A Parametric Study on Flutter Analysis of Cantilevered Trapezoidal FG Sandwich Plates

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr/Isfahan, Iran

2 Faculty of Mechanical Engineering, University of Isfahan, Isfahan, Iran

Abstract

In this paper, supersonic flutter analysis of cantilevered trapezoidal plates composed of
two functionally graded face sheets and an isotropic homogeneous core is presented. Using Hamilton’s
principle, the set of governing equations and external boundary conditions are derived. A transformation
of coordinates is used to convert the governing equations and boundary conditions from the original
coordinates into the new dimensionless computational ones. Generalized differential quadrature method
(GDQM) is employed as a numerical method and critical aerodynamic pressure and flutter frequencies
are derived. Convergence, versatility, and accuracy of the presented solution are confirmed using
numerical and experimental results presented by other authors. The effect of power-law index, thickness
of the core, total thickness of the plate, aspect ratio and angles of the plate on the flutter boundaries are
investigated. It is concluded that any attempt to increase the critical aerodynamic pressure leads to a
decrease in lift force or rise in total weight of the plate.

Highlights

[1] K. Torabi, H. Afshari, Generalized differential quadrature method for vibration analysis of cantilever trapezoidal FG thick plate, Journal of Solid Mechanics, 8(1) (2016) 184-203.

[2] K. Torabi, H. Afshari, Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness, Engineering Solid Mechanics, 5(1) (2017) 71-92.

[3] R. Srinivasan, B. Babu, Flutter analysis of cantilevered quadrilateral plates, Journal of Sound and Vibration, 98(1) (1985) 45-53.

[4] T. Chowdary, P. Sinha, S. Parthan, Finite element flutter analysis of composite skew panels, Computers & structures, 58(3) (1996) 613-620.

[5] M.K. Singha, M. Ganapathi, A parametric study on supersonic flutter behavior of laminated composite skew flat panels, Composite structures, 69(1) (2005) 55-63.

[6] T. Prakash, M. Ganapathi, Supersonic flutter characteristics of functionally graded flat panels including thermal effects, Composite Structures, 72(1) (2006) 10-18.

[7] M. Singha, M. Mandal, Supersonic flutter characteristics of composite cylindrical panels, Composite Structures, 82(2) (2008) 295-301.

[8] S.-Y. Kuo, Flutter of rectangular composite plates with variable fiber pacing, Composite Structures, 93(10) (2011) 2533-2540.

[9] M.-C. Meijer, L. Dala, Zeroth-order flutter prediction for cantilevered plates in supersonic flow, Journal of Fluids and Structures, 57 (2015) 196-205.

[10] A. Sankar, S. Natarajan, T.B. Zineb, M. Ganapathi, Investigation of supersonic flutter of thick doubly curved sandwich panels with CNT reinforced facesheets using higher-order structural theory, Composite Structures, 127 (2015) 340-355.

[11] A. Cunha-Filho, A. de Lima, M. Donadon, L. Leão, Flutter suppression of plates using passive constrained viscoelastic layers, Mechanical Systems and Signal Processing, 79 (2016) 99-111.

[12] H. Navazi, H. Haddadpour, Nonlinear aero-thermoelastic analysis of homogeneous and functionally graded plates in supersonic airflow using coupled models, Composite Structures, 93(10) (2011) 2554-2565.

[13] V.V. Vedeneev, Panel flutter at low supersonic speeds, Journal of fluids and structures, 29 (2012) 79-96.

[14] V.V. Vedeneev, Effect of damping on flutter of simply supported and clamped panels at low supersonic speeds, Journal of Fluids and Structures, 40 (2013) 366-372.

[15] H. Haddadpour, S. Mahmoudkhani, H. Navazi, Supersonic flutter prediction of functionally graded cylindrical shells, Composite Structures, 83(4) (2008) 391-398.

