Nonlinear vibrations of simply-supported plates by the p-version finite element method

2005 ◽  
Vol 41 (9-10) ◽  
pp. 911-924 ◽  
Author(s):  
P. Ribeiro
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Nonlinear Vibrations ◽  
Simply Supported ◽  
Element Method

Parametric Study of a Simply Supported Composite Plate Using Finite Element Method

2014 ◽  
Vol 4 (4) ◽  
pp. 26-33
Author(s):  
P.Deepak Kumar ◽  
◽  
Ishan Sharma ◽  
P.R. Maiti ◽  
◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parametric Study ◽  
Composite Plate ◽  
Simply Supported ◽  
Element Method

Buckling Analysis of Circular FGM Plate Having Variable Thickness Under Uniform Compression by Finite Element Method

2005 ◽  
Author(s):  
Abazar Shamekhi ◽  
Mohammad H. Naei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variable Thickness ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Thin Plates ◽  
Thickness Variation ◽  
Simply Supported ◽  
Element Method

This study presents the buckling analysis of radially-loaded circular plate with variable thickness made of functionally-graded material. The boundary conditions of the plate is either simply supported or clamped. The stability equations were obtained using energy method based on Love-Kichhoff hypothesis and Sander’s non-linear strain-displacement relation for thin plates. The finite element method is used to determine the critical buckling load. The results obtained show good agreement with known analytical and numerical data. The effects of thickness variation and Poisson’s ratio are investigated by calculating the buckling load. These effects are found not to be the same for simply supported and clamped plates.

Free Vibration Analysis of Circular FGM Plate Having Variable Thickness Under Axisymmetric Condition by Finite Element Method

2005 ◽  
Author(s):  
M. Nikkhah-Bahrami ◽  
Abazar Shamekhi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Variable Thickness ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Thickness Variation ◽  
Simply Supported ◽  
Element Method

This study presents the free vibration analysis of circular plate having variable thickness made of functionally-graded material. The boundary conditions of the plate is either simply supported or clamped. Dynamic equations were obtained using energy method based on Love-Kichhoff hypothesis and Sander’s non-linear strain-displacement relation for thin plates. The finite element method is used to determine the natural frequencies. The results obtained show good agreement with known analytical data. The effects of thickness variation and Poisson’s ratio are investigated by calculating the natural frequencies. These effects are found not to be the same for simply supported and clamped plates.

Modal analysis of double-walled carbon nanocones using the finite element method

2017 ◽  
Vol 31 (32) ◽  
pp. 1750262 ◽  
Author(s):  
S. Rouhi ◽  
R. Ansari ◽  
S. Nickabadi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Beam ◽  
Van Der Waals Interactions ◽  
Mode Shapes ◽  
Carbon Nanocones ◽  
Simply Supported ◽  
Linear Elastic ◽  
Carbon Carbon Bond ◽  
Element Method

The vibrational properties of double-walled carbon nanocones are investigated herein. The double-walled carbon nanocones with different geometries including apex angles and lengths are considered. The simply supported–simply supported, clamped-free and clamped–clamped boundary conditions are applied on the nanocones. A linear elastic beam-based finite element method is employed to obtain the frequencies of the double-walled carbon nanocones. Elastic beam elements are used to model the carbon–carbon bond in the structure of the nanocones. Besides, the spring elements are employed to describe the nonbonding van der Waals interactions between different layers. Natural frequencies and mode shapes of the double-walled carbon nanocones are extracted by solving the eigenvalue problem. It is observed that increasing the disclination angle of nanocones increases their natural frequency. However, increasing the nanocone’s height leads to decreasing the frequency.

scholarly journals Parametric Earthquake Analysis of Thick Plates Using Mindlin’s Theory

2010 ◽  
Vol 17 (6) ◽  
pp. 771-785
Author(s):  
Y.I. Özdemir ◽  
Y. Ayvaz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Aspect Ratio ◽  
Time Integration ◽  
Mode Shapes ◽  
Spatial Integration ◽  
Thick Plates ◽  
Simply Supported ◽  
Mindlin’S Theory ◽  
Element Method

The purpose of this paper is to study parametric earthquake analysis of thick plates using Mindlin's theory, to determine the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick plates subjected to earthquake excitations and to present the frequency parameters and the mode shapes of the same plates. In the analysis, finite element method is used for spatial integration and the Newmark-βmethod is used for time integration. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 8-noded finite element is used. Graphs and tables are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio. It is also concluded that the effects of the change in the thickness/span ratio on the frequency parameter of the thick plates are always larger than those of the change in the aspect ratio.

