A Cell-Based Smoothed Finite Element Method for Free Vibration Analysis of a Rotating Plate

2019 ◽  
Vol 16 (05) ◽  
pp. 1840003 ◽  
Author(s):  
C. F. Du ◽  
D. G. Zhang ◽  
G. R. Liu
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Smoothed Finite Element Method ◽  
A Cell ◽  
Mindlin Plate Theory ◽  
Rotating Plate

A cell-based smoothed finite element method (CS-FEM) is formulated for nonlinear free vibration analysis of a plate attached to a rigid rotating hub. The first-order shear deformation theory which is known as Mindlin plate theory is used to model the plate. In the process of formulating the system stiffness matrix, the discrete shear gap (DSG) method is used to construct the strains to overcome the shear locking issue. The effectiveness of the CS-FEM is first demonstrated in some static cases and then extended for free vibration analysis of a rotating plate considering the nonlinear effects arising from the coupling of vibration of the flexible structure with the undergoing large rotational motions. The nonlinear coupling dynamic equations of the system are derived via employing Lagrange’s equations of the second kind. The effects of different parameters including thickness ratio, aspect ratio, hub radius ratio and rotation speed on dimensionless natural frequencies are investigated. The dimensionless natural frequencies of CS-FEM are compared with those other existing method including the FEM and the assumed modes method (AMM). It is found that the CS-FEM based on Mindlin plate theory provides more accurate and “softer” solution compared with those of other methods even if using coarse meshes. In addition, the frequency loci veering phenomena associated with the mode shape interaction are examined in detail.

Free Vibration Analysis for Elastic Plate Resting on Two-Parameter Foundation by Coupling FEM and BEM

2011 ◽  
Vol 368-373 ◽  
pp. 1332-1337
Author(s):  
Hong Yang Xie ◽  
Huan Yang ◽  
Jin Quan Yin
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Variation Principle ◽  
Elastic Plates ◽  
Foundation Model ◽  
Mindlin Plate Theory ◽  
Two Parameter

Based on two-parameter foundation model and Mindlin plate theory, the FEM equation for free vibration analysis of elastic plates resting on elastic foundation is derived by Hamilton variation principle. The effect of foundation beneath the plate is combined in the stiffness matrix of the plate element, and the effect of the foundation outside the plate domain is taken into account by boundary element method. By coupling FEM and BEM, numerical analyses for the free vibration of foundation plates are carried out. Calculated frequencies are in good agreement with measured results, which proves the accuracy and efficiency of the present approach.

On the Application of Mindlin’s Plate Theory to Free Vibration Analysis of Piezoelectric Coupled Circular FGM Plate

2008 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Abbas Rastgoo
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Piezoelectric Layers ◽  
Mindlin Plate Theory ◽  
Clamped Edge

In this paper, a free vibration analysis of moderately thick circular functionally graded (FG) plate integrated with two thin piezoelectric (PZT4) layers is presented based on Mindlin plate theory. The material properties of the FG core plate are assumed to be graded in the thickness direction while the distribution of electric potential field along the thickness of piezoelectric layers is simulated by sinusoidal function. The differential equations of motion are solved analytically for two boundary conditions of the plate: clamped edge and simply supported edge. The analytical solution is validated by comparing the obtained resonant frequencies with those of an isotropic host plate. The emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. Good agreement between the results of this paper and those of the finite element analyses validated the presented approach.