[16] S. Mahmoudkhani, H. Haddadpour, H. Navazi, Supersonic flutter prediction of functionally graded conical shells, Composite Structures, 92(2) (2010) 377- 386.

[17] M. Kouchakzadeh, M. Rasekh, H. Haddadpour, Panel flutter analysis of general laminated composite plates, Composite Structures, 92(12) (2010) 2906-2915.

[18] J. Li, Y. Narita, Analysis and optimal design for supersonic composite laminated plate, Composite Structures, 101 (2013) 35-46.

[19] J. Li, Y. Narita, Multi-objective design for aeroelastic flutter of laminated shallow shells under variable flow angles, Composite Structures, 111 (2014) 530-539.

[20] K. Torabi, H. Afshari, Optimization for flutter boundaries of cantilevered trapezoidal thick plates, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(5) (2017) 1545-1561.

[21] S. Hosseini-Hashemi, M. Fadaee, S.R. Atashipour, A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates, International Journal of Mechanical Sciences, 53(1) (2011) 11-22.

[22] R. Mindlin, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, J. appl. Mech., 18 (1951) 31.

[23] T. Kaneko, On Timoshenko's correction for shear in vibrating beams, Journal of Physics D: Applied Physics, 8(16) (1975) 1927.

[24] W.-H. Shin, I.-K. Oh, J.-H. Han, I. Lee, Aeroelastic characteristics of cylindrical hybrid composite panels with viscoelastic damping treatments, Journal of Sound and Vibration, 296(1) (2006) 99-116.

[25] C.W. Bert, M. Malik, Differential quadrature method in computational mechanics: a review, Applied Mechanics Reviews, 49 (1996) 1-28.

[26] E. Viola, F. Tornabene, N. Fantuzzi, Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape, Composite Structures, 106 (2013) 815-834.

[27] N. Fantuzzi, F. Tornabene, Strong formulation finite element method for arbitrarily shaped laminated plates– Part I. Theoretical analysis, Adv. Aircr. Spacecr. Sci, 1(2) (2014).

[28] N. Fantuzzi, F. Tornabene, Strong formulation finite element method for arbitrarily shaped laminated plates– Part II. Numerical analysis, Adv. Aircr. Spacecr. Sci, 1(2) (2014).

[29] N. Fantuzzi, F. Tornabene, E. Viola, A. Ferreira, A strong formulation finite element method (SFEM) based on RBF and GDQ techniques for the static and dynamic analyses of laminated plates of arbitrary shape, Meccanica, 49(10) (2014) 2503-2542.

[30] F. Tornabene, N. Fantuzzi, F. Ubertini, E. Viola, Strong formulation finite element method based on differential quadrature: a survey, Applied Mechanics Reviews, 67(2) (2015) 020801.

[31] N. Fantuzzi, F. Tornabene, E. Viola, Four-parameter functionally graded cracked plates of arbitrary shape: a GDQFEM solution for free vibrations, Mechanics of Advanced Materials and Structures, 23(1) (2016) 89- 107.

[32] N. Fantuzzi, M. Bacciocchi, F. Tornabene, E. Viola, A.J. Ferreira, Radial basis functions based on differential quadrature method for the free vibration analysis of laminated composite arbitrarily shaped plates, Composites Part B: Engineering, 78 (2015) 65-78.

[33] N. Fantuzzi, F. Tornabene, Strong Formulation Isogeometric Analysis (SFIGA) for laminated composite arbitrarily shaped plates, Composites Part B: Engineering, 96 (2016) 173-203.

[34] F. Tornabene, N. Fantuzzi, M. Bacciocchi, A.M. Neves, A.J. Ferreira, MLSDQ based on RBFs for the free vibrations of laminated composite doubly-curved shells, Composites Part B: Engineering, 99 (2016) 30-47.

[35] H. Du, M. Lim, R. Lin, Application of generalized differential quadrature method to structural problems, International Journal for Numerical Methods in Engineering, 37(11) (1994) 1881-1896.

