scholarly journals Free Vibration of Axially Functionally Graded Beam

2020 ◽  
Author(s):  
Dongxing Cao ◽  
Bin Wang ◽  
Wenhua Hu ◽  
Yanhui Gao
Keyword(s):  
Free Vibration ◽  
Functionally Graded ◽  
Functionally Graded Beam

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

2020 ◽  
Vol 23 (16) ◽  
pp. 3415-3428
Author(s):  
Yusuf Cunedioglu ◽  
Shkelzen Shabani
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Crack Depth ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Single Edge ◽  
Functionally Graded Beam ◽  
Cross Sectional

Free vibration analysis of a single edge cracked multi-layered symmetric sandwich stepped Timoshenko beams, made of functionally graded materials, is studied using finite element method and linear elastic fracture mechanic theory. The cantilever functionally graded beam consists of 50 layers, assumed that the second stage of the beam (step part) is created by machining. Thus, providing the material continuity between the two beam stages. It is assumed that material properties vary continuously, along the thickness direction according to the exponential and power laws. A developed MATLAB code is used to find the natural frequencies of three types of the stepped beam, concluding a good agreement with the known data from the literature, supported also by ANSYS software in data verification. In the study, the effects of the crack location, crack depth, power law gradient index, different material distributions, different stepped length, different cross-sectional geometries on natural frequencies and mode shapes are analysed in detail.

Geometrically Nonlinear Free Vibration of Composite Materials: Clamped-Clamped Functionally Graded Beam with an Edge Crack Using Homogenisation Method

2017 ◽  
Vol 730 ◽  
pp. 521-526 ◽  
Author(s):  
Mohcine Chajdi ◽  
El Bekkaye Merrimi ◽  
Khalid El Bikri
Keyword(s):  
Free Vibration ◽  
Edge Crack ◽  
Volume Fraction ◽  
Crack Depth ◽  
Beam Theory ◽  
Functionally Graded ◽  
Geometrically Nonlinear ◽  
Nonlinear Free Vibration ◽  
Functionally Graded Beam ◽  
Euler Bernoulli Beam

The problem of geometrically nonlinear free vibration of a clamped-clamped functionally graded beam containing an open edge crack in its center is studied in this paper. The study is based on Euler-Bernoulli beam theory and Von Karman geometric nonlinearity assumptions. The cracked section is modeled by an elastic spring connecting two intact segments of the beam. It is assumed that material properties of the functionally graded composites are graded in the thickness direction and estimated through the rule of mixture. The homogenisation method is used to reduce the problem to that of isotropic homogeneous cracked beam. Direct iterative method is employed for solving the eigenvalue equation for governing the frequency nonlinear vibration, in order to show the effect of the crack depth and the influences of the volume fraction on the dynamic response.

Nonlinear bending and free vibration response of SUS316-Al2O3 functionally graded plasma sprayed beams: theoretical and experimental study

2016 ◽  
Vol 24 (6) ◽  
pp. 1171-1184 ◽  
Author(s):  
Pravin Malik ◽  
Ravikiran Kadoli
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Maximum Error ◽  
Functionally Graded ◽  
Nonlinear Finite Element ◽  
Functionally Graded Beam ◽  
Element Analysis ◽  
Nonlinear Bending ◽  
Plasma Sprayed ◽  
3D Solid

Functionally graded SUS316-Al2O3 beams with ceramic content varying from 0 to 40% were prepared by a plasma spraying technique. Nonlinear finite element analysis was used to obtain the static deflection and free vibration of a clamped-free functionally graded beam. Von Kármán geometric nonlinearity and power law variation in material gradation through the beam thickness are considered in the analysis. The maximum error between the experimental and nonlinear finite element results for deflection is 6.68% and 14.31% on the fundamental frequency. Numerical results have also been attempted using ANSYS 3D solid element and they compare more closely with the experimental results.

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