World Journal of Mechanics

Volume 2, Issue 6 (December 2012)

ISSN Print: 2160-049X   ISSN Online: 2160-0503

Google-based Impact Factor: 1  Citations  h5-index & Ranking

Free Vibration Analysis of Functionally Graded Beams with General Elastically End Constraints by DTM

HTML  Download Download as PDF (Size: 902KB)  PP. 297-310  
DOI: 10.4236/wjm.2012.26036    4,594 Downloads   10,473 Views  Citations

ABSTRACT

The differential transformation method (DTM) is applied to investigate free vibration of functionally graded beams supported by arbitrary boundary conditions, including various types of elastically end constraints. The material properties of functionally graded beams are assumed to obey the power law distribution. The main advantages of this method are known for its excellence in high accuracy with small computational expensiveness. The DTM also provides all natural frequencies and mode shapes without any frequency missing. Fundamental frequencies as well as their higher frequencies and mode shapes are presented. The significant aspects such as boundary conditions, values of translational and rotational spring constants and the material volume fraction index on the natural frequencies and mode shapes are discussed. For elastically end constraints, some available results of special cases for isotropic beams are used to validate the present results. The new frequency results and mode shapes of functionally graded beams resting on elastically end constraints are presented.

Share and Cite:

N. Wattanasakulpong and V. Ungbhakorn, "Free Vibration Analysis of Functionally Graded Beams with General Elastically End Constraints by DTM," World Journal of Mechanics, Vol. 2 No. 6, 2012, pp. 297-310. doi: 10.4236/wjm.2012.26036.

Cited by

[1] Free vibration of axially or transversely graded beams using finite-element and artificial intelligence
Alexandria Engineering Journal, 2022
[2] Modeling and Analyzing the Free Vibration of Simply Supported Functionally Graded Beam
Journal of Aerospace …, 2022
[3] Investigating the free vibration of viscoelastic FGM Timoshenko nanobeams resting on viscoelastic foundations with the shear correction factor using finite element …
… Based Design of …, 2022
[4] Transverse vibration of cracked graded shear beam with axial motion
International Journal of Energy and …, 2021
[5] Vibrations Analysis of Functionally Graded Beams at Different Boundary Conditions
2021
[6] Calculating the fundamental frequency of power law functionally graded beam using ANSYS software
2021
[7] Analytical solution for analyzing initial curvature effect on vibrational behavior of PM beams integrated with FGP layers based on trigonometric theories
Advances in nano …, 2021
[8] Analytical solution of free vibration of FG beam utilizing different types of beam theories: A comparative study
Alwan, M Avcar - Computers and Concrete, An International …, 2020
[9] Analisis de vibracion de vigas funcionalmente graduadas aplicando el metodo de elemento finitos
2020
[10] A Comprehensive Review on Vibration Analysis of Functionally Graded Beams
2020
[11] DYNAMIC ANALYSIS OF UNIFORM AND NON-UNIFORM CROSS-SECTION CANTILEVER SANDWICH BEAMS
2019
[12] Assessing the Effects of Porosity on the Bending, Buckling, and Vibrations of Functionally Graded Beams Resting on an Elastic Foundation by Using a New Refined …
2019
[13] Free vibration of imperfect sigmoid and power law functionally graded beams
2019
[14] Modeling and analysis of functionally graded sandwich beams: A review
Mechanics of Advanced Materials and Structures, 2018
[15] Free vibration of functionally graded beams resting on Winkler-Pasternak foundation
Arabian Journal of Geosciences, 2018
[16] Effect of Taper on Free Vibration of Functionally Graded Rotating Beam by Mori-Tanaka Method
Journal of The Institution of Engineers (India): Series C, 2018
[17] The isogeometric free vibration and transient response of functionally graded piezoelectric curved beam with elastic restraints
Results in Physics, 2018
[18] NATURAL FREQUENCY ANALYSIS OF LAYERED FUNCTIONALLY GRADED BEAMS.
2018
[19] NATURAL FREQUENCY ANALYSIS OF LAYERED FUNCTIONALLY GRADED BEAMS
Anadolu üniversitesi Bilim Ve Teknoloji Dergisi A-Uygulamal? Bilimler ve Mühendislik, 2018
[20] Elastostatic analysis of two-directional functionally graded beams using various beam theories and Symmetric Smoothed Particle Hydrodynamics method
Composite Structures, 2017
[21] Contribution à l'étude du contrôle actif de structures composites par incorporation des matériaux intelligents
2017
[22] Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3d shear deformation theory
Composite Structures, 2017
[23] Mode Shape Analysis of Multiple Cracked Functionally Graded Timoshenko Beams
2017
[24] Vibration Analysis of Functionally Graded Timoshenko Beams
International Journal of Structural Stability and Dynamics, 2017
[25] Free Vibration of Functionally Graded Rayleigh Beam
2017
[26] Vibration Analysis of Non-Uniform Imperfect Functionally Graded Beams with Porosities in Thermal Environment
Journal of Mechanics, 2017
[27] Closed-Form Solutions for Free Vibration Frequencies of Functionally Graded Euler-Bernoulli Beams
Mechanics of Composite Materials, 2017
[28] Free vibration analysis of functionally graded beams using complementary functions method
Archive of Applied Mechanics, 2017
[29] Mode shape analysis of multiple cracked functionally graded beam-like structures by using dynamic stiffness method
2017
[30] Static behaviour of two-directional functionally graded sandwich beams using various beam theories
2017
[31] Geometric Nonlinear Finite Element and Genetic Algorithm Based Vibration Energy Harvesting from Functionally Graded Nonprismatic Piezolaminated Beams
2017
[32] Free vibration of functionally graded thin beams made of saturated porous materials
2016
[33] FREE VIBRATION ANALYSIS OF FGM BEAM WITH GEN-ERAL BOUNDARY CONDITIONS BY ISOGEOMETRIC AP-PROACH
2016
[34] Static and free vibration analysis of functionally graded beams by combination Timoshenko theory and finite volume method
Composite Structures, 2016
[35] Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method
KSCE Journal of Civil Engineering, 2016
[36] Finite Element Modelling for Static and Free Vibration Response of Functionally Graded Beam
2016
[37] Nonlinear dynamics and contact interactions of the structures composed of beam-beam and beam-closed cylindrical shell members
Chaos, Solitons & Fractals, 2016
[38] An approach to free vibration analysis of axially graded beams
Journal of Theoretical and Applied Mechanics, 2016
[39] Analysis of Bending Deflections of Functionally Graded Beams by Using Different Beam Theories and Symmetric Smoothed Particle Hydrodynamics
International Journal of Engineering Technologies IJET, 2016
[40] Active vibration control of functionally graded beams with piezoelectric layers based on higher order shear deformation theory
Earthquake Engineering and Engineering Vibration, 2016
[41] An approach for free vibration analysis of axially graded beams
2016
[42] Exact solutions for static and dynamic analyses of carbon nanotube-reinforced composite plates with Pasternak elastic foundation
Applied Mathematical Modelling, 2015
[43] On vibration behavior of rotating functionally graded double-tapered beam with the effect of porosities
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2015
[44] A Review on Vibrational Analysis of a Functionlly Graded Beams
International Journal of Engineering Research & Technology, 2014
[45] 双参数弹性地基上 FGM 梁的自由振动分析
兰州理工大学学报, 2014
[46] A Review on Vibrational Analysis of a Functionally Graded Beams
International Journal of Engineering …, 2014
[47] Free Vibration Analysis of Simply Supported Power Law Functionally Graded Beam Using Finite Element Method

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.