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Erschienen in: Meccanica 4/2015

01.04.2015

Vibration characteristics of stepped beams made of FGM using differential transformation method

verfasst von: Nuttawit Wattanasakulpong, Jarruwat Charoensuk

Erschienen in: Meccanica | Ausgabe 4/2015

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Abstract

The present paper is given to investigate free vibration analysis of stepped beams produced from functionally graded materials (FGMs). The differential transformation method is employed to solve the governing differential equations of the beams to obtain their natural frequencies and mode shapes. The power law distribution is used and modified for describing material compositions across the thickness of the stepped beams made of FGM. Two main types of the stepped FGM beams in which their material compositions can be described by the modified power law distribution are selected to investigate the free vibration behaviour. The significant parametric studies such as step ratio, step location, boundary conditions and material volume fraction are also covered in this paper.

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Literatur
1.
Zurück zum Zitat Suresh S, Mortensen A (1998) Fundamental of functionally graded materials. Maney, London Suresh S, Mortensen A (1998) Fundamental of functionally graded materials. Maney, London
2.
Zurück zum Zitat Wattanasakulpong N, Prusty BG, Kelly DW, Hoffman M (2012) Free vibration analysis of layered functionally graded beams with experimental validation. Mater Des 36:182–190CrossRef Wattanasakulpong N, Prusty BG, Kelly DW, Hoffman M (2012) Free vibration analysis of layered functionally graded beams with experimental validation. Mater Des 36:182–190CrossRef
3.
Zurück zum Zitat Kapuria S, Bhattacharyya M, Kumar AN (2008) Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation. Compos Struct 82:390–402CrossRef Kapuria S, Bhattacharyya M, Kumar AN (2008) Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation. Compos Struct 82:390–402CrossRef
4.
Zurück zum Zitat Kapuria S, Bhattacharyya M, Kumar AN (2008) Theoretical modeling and experimental validation of thermal response of metal-ceramic functionally graded beams. J Therm Stresses 31:759–787CrossRef Kapuria S, Bhattacharyya M, Kumar AN (2008) Theoretical modeling and experimental validation of thermal response of metal-ceramic functionally graded beams. J Therm Stresses 31:759–787CrossRef
5.
Zurück zum Zitat Sina SA, Navazi HM, Haddadpour H (2009) An analytical method for free vibration analysis of functionally graded beams. Mater Des 30:741–747CrossRef Sina SA, Navazi HM, Haddadpour H (2009) An analytical method for free vibration analysis of functionally graded beams. Mater Des 30:741–747CrossRef
6.
Zurück zum Zitat Simsek M (2010) Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nuclear Eng Des 240:697–705CrossRef Simsek M (2010) Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nuclear Eng Des 240:697–705CrossRef
7.
Zurück zum Zitat Yang J, Chen Y (2008) Free vibration and buckling analysis of functionally graded beams with edge cracks. Compos Struct 83:48–60CrossRef Yang J, Chen Y (2008) Free vibration and buckling analysis of functionally graded beams with edge cracks. Compos Struct 83:48–60CrossRef
8.
Zurück zum Zitat Kitipornchai S, Ke LL, Yang J, Xiang Y (2009) Nonlinear vibration of edge cracked functionally graded Timoshenko beams. J Sound Vib 324:962–982CrossRefADS Kitipornchai S, Ke LL, Yang J, Xiang Y (2009) Nonlinear vibration of edge cracked functionally graded Timoshenko beams. J Sound Vib 324:962–982CrossRefADS
9.
Zurück zum Zitat Wattanasakulpong N, Prusty BG, Kelly DW (2011) Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams. Int J Mech Sci 53:734–743CrossRef Wattanasakulpong N, Prusty BG, Kelly DW (2011) Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams. Int J Mech Sci 53:734–743CrossRef
10.
