Free vibration analysis of 2D-FGM truncated conical shell resting on Winkler

Abstract

Based on the first-order shear deformation theory, this paper focuses on the free vibration behavior of two-dimensional functionally graded material truncated conical shells resting on Winkler–Pasternak foundations. The materials are assumed to be isotropic and inhomogeneous in the length and thickness directions of truncated conical shell. The material properties of the truncated conical shell are varied in these directions according to power law functions. The derived governing equations are solved using differential quadrature method. Convergence of this method is checked and the fast rate of convergence is observed. The primary results of this study are obtained for (S_S−S_L), (C_S−C_L), and (C_S−S_L) boundary conditions and compared with those available in the literatures. Furthermore, effects of geometrical parameters, material power indexes, mechanical boundary conditions, Winkler and Pasternak foundation moduli on the nondimensional frequency parameters of the two-dimensional functionally graded material truncated conical shell are studied.

Keywords

Truncated conical shell free vibration functionally graded material differential quadrature method Winkler–Pasternak foundations

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References

Pan

Han

. Exact solution for functionally graded and layered magnetoelectro-elastic plates. Int J Eng Sci 2004; 43: 321–339.

Hosseini-Hashemi

Rokni

Damavandi

. Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Appl Math Model 2010; 34: 1276–1291.

Malekzadeh

. Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations. Compos Struct 2009; 89: 367–373.

Yas

Sobhani Aragh

. Free vibration analysis of continuous grading fiber reinforced plates on elastic foundation. Int J Eng Sci 2010; 48: 1881–1895.

Chiroiu

Munteanu

. On the free vibrations of a piezoceramic hollow sphere. Mech Res Commun 2007; 34: 123–129.

Chen

. Vibration theory of non-homogeneous, spherically isotropic piezoelastic bodies. J Sound Vib 2000; 229: 833–860.

Haddadpour

Mahmoudkhani

Navazi

. Free vibration analysis of functionally graded cylindrical shells including thermal effects. Thin-Walled Struct 2007; 45: 591–599.

Sobhani Aragh

Yas

. Three-dimensional free vibration of functionally graded fiber orientation and volume fraction cylindrical panels. Mater Des 2010; 31: 4543–4552.

Yas

Sobhani Aragh

. Three-dimensional analysis for thermoelastic response of functionally graded fiber reinforced cylindrical panel. Compos Struct 2010; 92: 2391–2399.

10.

Bahtui

Eslami

. Coupled thermo-elasticity of functionally graded cylindrical shells. Mech Res Commun 2007; 34: 1–18.

11.

Thambiratnam

Zhuge

. Axisymmetric free vibration analysis of conical shells. Eng Struct 1993; 15: 83–89.

12.

Tong

. Free vibration of orthotropic conical shells. Int J Eng Sci 1993; 31: 719–733.

13.

Leissa

. Vibration of shells, New York: The Acoustic Society of America, 1993.

14.

Liew

Lim

. Vibratory characteristics of cantilevered rectangular shallow shells of variable thickness. AIAA J 1994; 32: 87–96.

15.

Liew

Lim

. Vibration of perforated doubly-curved shallow shells with rounded corners. Int J Solids Struct 1994; 31: 19–36.

16.

Shu

. Free vibration analysis of composite laminated conical shells by generalized differential quadrature. J Sound Vib 1996; 194: 587–604.

17.

Bardell

Dunsdon

Langley

. Free vibration of thin, isotropic, open, conical panels. J Sound Vib 1998; 217: 297–320.

18.

Wang

Liu

Wang

. Free vibration analysis of truncated conical shells by the differential quadrature method. J Sound Vib 1999; 224: 387–394.

19.

Sofiyev

. The vibration and stability behavior of freely supported FGM conical shells subjected to external pressure. Compos Struct 2009; 89: 56–66.

20.

Liew

Zhao

. Free vibration analysis of conical shells via the element-free kp-Ritz method. J Sound Vib 2005; 281: 627–645.

21.

