scholarly journals Vibration Analysis of Functionally Graded Sandwich Beam with Variable Cross-Section

2013 ◽  
Vol 18 (3) ◽  
pp. 351-360 ◽  
Author(s):  
Hasan Çallıoğlu ◽  
Ersin Demir ◽  
Yasin Yılmaz ◽  
Metin Sayer
Keyword(s):  
Cross Section ◽  
Vibration Analysis ◽  
Sandwich Beam ◽  
Variable Cross Section ◽  
Functionally Graded ◽  
Variable Cross

Vibration analysis of sandwich beams with variable cross section on variable Winkler elastic foundation

2013 ◽  
Vol 20 (4) ◽  
pp. 359-370 ◽  
Author(s):  
Ersin Demir ◽  
Hasan Çallioğlu ◽  
Metin Sayer
Keyword(s):  
Elastic Foundation ◽  
Cross Section ◽  
Natural Frequencies ◽  
Slenderness Ratio ◽  
Sandwich Beam ◽  
Variable Cross Section ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Variable Cross ◽  
Winkler Elastic Foundation

AbstractIn this study, free vibration behavior of a multilayered symmetric sandwich beam made of functionally graded materials (FGMs) with variable cross section resting on variable Winkler elastic foundation are investigated. The elasticity and density of the functionally graded (FG) sandwich beam vary through the thickness according to the power law. This law is related to mixture rules and laminate theory. In order to provide this, a 50-layered beam is considered. Each layer is isotropic and homogeneous, although the volume fractions of the constituents of each layer are different. Furthermore, the width of the beam varies exponentially along the length of the beam, and also the beam is resting on an elastic foundation whose coefficient is variable along the length of the beam. The natural frequencies are computed for conventional boundary conditions of the FG sandwich beam using a theoretical procedure. The effects of material, geometric, elastic foundation indexes and slenderness ratio on natural frequencies and mode shapes of the beam are also computed and discussed. Finally, the results obtained are compared with a finite-element-based commercial program, ANSYS®, and found to be consistent with each other.

A new developed method for the vibration analysis of a beam with variable cross section

2012 ◽  
Vol 131 (4) ◽  
pp. 3343-3343
Author(s):  
Gang Wang ◽  
Wanyou Li ◽  
Wenlong Li ◽  
Binglin Lv
Keyword(s):  
Cross Section ◽  
Vibration Analysis ◽  
Variable Cross Section ◽  
Variable Cross

A unified procedure for the vibration analysis of elastically restrained Timoshenko beams with variable cross sections

2020 ◽  
Vol 68 (1) ◽  
pp. 38-47
Author(s):  
Gang Wang ◽  
Wen L. Li ◽  
Wanyou Li ◽  
Zhihua Feng ◽  
Junfang Ni
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Vibration Analysis ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Timoshenko Beams ◽  
Unified Approach ◽  
Cross Section Area ◽  
Section Area ◽  
Elastically Restrained

A generalized analytical method is developed for the vibration analysis of Timoshenko beams with elastically restrained ends. For a beam with any variable cross section along the lengthwise direction, the finite element method is the only unified approach to handle those kinds of problems, since the analytical solutions could not be obtained by the governing equations when the cross section area and the second moment of area changing variably lengthwise. In this article, a unified approach is proposed to study the Timoshenko beam with any variable cross sections. The cross section area and second moment of area of the beam are both expanded into cosine series, which are mathematically capable of representing any variable cross section. The translational displacement and rotation of cross section are expressed in the Fourier series by adding some admissible functions which are used to handle the elastic boundary conditions with more accuracy and high convergence rate. By using Hamilton's principle, the eigenvalues and the coefficients of the Fourier series are both obtained. Some examples are presented to illustrate the excellent accuracy of this method. Analytical solutions of the vibration of the beam are achieved for different combinations of boundary conditions including classical and elastically restrained ones. The derived results can be used as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of Timoshenko beams with any variable cross section.

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