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Meccanica
Erschienen in: Meccanica 5/2013

01.07.2013

Buckling and vibration of axially functionally graded nonuniform beams using differential transformation based dynamic stiffness approach

verfasst von: S. Rajasekaran

Erschienen in: Meccanica | Ausgabe 5/2013

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Abstract

The free vibration of axially functionally graded (FG) non-uniform beams with different boundary conditions is studied using Differential Transformation (DT) based Dynamic Stiffness approach. This method is capable of modeling any beam (Timoshenko or Euler, centrifugally stiffened or not) whose cross sectional area, moment of Inertia and material properties vary along the beam. The effectiveness of the method is confirmed by comparing the present results with existing closed form solutions and numerical results. In FG beams, flexural rigidity and mass density may take majority of functions including polynomials, trigonometric and exponential functions (converted to polynomial expressions). DT based Dynamic stiffness approach is proved to be a versatile and simple approach compared to many other methods already proposed.
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Literatur
1.
Koizumi M (1993) The concept of FGM. Ceramic Trans Funct Grad Mater 34:3–10
2.
Koizumi M (1997) FGM activities in Japan. Composites, Part B, Eng 28:1–4 CrossRef
3.
Elishakoff I, Perez A (2005) Design of a polynomially inhomogeneous bar with a tip mass for specified mode shape and natural frequency. J Sound Vib 287(4–5):1004–1012 ADSCrossRef
4.
Elishakoff I, Pentaras D (2006) Apparently the first closed-form solution of inhomogeneous elastically restrained vibrating beams. J Sound Vib 298(1–2):439–445 MathSciNetADSMATHCrossRef
5.
Banerjee JR (1997) Dynamic stiffness formulation for structural elements: a general approach. Comput Struct 63:101–103 MATHCrossRef
6.
Banerjee JR (2000) Free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method. J Sound Vib 233(5):857–875 ADSMATHCrossRef
7.
Wang G, Wereley NM (2004) Free vibration analysis of rotating blades with uniform tapers. AIAA J 42(12):429–437 CrossRef
8.
Banerjee JR, Su H, Jackson DR (2006) Free vibration of rotating tapered beams using the dynamic stiffness method. J Sound Vib 298(4–5):1034–1054 ADSCrossRef
9.
Vinod KG, Gopalakrishnan S, Ganguli R (2007) Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements. Int J Solids Struct 44:5875–5893 MATHCrossRef
10.
Doyle JF (1977) Wave propagation in structures, 2nd edn. Springer, Berlin (Chap 5)
11.
Wright AD, Smith VR, Thresher TW, Wang JLC (1982) Vibration modes of centrifugally stiffened beams. ASME J Appl Mech 49(2):197–202 MATHCrossRef
12.
Huang Y, Li XF (2010) A new approach for free vibration of axially functionally graded beams with non-uniform cross section. J Sound Vib 329(11):2291–2303 ADSCrossRef
13.
Mabie HH, Rogers CB (1972) Transverse vibration of double-tapered cantilever beams. J Acoust Soc Am 51:1771–1774 ADSCrossRef
14.
Downs B (1977) Transverse vibration of cantilever beam having unequal breadth and depth tapers. ASME J Appl Mech 44:737–742 CrossRef
15.
Gupta RS, Rao SS (1978) Finite element eigen value analysis of tapered and twisted Timoshenko beams. J Sound Vib 56(2):187–200 ADSMATHCrossRef
16.
Dawe DJ (1978) A finite element for the vibration analysis of Timoshenko beams. J Sound Vib 60(1):11–20 ADSMATHCrossRef
17.
To CWS (1981) A linearly tapered beam finite element incorporating shear deformation and rotary inertia for vibration analysis. J Sound Vib 78(4):475–484 ADSCrossRef
18.
19.
Lee SY, Lin SM (1994) Bending vibrations of rotating non-uniform Timoshenko beams with an elastically restrained root. ASME J Appl Mech 61:949–955 MATHCrossRef
20.
Du H, Lim MK, Liew KK (1994) A power series solution for vibration of a rotating Timoshenko beam. J Sound Vib 175(4):505–523 ADSMATHCrossRef
21.
Nagaraj VT (1996) Approximate formula for the frequencies of a rotating Timoshenko beam. J Aircr 33:637–639 CrossRef
22.
Lin SC, Hsiao KM (2001) Vibration analysis of a rotating Timoshenko beam. J Sound Vib 240(2):303–322 ADSMATHCrossRef
23.
Choi DT, Chou YT (2001) Vibration analysis of elastically supported turbo machinery blades by the modified differential quadrature methods. J Sound Vib 240(5):937–953 ADSCrossRef
24.
Irie T, Yamada G, Takahashi I (1979) Determination of the steady state response of a Timoshenko beam of varying section by the use of the spline interpolation technique. J Sound Vib 63(2):287–295 ADSMATHCrossRef