An Extended Cell-Based Smoothed Three-Node Mindlin Plate Element (XCS-MIN3) for Free Vibration Analysis of Cracked FGM Plates

2017 ◽  
Vol 14 (02) ◽  
pp. 1750011 ◽  
Author(s):  
T. Nguyen-Thoi ◽  
T. Rabczuk ◽  
V. Ho-Huu ◽  
L. Le-Anh ◽  
H. Dang-Trung ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Plate Element ◽  
Softening Effect ◽  
Strain Smoothing ◽  
Graded Material ◽  
A Cell

A cell-based smoothed three-node Mindlin plate element (CS-MIN3) was recently proposed and proven to be robust for static and free vibration analyses of Mindlin plates. The method improves significantly the accuracy of the solution due to softening effect of the cell-based strain smoothing technique. In addition, it is very flexible to apply for arbitrary complicated geometric domains due to using only three-node triangular elements which can be easily generated automatically. However so far, the CS-MIN3 has been only developed for isotropic material and for analyzing intact structures without possessing internal cracks. The paper hence tries to extend the CS-MIN3 by integrating itself with functionally graded material (FGM) and enriched functions of the extended finite element method (XFEM) to give a so-called extended cell-based smoothed three-node Mindlin plate (XCS-MIN3) for free vibration analysis of cracked FGM plates. Three numerical examples with different conditions are solved and compared with previous published results to illustrate the accuracy and reliability of the XCS-MIN3 for free vibration analysis of cracked FGM plates.

Free Vibration Analysis of a Fiber Reinforced Mindlin Plate by Using Ritz Method

2011 ◽  
Vol 110-116 ◽  
pp. 350-356
Author(s):  
S.H. Hosseini Hashemi ◽  
S. Fazeli
Keyword(s):  
Free Vibration ◽  
Analytical Solutions ◽  
Fiber Orientation ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Fiber Reinforced ◽  
Displacement Fields

In this paper the free vibration analysis of a fiber reinforced mindlin plate is presented.energy method based on the ritz method is used to obtain natural frequencies of the plate. Displacement fields of the plate are postulated by trigonometric series function. depending on the arrangement and orientation of the fibers, mindlin plate is assumed to be orthotropic or monoclinic.this analysis is useful to study the mechanical behavior of an angle ply lamina and effect of fiber orientation on the frequency response of the plate.the analysis can be extended for the laminates where the analytical solutions are not available. Finally the results are compared with those reported in the literature.

scholarly journals Application of the Modified Vlasov Model to the Free Vibration Analysis of Thick Plates Resting on Elastic Foundations

2009 ◽  
Vol 16 (5) ◽  
pp. 439-454 ◽  
Author(s):  
Korhan Ozgan ◽  
Ayse T. Daloglu
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Thick Plates ◽  
Elastic Foundations ◽  
Plates On Elastic Foundation ◽  
Quadrilateral Finite Element

The Modified Vlasov Model is applied to the free vibration analysis of thick plates resting on elastic foundations. The effects of the subsoil depth, plate dimensions and their ratio, the value of the vertical deformation parameter within the subsoil on the frequency parameters of plates on elastic foundations are investigated. A four-noded, twelve degrees of freedom quadrilateral finite element (PBQ4) is used for plate bending analysis based on Mindlin plate theory which is effectively applied to the analysis of thin and thick plates when selective reduced integration technique is used. The first ten natural frequency parameters are presented in tabular and graphical forms to show the effects of the parameters considered in the study. It is concluded that the effect of the subsoil depth on the frequency parameters of the plates on elastic foundation is generally larger than that of the other parameters considered in the study.

Free vibration analysis of the hard-coating splitter blisk using the energy-based finite element method

2019 ◽  
Vol 233 (13) ◽  
pp. 4577-4589 ◽  
Author(s):  
Feng Gao ◽  
Wei Sun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Complex Modulus ◽  
Free Vibration Analysis ◽  
Hard Coating ◽  
Mindlin Plate ◽  
Element Method

This paper presents the free vibration analysis of the hard-coating splitter blisk (known as the splitter blisk deposited hard coating) and the damping-improved performance of the hard coating for vibration suppression of the splitter blisk. Based on the proposed energy-based finite element method by the energy considerations, complex modulus theory and composite Mindlin plate theory, the equations of motion of hard-coating splitter blisk are formulated. And, the complex solutions for free vibration problem are then solved, whose real and imaginary parts are closely related to natural frequencies and loss factors. Considering the academic splitter blisk deposited NiCoCrAlY+YSZ hard coating as the benchmark, the comparisons for vibration characteristics of hard-coating splitter blisk originating from different sources are performed for model validation, and the influence of hard coating on the dynamics of splitter blisk are also investigated. The numerical results reveal that the vibration amplitudes of splitter blisk are suppressed remarkably by the hard coating without altering natural frequencies significantly.