[36] J. Gao, W. Liao, Vibration analysis of simply supported beams with enhanced self-sensing active constrained layer damping treatments, Journal of Sound and Vibration, 280(1) (2005) 329-357.

[37] G. Romero, L. Alvarez, E. Alan.., L. Nallim, R. Grossi, Study of a vibrating plate: comparison between experimental (ESPI) and analytical results, Optics and lasers in engineering, 40(1) (2003) 81-90.

Keywords

References

[1] K. Torabi, H. Afshari, Generalized differential quadrature method for vibration analysis of cantilever trapezoidal FG thick plate, Journal of Solid Mechanics, 8(1) (2016) 184-203.
[2] K. Torabi, H. Afshari, Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness, Engineering Solid Mechanics, 5(1) (2017) 71-92.
[3] R. Srinivasan, B. Babu, Flutter analysis of cantilevered quadrilateral plates, Journal of Sound and Vibration, 98(1) (1985) 45-53.
[4] T. Chowdary, P. Sinha, S. Parthan, Finite element flutter analysis of composite skew panels, Computers & structures, 58(3) (1996) 613-620.
[5] M.K. Singha, M. Ganapathi, A parametric study on supersonic flutter behavior of laminated composite skew flat panels, Composite structures, 69(1) (2005) 55-63.
[6] T. Prakash, M. Ganapathi, Supersonic flutter characteristics of functionally graded flat panels including thermal effects, Composite Structures, 72(1) (2006) 10-18.
[7] M. Singha, M. Mandal, Supersonic flutter characteristics of composite cylindrical panels, Composite Structures, 82(2) (2008) 295-301.
[8] S.-Y. Kuo, Flutter of rectangular composite plates with variable fiber pacing, Composite Structures, 93(10) (2011) 2533-2540.
[9] M.-C. Meijer, L. Dala, Zeroth-order flutter prediction for cantilevered plates in supersonic flow, Journal of Fluids and Structures, 57 (2015) 196-205.
[10] A. Sankar, S. Natarajan, T.B. Zineb, M. Ganapathi, Investigation of supersonic flutter of thick doubly curved sandwich panels with CNT reinforced facesheets using higher-order structural theory, Composite Structures, 127 (2015) 340-355.
[11] A. Cunha-Filho, A. de Lima, M. Donadon, L. Leão, Flutter suppression of plates using passive constrained viscoelastic layers, Mechanical Systems and Signal Processing, 79 (2016) 99-111.
[12] H. Navazi, H. Haddadpour, Nonlinear aero-thermoelastic analysis of homogeneous and functionally graded plates in supersonic airflow using coupled models, Composite Structures, 93(10) (2011) 2554-2565.
[13] V.V. Vedeneev, Panel flutter at low supersonic speeds, Journal of fluids and structures, 29 (2012) 79-96.
[14] V.V. Vedeneev, Effect of damping on flutter of simply supported and clamped panels at low supersonic speeds, Journal of Fluids and Structures, 40 (2013) 366-372.
[15] H. Haddadpour, S. Mahmoudkhani, H. Navazi, Supersonic flutter prediction of functionally graded cylindrical shells, Composite Structures, 83(4) (2008) 391-398.
[16] S. Mahmoudkhani, H. Haddadpour, H. Navazi, Supersonic flutter prediction of functionally graded conical shells, Composite Structures, 92(2) (2010) 377- 386.
[17] M. Kouchakzadeh, M. Rasekh, H. Haddadpour, Panel flutter analysis of general laminated composite plates, Composite Structures, 92(12) (2010) 2906-2915.
[18] J. Li, Y. Narita, Analysis and optimal design for supersonic composite laminated plate, Composite Structures, 101 (2013) 35-46.
[19] J. Li, Y. Narita, Multi-objective design for aeroelastic flutter of laminated shallow shells under variable flow angles, Composite Structures, 111 (2014) 530-539.
