Optimization of flutter boundaries of cantilevered trapezoidal functionally graded sandwich plates

Abstract

As a useful tool for designing wings and tail fins of aircrafts, this paper presents an optimization for flutter characteristics of cantilevered functionally graded sandwich plates. The plate is composed of an isotropic homogeneous core and two functionally graded face sheets. The plate is modeled based on the first-order shear deformation theory. The aerodynamic pressure is estimated using supersonic piston theory and using Hamilton's principle, the set of governing equations and boundary conditions are then derived. Applying a transformation of coordinates, governing equations and boundary conditions are converted and solved numerically by differential quadrature method. Natural frequencies, damping ratio, corresponding mode shapes, critical aerodynamic pressure, and flutter frequency are calculated. In order to achieve an optimum design, particle swarm optimization is employed to find the best values of aspect ratio, thickness of the plate, thickness of the core, power law index, and angles of the plate which increase critical aerodynamic pressure. Some constrains on the angles of the plate and its mass and area (lift force) are also considered.

Keywords

Optimization flutter trapezoidal plate functionally graded sandwich plate

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References

Srinivasan

Babu

BJC

. Flutter analysis of cantilevered quadrilateral plates. J Sound Vib 1985; 98: 45–53.

Chowdary

TVR

Sinha

Parthan

. Finite element flutter analysis of composite skew panels. Comput Struct 1996; 58: 613–620.

Singha

Ganapathi

. A parametric study on supersonic flutter behavior of laminated composite skew flat panels. Compos Struct 2005; 69: 5–63.

Prakash

Ganapathi

. Supersonic flutter characteristics of functionally graded flat panels including thermal effects. Compos Struct 2006; 72: 10–18.

Singh

Mandal

. Supersonic flutter characteristics of composite cylindrical panels. Compos Struct 2008; 82: 295–301.

Kuo

. Flutter of rectangular composite plates with variable fiber pacing. Compos Struct 2011; 93: 2533–2540.

Majer

Dala

. Zeroth-order flutter prediction for cantilevered plates in supersonic flow. J Fluids Struct 2015; 57: 196–205.

Sankar

Natarajan

Haboussi

et al.

Panel flutter characteristics of sandwich plates with CNT reinforced facesheets using an accurate higher-order theory. J Fluids Struct 2014; 50: 376–391.

Sankar

Natarajan

Ben Zineb

et al.

Investigation of supersonic flutter of thick doubly curved sandwich panels with CNT reinforced face sheets using higher-order structural theory. Compos Struct 2015; 127: 340–355.

10.

Grover

Singh

Maiti

. An inverse trigonometric shear deformation theory for supersonic flutter characteristics of multilayered composite plates. Aero Sci Technol 2016; 52: 41–51.

11.

Navazi

Haddadpour

. Nonlinear aero-thermoelastic analysis of homogeneous and functionally graded plates in supersonic airflow using coupled models. Compos Struct 2011; 93: 2554–2565.

12.

Kouchakzadeh

Rasekh

Haddadpour

. Panel flutter analysis of general laminated composite plates. Compos Struct 2010; 92: 2906–2915.

13.

Song ZG, Zhang LW and Liew KM. Aeroelastic analysis of CNT reinforced functionally graded composite panels in supersonic airflow using a higher-order shear deformation theory. Compos Struct 2016; 141: 79–90.

14.

Narita

. Analysis and optimal design for supersonic composite laminated plate. Compos Struct 2013; 101: 35–46.

15.

Narita

. Multi-objective design for aeroelastic flutter of laminated shallow shells under variable flow angles. Compos Struct 2014; 111: 530–539.

16.

Kennedy J and Eberhart RC. Particle swarm optimization. In: Proceedings of the 1995 IEEE international conference on neural networks, IEEE Service Center, Piscataway, NJ, 1995.

17.

Mindlin

. Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. J Appl Mech ASME 1951; 18: 31–38.

18.

Kaneko

. On Timoshenko’s correction for shear in vibrating beams. J Phys D Appl Phys 1975; 8: 1928–1937.