25.
Irie T, Yamada G, Takahashi I (1980) Vibration and stability of a non-uniform Timoshenko beam subjected to follower force. J Sound Vib 70(4):503–512 ADSMATHCrossRef
26.
Lee SY, Lin SM (1992) Exact vibration solutions for non-uniform Timoshenko beams with attachments. AIAA J 30(12):2930–2934 ADSMATHCrossRef
27.
Shahba A, Attarnejad R, Tavanaie Marvi M, Hajilar S (2011) Free vibration and stability of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions. Composites, Part B, Eng 42(4):801–808 CrossRef
28.
Attarnejad R, Semnani SJ, Shahba A (2010) Basic displacement functions for free vibration analysis of non-prismatic Timoshenko beams. Finite Elem Anal Des 46:916–929 MathSciNetCrossRef
29.
Attarnejad R, Shahba A (2011) Basic displacement functions for centrifugally stiffened tapered beam. Int J Numer Methods Biomed Eng 27:1385–1397 MATH
30.
Attarnejad R, Shahba A (2011) Basic displacement functions in analysis of centrifugally stiffened tapered beams. Arab J Sci Eng 36:841–853 CrossRef
31.
Zhou JK (1986) Differential transformation and its application for electrical circuits. Huazhong University Press, China
32.
Chen CK, Ju SP (2004) Application of differential transformation to transient advective-dispersive transport equation. J Appl Math Comput 155(1):25–38 MathSciNetMATHCrossRef
33.
Arikoglu A, Ozkol I (2004) Solution of boundary value problems for integro-differential equations by using differential transformation method. J Appl Math Comput 168(2):1145–1158 MathSciNet
34.
Bert CW, Zeng H (2004) Analysis of axial vibration of compound bars by differential transformation method. J Sound Vib 275(3–5):641–647 ADSCrossRef
35.
Kaya MO (2006) Free vibration analysis of a rotating Timoshenko beam by differential transformation method. Aircr Eng Aerosp Technol 78:194–203 CrossRef
36.
Banerjee JR, Sobey AJ (2002) Energy expressions for rotating tapered Timoshenko beam. J Sound Vib 254(4):818–822 ADSCrossRef
37.
Wilson EL (2002) Three dimensional static and dynamic analysis of structures. Computers and Structures, Berkeley
38.
Wakashima K, Hirano T, Nino M (1990) Space applications of advanced structural materials. ESA SP 303:97
39.
Nakamura T, Wang T, Sampath S (2000) Determination of properties of graded materials by inverse analysis and instrumented indentation. Acta Mater 48:4293–4306 CrossRef
40.
Ozgumus OO, Kaya MO (2010) Vibration analysis of a rotating tapered Timoshenko beam using DTM. Meccanica 45:33–42 MATHCrossRef
41.
Attarnejad R, Shahba A (2011) Dynamic displacement functions in free vibration analysis of centrifugally stiffened tapered beams. Meccanica 46(6):1267–1281 MathSciNetCrossRef
42.
Tang B (2008) Combined dynamic stiffness matrix and precise time integration method for transient forced vibration response analysis of beams—short communication. J Sound Vib 309:868–876 ADSCrossRef
43.
Zhong WX, Williams FW (1994) A precise time step integration method. Proc IME C J Mech Eng Sci 208:427–430 CrossRef
44.
Wang CM, Wang CY, Reddy JN (2005) Exact solutions for buckling of structural members. CRC Press, Boca Raton
45.
Hodges DH, Rutkowski MJ (1981) From vibration analysis of rotating beam by a variable order finite element method. AIAA J 19:1459–1466 ADSMATHCrossRef
46.
Zarrinzadeh H, Attarnejad R, Shahba A (2012) Free vibration of rotating axially functionally graded tapered beams. Proc IME G J Aero Eng 226(4):363–379 CrossRef
47.
Ozgumus OO, Kaya MO (2006) Flapwise bending vibration analysis of double tapered rotating Euler-Bernoulli beam by using the differential transform method. Meccanica 41:661–670 MATHCrossRef
48.
49.
Huang Y, Li XF (2011) Buckling analysis of nonuniform and axially graded columns with varying flexural rigidity. ASCE J Eng Mech 137(1):73–81 CrossRef
50.
Rajasekaran S (2012) Free vibration of centrifugally stiffened axially functionally graded tapered Timoshenko beams using differential transformation and quadrature methods. Appl Math Model. doi:10.​1016/​j.​apm.​2012.​09.​024
51.
Shahba A, Rajasekaran S (2012) Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials. Appl Math Model 36:3094–3111 MathSciNetMATHCrossRef
52.
Metadaten
Titel
Buckling and vibration of axially functionally graded nonuniform beams using differential transformation based dynamic stiffness approach
verfasst von
S. Rajasekaran
Publikationsdatum
01.07.2013
Verlag
Springer Netherlands
Erschienen in
Meccanica / Ausgabe 5/2013
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-012-9651-1

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