 32 publications

(7 citation statements)

References 19 publications

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“…5 A new approach is introduced for analysing unstiffened and stiffened plates with arbitrary shapes. 6,7 A method is proposed to determine the free vibration frequencies of annular 8 and circular plates. 9 A truncated far boundary is developed for compressible fluid 10 and incompressible fluid.…”

Section: Introductionmentioning

confidence: 99%

Analysis of isotropic stiffened plate structure

Singh,

Agarwal

2023

Noise & Vibration Worldwide

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The analysis of stiffened plate has been carried out using finite element method. The study is divided into static and dynamic analyses. Primarily, free vibration frequencies of the stiffened plate have been determined followed by determination of deflection and von Mises stress for the stiffened plate subjected to the unit uniformly distributed load (1 kN/m2). Further, deflection and von Mises stress are determined, when the plate structure is subjected to hydrostatic loading. The analyses, static and dynamic, have been done using ANSYS Workbench 15.0. A single flat stiffener is used to stiffen the plate structure and the results are evaluated by varying the stiffener geometry, keeping the volume of material almost same as the unstiffened plate. Stiffened plate structure is very popular in the structural engineering domain and has a wide range of engineering applications from ship to aerospace structures. The material used to model stiffener is extracted from the primary plate for keeping the same volume of material. The plate structure is stiffened to reduce the out-of-plane bending even if the same (approximately) amount of material is utilised. Eight-noded plate bending and two-noded beam elements are used to model the plate and stiffener, respectively. The obtained results are compared with the published results and the effect of varying stiffener geometry is further examined. It may be concluded that the response of the stiffened plates are better compared to unstiffened plate even if the same or even less quantity of material is utilised in stiffening. The present findings are useful for the designers when the plate structure is influenced by the surrounding fluid.

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Section: Introductionmentioning

confidence: 99%

Analysis of isotropic stiffened plate structure

Singh,

Agarwal

2023

Noise & Vibration Worldwide

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“…With the progress of computational science, many different methods such as the Haar wavelet discretization method [ 6 ], geometric analysis (IGA) method [ 7 ], spectral-Tchebychev solution technique [ 8 ], Ritz method [ 9 , 10 ] and finite element method [ 11 , 12 , 13 ] are employed for dynamic characteristics analysis of the composite structures. Ye et al [ 14 ] derived the classical open shell formula on the basis of FSDT, and used Chebyshev polynomial to construct the displacement shape function, and solved the free vibration frequency of the open shell through the Rayleigh Ritz program.…”

Section: Introductionmentioning

confidence: 99%

Meshless Chebyshev RPIM Solution for Free Vibration of Rotating Cross-Ply Laminated Combined Cylindrical-Conical Shells in Thermal Environment

Zhong

et al. 2022

Materials

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This paper provides a numerical solution to the vibration of a rotating cross-ply laminated combined conical-cylindrical shell in the thermal environment. Its numerical discrete solution method uses the meshless method. The combined shell assumed the temperature independence of material property is divided to the fundamental conical and cylindrical shell substructures, and the theoretical formulation for each substructure is derived based on the first order shear deformation theory (FSDT) and Hamilton’s principle. The effects of the initial hoop tension and temperature change are considered through the kinetic energy reflecting the effects of centrifugal and Coriolis forces and additional strain energy by the nonlinear part of the Green–Lagrange strains. The substructures are then assembled according to the continuity conditions. The boundary and continuity conditions are simulated by introducing artificial virtual spring technology. The displacement component in the theoretical formulation is approximated using a meshless Chebyshev-RPIM shape function. The reliability of the method is verified by comparing with mature and reliable results. The free vibration characteristics of the rotating combined conical-cylindrical shell structure under various sizes, speeds and temperatures are given by numerical examples.

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“…Natarajan et al [19] used the FSDT in order to study the flutter behavior of functionally graded material plates immersed in a supersonic flow. For static and dynamic analysis of various plates and shells, several effective methods including semi analytical method [27], spectral-Tchebychev solution technique [28], Chebyshev-Ritz method [29], Fourier series solution method [30], and finite element method [31][32][33][34] have been applied. Ye et al [35] developed a general classical shell theory in conjunction with Chebyshev polynomials and Rayleigh-Ritz procedure for the free vibration analysis of open shells subjected to arbitrary boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Bulkhead-Stiffened Functionally Graded Open Shell Using a Meshless Method

Kwak¹,

Kim²,

Pang³

et al. 2022

Shock and Vibration

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This paper focuses on the free vibration analysis of bulkhead-stiffened functionally graded open shell (FGOS) by means of the first-order shear deformation theory (FSDT) and the meshless strong form method. The bulkhead-stiffened FGOS is decomposed into several segments without bulkhead, and the equations of motion and boundary conditions for each segment are discretized by meshless strong form method, and the displacement components are approximated using meshfree Legendre–RIPM shape function using the combined basis of multi-quadrics (MQ) radial function and Legendre polynomials. The continuous conditions of displacement are applied at the interfaces between segments. The boundary and continuous conditions are enforced by using the artificial spring technique. The accuracy and reliability of the current method are validated by comparing the present results with those of the kinds of literature and the finite element program ABAQUS. The effects of some geometrical parameters and boundary conditions on the natural frequencies of bulkhead-stiffened FGOS are investigated through numerical examples, which may serve as benchmark data.

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Finite element free flexural vibration analysis of arbitrary plates

Cited by 32 publications

References 19 publications

Analysis of isotropic stiffened plate structure

Analysis of isotropic stiffened plate structure

Meshless Chebyshev RPIM Solution for Free Vibration of Rotating Cross-Ply Laminated Combined Cylindrical-Conical Shells in Thermal Environment

Free Vibration Analysis of Bulkhead-Stiffened Functionally Graded Open Shell Using a Meshless Method

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