scholarly journals Analysis of vibration of beams with regularly located openings

2021 ◽  
pp. 22-28
Author(s):  
А.И. Притыкин
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Comparative Analysis ◽  
Natural Frequencies ◽  
The Finite Element Method ◽  
Program Complex ◽  
Simply Supported ◽  
Analytical Relations ◽  
Element Method

В справочной литературе содержатся расчетные зависимости для частот свободных колебаний балок со сплошной стенкой, но отсутствуют данные по собственным колебаниям перфорированных балок. В то же время в судостроении и строительной практике широко распространены балки с перфорированной стенкой, содержащей вырезы круглой, овальной и прямоугольной формы. В статье проведен анализ влияния вырезов на частоту свободных колебаний перфорированных свободно опертых балок. При этом первоначально рассматривались балки со сплошной стенкой, а затем балки таких же размеров с вырезами. Для удобства практических вычислений известная зависимость была трансформирована к виду, позволяющему оценить частоту колебаний только по соотношению площадей полки и стенки и габаритным размерам балки без необходимости определения ее момента инерции и погонной массы. Аналогичные зависимости были получены и для перфорированных балок с круглыми и прямоугольными вырезами, в которых дополнительными факторами являлись параметры перфорации: относительная высота вырезов и относительная ширина перемычек. При отсутствии вырезов формулы для перфорированных балоксводятся к формуле для балки со сплошной стенкой.Сравнительный анализ частот проводился путем расчета по аналитическим зависимостям и методом конечных элементов с использованием программного комплекса ANSYS. На основе проведенного анализа сделан вывод, что наличие регулярно расположенных вырезов с высотой, не превышающей рекомендации Морского Регистра РФ, в зависимости от параметров перфорации приводит к разному повышению частот собственных колебаний однопролетных балок, хотя степень их повышения невелика. Предложенные аналитические зависимости для балок разного конструктивного оформления удовлетворительно согласуются с результатами расчетов МКЭ. In manual on the ship structural mechanics the analytical relations for determination of the natural frequencies of the beams with solid web are given, but there are no data about proper vibration of perforated beams. At the same time in shipbuilding and in structural industry the perforated beams with circular, rectangular and oval openings are widely used. In this article the analysis of influence of openings on the natural frequencies of the simply supported perforated beams is performed. Initially it was considered beams with solid web and then beams of the same dimensions with openings. For commodity of practical calculations, the well-known relation was transformed to the form allowing to appreciate frequency of vibration only with knowledge of ratio of areas of shelves and web without necessity of finding their moment of inertia and running mass of beam. Similar relations were obtained for perforated beams with circular and rectangular openings, in which additional arguments were such parameters of perforation as related depth of openings and related width of web-posts. In case of absence of openings, the formulas for perforated beams are reduced to formula for beam with solid web. Comparative analysis was performed by calculations according to analytical relations and with the finite element method using the program complex ANSYS. On base of performed analysis it was made conclusion that existence of regularly located openings with depth not extending recommendations of Russian Maritime Register, in dependence on parameters of perforation brings to different increasing of natural frequencies of vibration of one span beams, although degree of this increasing is not high. Suggested analytical relations for beams of different constructive design are in a good correlation with results obtained by the finite element method.

Buckling analysis of circular functionally graded material plate having variable thickness under uniform compression by finite-element method

2007 ◽  
Vol 221 (11) ◽  
pp. 1241-1247 ◽  
Author(s):  
M H Naei ◽  
A Masoumi ◽  
A Shamekhi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Functionally Graded Material ◽  
Variable Thickness ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Simply Supported ◽  
Graded Material ◽  
Element Method

The current study presents the buckling analysis of radially-loaded circular plate with variable thickness made of functionally graded material. The boundary conditions of the plate is either simply supported or clamped. The stability equations were obtained using energy method based on Love-Kichhoff hypothesis and Sander's non-linear strain-displacement relation for thin plates. The finite-element method is used to determine the critical buckling load. The results obtained show good agreement with known analytical and numerical data. The effects of thickness variation and Poisson's ratio are investigated by calculating the buckling load. These effects are found not to be the same for simply supported and clamped plates.

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