Bhangale

Ganesan

Padmanabhan

. Linear thermoelastic buckling and free vibration behavior of functionally graded truncated conical shells. J Sound Vib 2006; 292: 341–371.

22.

Tornabene

. Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution. Comput Meth Appl Mech Eng 2009; 198: 2911–2935.

23.

Nezhadi

Abdul Rahman

Ayob

. Comparison of two kinds of functionally graded conical shells with various gradient index for vibration analysis. J Am Sci 2012; 8: 651–657.

24.

Malekzadeh

Fiouz

Sobhrouyan

. Three-dimensional free vibration of functionally graded truncated conical shells subjected to thermal environment. Int J Pres Ves Pip 2012; 89: 210–221.

25.

Sofiyev

. The non-linear vibration of FGM truncated conical shells. Compos Struct 2012; 94: 2237–2245.

26.

Sofiyev

Schnack

. The buckling of cross-ply laminated non-homogeneous orthotropic composite conical thin shells under a dynamic external pressure. Acta Mech 2003; 162: 29–40.

27.

Sofiyev

Deniz

Akçay

. The vibration and stability of a three-layered conical shell containing an FGM layer subjected to axial compressive load. Acta Mech 2006; 183: 129–144.

28.

Nemat-Alla

. Reduction of thermal stresses by developing two dimensional functionally graded materials. Int J Solids Struct 2003; 40: 7339–7356.

29.

Dhaliwal

Singh

. On the theory of elasticity of a non-homogeneous medium. J Elasticity 1978; 8: 211–219.

30.

Clements

Budhi

. A boundary element method for the solution of a class of steady-state problems for anisotropic media. Int J Heat Transfer 1999; 121: 462–465.

31.

Aboudi

Pindera

Arnold

. Thermoelastic theory for the response of materials functionally graded in two directions. Int J Solids Struct 1996; 33: 931–966.

32.

Hedia

Midany

Shabara

. Development of cementless metal-backed acetabular cup prosthesis using functionally graded material. Int J Mech Mater Des 2005; 2: 259–267.

33.

Goupee

Vel

. Optimization of natural frequencies of bi-directional functionally graded beams. Struct Multidiscip Optim 2006; 32(6): 473–484.

34.

Asgari

Akhlaghi

Hosseini

. Dynamic analysis of two-dimensional functionally graded thick hollow cylinder with finite length under impact loading. Acta Mech 2009; 208: 163–180.

35.

Asgari

Akhlaghi

. Transient heat conduction in two-dimensional functionally graded hollow cylinder with ﬁnite length. J Heat Mass Transfer 2009; 45: 1383–1392.

36.

Asgari

Akhlaghi

. Transient thermal stresses in two-dimensional functionally graded thick hollow cylinder with ﬁnite length. Arch Appl Mech 2009; 80: 353–376.

37.

Asgari

Akhlaghi

. Natural frequency analysis of 2D-FGM thick hollow cylinder based on three-dimensional elasticity equations. Eur J Mech A-Solid 2011; 30: 72–81.

38.

Asemi

Salehi

Akhlaghi

. Elastic solution of a two-dimensional functionally graded thick truncated cone with finite length under hydrostatic combined loads. Acta Mech 2011; 217: 119–134.

39.

Paliwal

Pandey

Nath

. Free vibration of circular cylindrical shell on Winkler and Pasternak foundations. Int J Pres Ves Pip 1996; 69: 79–89.

40.

Civalek

. Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of harmonic differential quadrature-finite difference methods. Int J Pres Ves Pip 2005; 82: 753–761.

41.

Golovko

Lugovoi

Meish

. Solution of axisymmetric dynamic problems for cylindrical shells on an elastic foundation. Int Appl Mech 2007; 43: 785–793.

42.

Sofiyev

Kuruoglu

. Natural frequency of laminated orthotropic shells with different boundary conditions and resting on the Pasternak type elastic foundation. Compos Part B: Eng 2011; 42: 1562–1570.

43.

Thai

H-T

Choi

D-H

. A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation. Compos Part B: Eng 2012; 43: 2335–2347.