Zurück zum Zitat Wattanasakulpong N, Prusty BG, Kelly DW, Hoffman M (2010) A theoretical investigation on the free vibration of functionally graded beams. In: Proceedings of the 10th international conference on computational structures technology, Valencia, Spain, 14–17 Sep 2010 Wattanasakulpong N, Prusty BG, Kelly DW, Hoffman M (2010) A theoretical investigation on the free vibration of functionally graded beams. In: Proceedings of the 10th international conference on computational structures technology, Valencia, Spain, 14–17 Sep 2010
11.
Zurück zum Zitat Fallah A, Aghdam MM (2012) Thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded beams on nonlinear elastic foundation. Composite: Part B Eng 43:1523–1530CrossRef Fallah A, Aghdam MM (2012) Thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded beams on nonlinear elastic foundation. Composite: Part B Eng 43:1523–1530CrossRef
12.
Zurück zum Zitat Vo TP, Thai HT, Nguyen TK, Inam F (2014) Static and vibration analysis of functionally graded beams using refined shear deformation theory. Meccanica 49:155–168CrossRefMATHMathSciNet Vo TP, Thai HT, Nguyen TK, Inam F (2014) Static and vibration analysis of functionally graded beams using refined shear deformation theory. Meccanica 49:155–168CrossRefMATHMathSciNet
13.
Zurück zum Zitat Rajasekaran S (2013) Buckling and vibration of axially functionally graded nonuniform beams using differential transformation based dynamic stiffness approach. Meccanica 48:1053–1070CrossRefMATHMathSciNet Rajasekaran S (2013) Buckling and vibration of axially functionally graded nonuniform beams using differential transformation based dynamic stiffness approach. Meccanica 48:1053–1070CrossRefMATHMathSciNet
14.
Zurück zum Zitat Rajasekaran S, Tochaei EN (2014) Free vibration analysis of axially functionally graded tapered Timoshenko beams using differential transformation element method and differential quadrature element method of lowest-order. Meccanica 49:995–1009CrossRefMATHMathSciNet Rajasekaran S, Tochaei EN (2014) Free vibration analysis of axially functionally graded tapered Timoshenko beams using differential transformation element method and differential quadrature element method of lowest-order. Meccanica 49:995–1009CrossRefMATHMathSciNet
15.
Zurück zum Zitat Ju F, Lee HP, Lee KH (1994) On the free vibration of stepped beams. Int J Solids Struct 31:3125–3137CrossRefMATH Ju F, Lee HP, Lee KH (1994) On the free vibration of stepped beams. Int J Solids Struct 31:3125–3137CrossRefMATH
16.
Zurück zum Zitat Naguleswaran S (2002) Vibration of an Euler-Bernoulli beam on elastic end supports and with up to three step changes in cross-section. Int J Mech Sci 44:2541–2555CrossRefMATH Naguleswaran S (2002) Vibration of an Euler-Bernoulli beam on elastic end supports and with up to three step changes in cross-section. Int J Mech Sci 44:2541–2555CrossRefMATH
17.
Zurück zum Zitat Dong XJ, Meng G, Li HG, Ye L (2005) Vibration analysis of a stepped laminated composite Timoshenko beam. Mech Res Commun 32:572–581CrossRefMATH Dong XJ, Meng G, Li HG, Ye L (2005) Vibration analysis of a stepped laminated composite Timoshenko beam. Mech Res Commun 32:572–581CrossRefMATH
18.
Zurück zum Zitat Mao Q, Pietrzko S (2010) Free vibration analysis of stepped beams by using Adomain decomposition method. Appli Math Comput 217:3429–3441CrossRefMATHMathSciNet Mao Q, Pietrzko S (2010) Free vibration analysis of stepped beams by using Adomain decomposition method. Appli Math Comput 217:3429–3441CrossRefMATHMathSciNet
19.
Zurück zum Zitat Malik M, Dang HH (1998) Vibration analysis of continuous systems by differential transformation. Appli Math Comput 96:17–26CrossRefMATHMathSciNet Malik M, Dang HH (1998) Vibration analysis of continuous systems by differential transformation. Appli Math Comput 96:17–26CrossRefMATHMathSciNet
20.
Zurück zum Zitat Kaya MO, Ozgumus OO (2007) Flexural–torsional-coupled vibration analysis of axially loaded closed-section composite Timoshenko beam by using DTM. J sound Vib 306:495–506CrossRefADS Kaya MO, Ozgumus OO (2007) Flexural–torsional-coupled vibration analysis of axially loaded closed-section composite Timoshenko beam by using DTM. J sound Vib 306:495–506CrossRefADS
