A simple finite element procedure for free vibration of rectangular thin and thick plates

2021 ◽  
Vol 401 ◽  
pp. 126104
Author(s):  
S.A. Eftekhari
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Thick Plates ◽  
Finite Element Procedure

Eigenvector and eigenvalue analysis of thick plates resting on elastic foundation with first order finite element

2018 ◽  
Vol 4 (2) ◽  
pp. 61
Author(s):  
Yaprak Itır Özdemir
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Winkler Foundation ◽  
Thick Plates ◽  
First Order ◽  
Element Method

The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin’s theory with first order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency parameters of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using first order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 4-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 4-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also 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.

Effect of crack on free vibration of a pre-stressed curved plate

2021 ◽  
pp. 095440622199486
Author(s):  
Can Gonenli ◽  
Hasan Ozturk ◽  
Oguzhan Das
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequency ◽  
Present Model ◽  
Mode Shapes ◽  
Load Parameter ◽  
Flexible Plate ◽  
Cantilever Plate ◽  
Finite Element Software ◽  
Aspect Ratios

In this study, the effect of crack on free vibration of a large deflected cantilever plate, which forms the case of a pre-stressed curved plate, is investigated. A distributed load is applied at the free edge of a thin cantilever plate. Then, the loading edge of the deflected plate is fixed to obtain a pre-stressed curved plate. The large deflection equation provides the non - linear deflection curve of the large deflected flexible plate. The thin curved plate is modeled by using the finite element method with a four-node quadrilateral element. Three different aspect ratios are used to examine the effect of crack. The effect of crack and its location on the natural frequency parameter is given in tables and graphs. Also, the natural frequency parameters of the present model are compared with the finite element software results to verify the reliability and validity of the present model. This study shows that the different mode shapes are occurred due to the change of load parameter, and these different mode shapes cause a change in the effect of crack.

Geometrically nonlinear static and dynamic analysis of CNT reinforced laminated composite plates: A finite element study

2021 ◽  
pp. 095440622110089
Author(s):  
Balakrishna Adhikari ◽  
BN Singh
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Dynamic Response ◽  
Integration Scheme ◽  
Static And Dynamic Analysis ◽  
Finite Element Study ◽  
Nonlinear Eigenvalues ◽  
Nonlinear Static ◽  
The Impact ◽  
Element Study

In this paper, a finite element study is conducted using the Green Lagrange strain field based on vonKarman assumptions for the geometric nonlinear static and dynamic response of the laminated functionally graded CNT reinforced (FG-CNTRC) composite plate. The governing equations for determining the nonlinear static and dynamic behavior of the FG-CNTRC plate are derived using the Lagrange equation of motion based on Reddy's higher order theory. Using the direct iteration technique, the nonlinear eigenvalues for analyzing the free vibration response are obtained and the nonlinear dynamic responses of the FG-CNTRC plate are encapsulated based on the nonlinear Newmark integration scheme. The impact of the amplitude of vibration on mode switching phenomena and the consequence of the duration of the pulse on the free vibration regime of the plate are outlined. Also, the effect of time dependent loads is studied on the normal stresses of the plate. Furthermore, the impact on the nonlinear static and dynamic response of the laminated FG-CNTRC plate of various parameters such as span-thickness ratio (b/h ratio), aspect ratio (a/b ratio), different edge constraints, CNT fiber gradation, etc. are also studied.

Analysis of Deformation for PC Thin-Wall Box Girders Exposed to Fire

2011 ◽  
Vol 368-373 ◽  
pp. 930-933
Author(s):  
Wei Hou ◽  
Shuan Hai He ◽  
Cui Juan Wang ◽  
Gang Zhang
Keyword(s):  
Finite Element ◽  
Thin Wall ◽  
Fire Load ◽  
Box Girders ◽  
Conduction Model ◽  
Load Model ◽  
Deformation Problem ◽  
Finite Element Procedure ◽  
Thin Walled

Being aimed to deformation problem of pre-stressed concrete thin-walled multi-room box girders exposed to co-action of fire and load, on the basis of enthalpy conduction model and thermo-mechanics parameters, the finite element procedure was applied to analyze the deformation of three spans pre-stressed concrete thin-walled multi-room box girders exposed to co-action of fire and load. In conclusion, the deflection is obvious under action of the variation width and fire load model.

scholarly journals Out-of-Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Hamdi Alper Özyiğit ◽  
Mehmet Yetmez ◽  
Utku Uzun
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Variable Cross ◽  
Additional Mass ◽  
Inertia Effects ◽  
Tapered Beam ◽  
Out Of Plane ◽  
Good Agreement

As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-of-plane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

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