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

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

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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