Smoothing Technique Based Beta FEM (βFEM) for Static and Free Vibration Analyses of Reissner–Mindlin Plates

2019 ◽  
Vol 17 (02) ◽  
pp. 1845006 ◽  
Author(s):  
F. Wu ◽  
W. Zeng ◽  
L. Y. Yao ◽  
M. Hu ◽  
Y. J. Chen ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Steel Plate ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Shear Locking ◽  
Smoothing Technique ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Good Agreement

Recently, the edge-based and node-based smoothed finite element method (ES-FEM and NS-FEM) has been proposed for Reissner–Mindlin plate problems. In this work, in order to utilize the numerical advantages of both ES-FEM and NS-FEM for static and vibration analysis, a hybrid smoothing technique based beta FEM ([Formula: see text]FEM) is presented for Reissner–Mindlin plate problems. A tunable parameter [Formula: see text] is introduced to tune the proportion of smoothing domains calculated by ES-FEM or NS-FEM, which controlled the accuracy of the results. Numerical illustrations in both static and free vibration analysis are conducted. The shear locking free property, converge property and dynamic stability are carefully examined via several well-known benchmark examples. Moreover, an experimental test is carefully designed and conducted for validations, in which the mode values and shape of a rectangular steel plate is tested. Numerical examples demonstrate the advantages of [Formula: see text]FEM, in comparison with the standard FEM, ES-FEM and NS-FEM using the same meshes. The numerical and experimental results are in good agreement with each other and the [Formula: see text]FEM achieves the best accuracy among all the methods for the static or free vibration analysis of plates.

Free Vibration Analysis of a PEMFC Using the Finite Element Method

2010 ◽  
Author(s):  
Hasnet E. U. Ahmed ◽  
Jean W. Zu ◽  
Aimy Bazylak
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequency ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Gas Diffusion ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Maximum Displacement

In this study, a free vibration analysis of a polymer electrolyte membrane fuel cell (PEMFC) is performed by modelling the PEMFC as a composite plate structure. The membrane, gas diffusion electrodes, and bi-polar plates are modelled as composite material plies. Energy equations are derived based on the Mindlin plate theory, and natural frequencies and mode shapes of the PEMFC are calculated using finite element modelling. A parametric study is conducted to investigate how the natural frequency varies as a function of thickness, Young’s modulus, and density for each component layer. It is observed that increasing the thickness of the bi-polar plates has the most significant effect on the lowest natural frequency, with a 25% increase in thickness resulting in an 11% increase in the natural frequency. The mode shapes of the PEMFC provide insight into the maximum displacement exhibited as well as the stresses experienced by the material under various vibration conditions.

Free Vibration Analysis of Functionally Graded FG Nano-Plates with Porosities

2020 ◽  
Vol 64 ◽  
pp. 61-74
Author(s):  
Merdaci Slimane ◽  
Adda Hadj Mostefa ◽  
Sabrina Boutaleb ◽  
Hadjira Hellal
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Analytical Solutions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Correction Factors ◽  
Simply Supported

This study presents the analytical solutions of free vibration analysis of simply supported nanoplate FG porous using nonlocal high order shear deformation plate theory. This theory contains four unknowns without the use of shear correction factors unlike the others. The objective of this article is to develop a model to use the function f (z) on vibration and the natural frequencies of functionally graded nanoplates nonlocal to study the effect of the various parameters. The validity of the theory is shown by comparing the present results with obtained with those reported in the literature. The effects of various parameters are all discussed.

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