Bending and free vibrations of beams with symmetrically varying mechanical properties-Shear effect

The subject of the paper is a beam with symmetrically varying mechanical properties in the depth direction. The proposed formulation of the functions of the properties makes a certain generalization in the research of functionally graded materials and allows to describe homogeneous, nonlinearly vari...

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Bibliographic Details
Published inMechanics of advanced materials and structures Vol. 27; no. 4; pp. 325 - 332
Main Authors Magnucki, Krzysztof, Witkowski, Dawid, Lewiński, Jerzy
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 17.02.2020
Taylor & Francis Ltd
Subjects
analytical modelling
bending
Differential equations
Equations of motion
FEM studies
FGB
Finite element method
Free vibration
Functionally gradient materials
Hamilton's principle
Mechanical properties
Sandwich structures
shear effect
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Summary:The subject of the paper is a beam with symmetrically varying mechanical properties in the depth direction. The proposed formulation of the functions of the properties makes a certain generalization in the research of functionally graded materials and allows to describe homogeneous, nonlinearly variable and sandwich structures with the use of only one, consistent analytical model. The individual nonlinear hypothesis for planar cross section is assumed. Basing on the Hamilton's principle two differential equations of motion are obtained. The system of equations is analytically solved. The results are compared with numerical solutions obtained with FEM.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1537-6494
1537-6532
DOI:10.1080/15376494.2018.1472350