[20] K. Torabi, H. Afshari, Optimization for flutter boundaries of cantilevered trapezoidal thick plates, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 39(5) (2017) 1545-1561.
[21] S. Hosseini-Hashemi, M. Fadaee, S.R. Atashipour, A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates, International Journal of Mechanical Sciences, 53(1) (2011) 11-22.
[22] R. Mindlin, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, J. appl. Mech., 18 (1951) 31.
[23] T. Kaneko, On Timoshenko's correction for shear in vibrating beams, Journal of Physics D: Applied Physics, 8(16) (1975) 1927.
[24] W.-H. Shin, I.-K. Oh, J.-H. Han, I. Lee, Aeroelastic characteristics of cylindrical hybrid composite panels with viscoelastic damping treatments, Journal of Sound and Vibration, 296(1) (2006) 99-116.
[25] C.W. Bert, M. Malik, Differential quadrature method in computational mechanics: a review, Applied Mechanics Reviews, 49 (1996) 1-28.
[26] E. Viola, F. Tornabene, N. Fantuzzi, Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape, Composite Structures, 106 (2013) 815-834.
[27] N. Fantuzzi, F. Tornabene, Strong formulation finite element method for arbitrarily shaped laminated plates– Part I. Theoretical analysis, Adv. Aircr. Spacecr. Sci, 1(2) (2014).
[28] N. Fantuzzi, F. Tornabene, Strong formulation finite element method for arbitrarily shaped laminated plates– Part II. Numerical analysis, Adv. Aircr. Spacecr. Sci, 1(2) (2014).
[29] N. Fantuzzi, F. Tornabene, E. Viola, A. Ferreira, A strong formulation finite element method (SFEM) based on RBF and GDQ techniques for the static and dynamic analyses of laminated plates of arbitrary shape, Meccanica, 49(10) (2014) 2503-2542.
[30] F. Tornabene, N. Fantuzzi, F. Ubertini, E. Viola, Strong formulation finite element method based on differential quadrature: a survey, Applied Mechanics Reviews, 67(2) (2015) 020801.
[31] N. Fantuzzi, F. Tornabene, E. Viola, Four-parameter functionally graded cracked plates of arbitrary shape: a GDQFEM solution for free vibrations, Mechanics of Advanced Materials and Structures, 23(1) (2016) 89- 107.
[32] N. Fantuzzi, M. Bacciocchi, F. Tornabene, E. Viola, A.J. Ferreira, Radial basis functions based on differential quadrature method for the free vibration analysis of laminated composite arbitrarily shaped plates, Composites Part B: Engineering, 78 (2015) 65-78.
[33] N. Fantuzzi, F. Tornabene, Strong Formulation Isogeometric Analysis (SFIGA) for laminated composite arbitrarily shaped plates, Composites Part B: Engineering, 96 (2016) 173-203.
[34] F. Tornabene, N. Fantuzzi, M. Bacciocchi, A.M. Neves, A.J. Ferreira, MLSDQ based on RBFs for the free vibrations of laminated composite doubly-curved shells, Composites Part B: Engineering, 99 (2016) 30-47.
[35] H. Du, M. Lim, R. Lin, Application of generalized differential quadrature method to structural problems, International Journal for Numerical Methods in Engineering, 37(11) (1994) 1881-1896.
[36] J. Gao, W. Liao, Vibration analysis of simply supported beams with enhanced self-sensing active constrained layer damping treatments, Journal of Sound and Vibration, 280(1) (2005) 329-357.
[37] G. Romero, L. Alvarez, E. Alan.., L. Nallim, R. Grossi, Study of a vibrating plate: comparison between experimental (ESPI) and analytical results, Optics and lasers in engineering, 40(1) (2003) 81-90.
AUT Journal of Mechanical Engineering
Volume 1, Issue 2
December 2017
Pages 191-210

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