21.
Zurück zum Zitat Ozgumus OO, Kaya MO (2006) Flapwise bending vibration analysis of double tapered rotating Euler–Burnoulli beam by using the differential transform method. Meccanica 41:661–670CrossRefMATH Ozgumus OO, Kaya MO (2006) Flapwise bending vibration analysis of double tapered rotating Euler–Burnoulli beam by using the differential transform method. Meccanica 41:661–670CrossRefMATH
22.
Zurück zum Zitat Ozgumus OO, Kaya MO (2010) Vibration analysis of a rotating tapered Timoshenko beam using DTM. Meccanica 45:33–42CrossRefMATH Ozgumus OO, Kaya MO (2010) Vibration analysis of a rotating tapered Timoshenko beam using DTM. Meccanica 45:33–42CrossRefMATH
23.
Zurück zum Zitat Pradhan SC, Reddy GK (2011) Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasticity theory and DTM. Comput Mater Sci 50:1052–1056CrossRef Pradhan SC, Reddy GK (2011) Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasticity theory and DTM. Comput Mater Sci 50:1052–1056CrossRef
24.
Zurück zum Zitat Wattanasakulpong N, Chaikittiratana A (2014) On the linear and nonlinear vibration response of elastically end restrained beams using DTM. Mech Des Struct Mach 42:135–150 Wattanasakulpong N, Chaikittiratana A (2014) On the linear and nonlinear vibration response of elastically end restrained beams using DTM. Mech Des Struct Mach 42:135–150
25.
Zurück zum Zitat Salehi P, Yaghoobi H, Torabi M (2012) Application of the differential transformation method and variational iteration method to large deformation of cantilever beams under point load. J Mech Sci Tech 26:2879–2887CrossRef Salehi P, Yaghoobi H, Torabi M (2012) Application of the differential transformation method and variational iteration method to large deformation of cantilever beams under point load. J Mech Sci Tech 26:2879–2887CrossRef
26.
Zurück zum Zitat Ni Q, Zhang ZL, Wang L (2011) Application of the differential transformation method to vibration analysis of pipes conveying fluid. Appl Math Comput 217:7028–7038CrossRefMATHMathSciNet Ni Q, Zhang ZL, Wang L (2011) Application of the differential transformation method to vibration analysis of pipes conveying fluid. Appl Math Comput 217:7028–7038CrossRefMATHMathSciNet
27.
Zurück zum Zitat Ke LL, Yang J, Kitipornchai S (2010) An analytical study on the nonlinear vibration of functionally graded beam. Meccanica 45:743–752CrossRefMATHMathSciNet Ke LL, Yang J, Kitipornchai S (2010) An analytical study on the nonlinear vibration of functionally graded beam. Meccanica 45:743–752CrossRefMATHMathSciNet
28.
Zurück zum Zitat Maurini C, Pouget J, dell’Isola F (2004) On a model of layered piezoelectric beams including transverse stress effect. Int J Solids Struct 41:4473–4502CrossRefMATH Maurini C, Pouget J, dell’Isola F (2004) On a model of layered piezoelectric beams including transverse stress effect. Int J Solids Struct 41:4473–4502CrossRefMATH
29.
Zurück zum Zitat Andreaus U, Baragatti P (2011) Cracked beam identification by numerically analysing the nonlinear behaviour of the harmonically forced response. J Sound Vib 330:721–742CrossRefADS Andreaus U, Baragatti P (2011) Cracked beam identification by numerically analysing the nonlinear behaviour of the harmonically forced response. J Sound Vib 330:721–742CrossRefADS
30.
Zurück zum Zitat Andreaus U, Baragatti P (2012) Experimental damage detection of cracked beams by using nonlinear characteristics of forced response. Mech Syst Sig Pro 31:382–404CrossRef Andreaus U, Baragatti P (2012) Experimental damage detection of cracked beams by using nonlinear characteristics of forced response. Mech Syst Sig Pro 31:382–404CrossRef
Metadaten
Titel
Vibration characteristics of stepped beams made of FGM using differential transformation method
verfasst von
Nuttawit Wattanasakulpong
Jarruwat Charoensuk
Publikationsdatum
01.04.2015
Verlag
Springer Netherlands
Erschienen in
Meccanica / Ausgabe 4/2015
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-014-0054-3

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