44.

Civalek

. Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution differential quadrature coupled approaches. Compos Part B: Eng 2013; 50: 171–179.

45.

Tornabene

Fantuzzi

Viola

. Winkler-Pasternak foundation effect on the static and dynamic analyses of laminated doubly-curved and degenerate shells and panels. Compos Part B: Eng 2014; 57(1): 269–296.

46.

Tornabene

Ceruti

. Free-form laminated doubly-curved shells and panels of revolution on Winkler-Pasternak elastic foundations: A 2D GDQ solution for static and free vibration analysis. World J Mech 2013; 3: 1–25.

47.

Tornabene

. Free vibrations of anisotropic doubly-curved shells and panels of revolution with a free-form meridian resting on Winkler-Pasternak elastic foundations. Compos Struct 2011; 94(1): 186–206.

48.

Sofiyev

Avcar

Ozyigit

. The free vibration of non-homogeneous truncated conical shells on a Winkler foundation. Int J Eng Appl Sci 2009; 1(1): 34–41.

49.

Pitakthapanaphong

Busso

. Self-consistent elastoplastic stress solutions for functionally graded material systems subjected to thermal transients. J Mech Phys Solids 2002; 50: 695–716.

50.

Sun

Huang

. The exact solution for the general bending problems of conical shells on the elastic foundation. Appl Math Mech 1998; 9: 455–469.

51.

Sofiev

Koruglu

. Natural frequency of laminated orthotropic shells with different boundary conditions and resting on the Pasternak type elastic foundation. Compos Part B: Eng 2011; 42: 1562–1570.

52.

Kerr

. Elastic and visco-elastic foundation models. J Appl Mech 1964; 31: 491–498.

53.

Gorbunov-Possadov

Malikova

Solomin

. Design of structures on elastic foundation, 3rd ed. Moscow: Gos Izd Lit po Stroit I Arkh (Strojizdat), 1964.

54.

Shadmehri

Hoa

Hojjati

. Buckling of conical composite shells. Compos Struct 2012; 94: 787–792.

55.

Asgari

Akhlaghi

. Natural frequency analysis of 2D-FGM thick hollow cylinder based on three-dimensional elasticity equations. Eur J Mech A-Solid 2011; 30: 72–81.

56.

Reddy

. Mechanics of laminated composite plates and shells. Theory and analysis, Boca Raton: CRC Press LLC, 2004.

57.

Kargarnovin MH and Shahsanami M. Buckling analysis of a composite cylindrical shell with fiber's material properties changing lengthwise using first-order shear deformation theory. In: International conference on mechanical, automotive and materials engineering, (ICMAME'2012), Dubai, 7--8 January 2012, pp.172–176.

58.

Hosseini-Hashemi

Es’haghi

Rokni Damavandi Taher

. Exact closed-form frequency equations for thick circular plates using a third order shear deformation theory. J Sound Vib 2010; 329: 3382–3396.

59.

Bert

Malik

. Differential quadrature method in computational mechanics: A review. Appl Mech Rev 1996; 49: 1–27.

60.

Bellman

Kashef

Casti

. Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations. J Comput Phys 1972; 10: 40–52.

61.

Ghorbanpour Arani

Kolahchi

Mosallaie Barzoki

. Elastic foundation effect on nonlinear thermo-vibration of embedded double layered orthotropic graphene sheets using differential quadrature method. Proc IMechE, Part C: J Mechanical Engineering Science. DOI: 10.1177/0954406212453808.

62.

Shu

. An efficient approach for free vibration analysis of conical shells. Int J Mech Sci 1996; 38: 935–949.

63.

Irie

Yamada

Tanaka

. Natural frequencies of truncated conical shells. J Sound Vib 1984; 92: 447–453.

64.

Lam

. Influence of boundary conditions on the frequency characteristics of a rotating truncated circular conical shell. J Sound Vib 1999; 223: 171–195.

Free vibration analysis of 2D-FGM truncated conical shell resting on Winkler–Pasternak foundations based on FSDT

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