19.

Shin

Han

et al.

Aeroelastic characteristics of cylindrical hybrid composite panels with viscoelastic damping treatments. J Sound Vib 2006; 296: 99–116.

20.

. Active aeroelastic flutter suppression of a supersonic plate with piezoelectric material. Int J Eng Sci 2012; 51: 190–203.

21.

McGee

Leissa

Huang

. Vibrations of cantilevered skewed trapezoidal and triangular plates with corner stress singularities. Int J Mech Sci 1992; 34: 63–84.

22.

Dozio

Carrera

. A variable kinematic Ritz formulation for vibration study of quadrilateral plates with arbitrary thickness. J Sound Vib 2011; 330: 4611–4632.

23.

Quintana

Nallim

. A general Ritz formulation for the free vibration analysis of thick trapezoidal and triangular laminated plates resting on elastic supports. Int J Mech Sci 2013; 69: 1–9.

24.

Shokrollahi

Shafaghat

. A global Ritz formulation for the free vibration analysis of hybrid metal-composite thick trapezoidal plates. Sci Iran B 2016; 23: 249–259.

25.

Zamani

Fallah

Aghdam

. Free vibration analysis of moderately thick trapezoidal symmetrically laminated plates with various combinations of boundary conditions. Eur J Mech A 2012; 36: 204–212.

26.

Torabi

Afshari

. Generalized differential quadrature method for vibration analysis of cantilever trapezoidal FG thick plate. J Solid Mech 2016; 8: 184–203.

27.

Torabi K and Afshari H. Vibration analysis of a cantilevered trapezoidal moderately thick plate with variable thickness. Eng Solid Mech 2017; 5: 71–92.

28.

Viola

Tornabene

Fantuzzi

. Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape. Compos Struct 2013; 106: 815–834.

29.

Fantuzzi

Tornabene

. Strong formulation finite element method for arbitrarily shaped laminated plates – Part I. Theoretical analysis. Adv Aircraft Spacecraft Sci 2014; 1: 125–143.

30.

Fantuzzi

Tornabene

. Strong formulation finite element method for arbitrarily shaped laminated plates – Part II. Numerical analysis. Adv Aircraft Spacecraft Sci 2014; 1: 145–175.

31.

Fantuzzi

Tornabene

Viola

et al.

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 2014; 49: 2503–2542.

32.

Tornabene

Fantuzzi

Ubertini

et al.

Strong formulation finite element method based on differential quadrature: a survey. Appl Mech Rev 2015; 67: 1–55.

33.

Fantuzzi

Tornabene

Viola

. Four-parameter functionally graded cracked plates of arbitrary shape: a GDQFEM solution for free vibrations. Mech Adv Mater Struct 2016; 23: 89–107.

34.

Fantuzzi

Bacciocchi

Tornabene

et al.

Radial basis functions based on differential quadrature method for the free vibration analysis of laminated composite arbitrarily shaped plates. Composites Part B 2015; 78: 65–78.

35.

Fantuzzi

Tornabene

. Strong formulation isogeometric analysis (SFIGA) for laminated composite arbitrarily shaped plates. Composites Part B 2016; 96: 173–203.

36.

Tornabene

Fantuzzi

Bacciocchi

et al.

MLSDQ based on RBFs for the free vibrations of laminated composite doubly-curved shells. Composites Part B 2016; 99: 30–47.

37.

Lim

Lin

. Application of generalized differential quadrature method to structural problems. Int J Numer Meth Eng 1994; 37: 1881–1896.

38.

Gao

Liao

. Vibration analysis of simply supported beams with enhanced self-sensing active constrained layer damping treatments. J Sound Vib 2005; 280: 329–357.

39.

Bert

Malik

. Differential quadrature method in computational mechanics: a review. Appl Mech Rev 1996; 49: 1–28.

40.

Rao SS. Engineering optimization: theory and practice. Hoboken, New Jersey: John Wiley & Sons, 2009.

41.

Liu

Lin

. Evolutionary computation of unconstrained and constrained problems using a novel momentum-type particle swarm optimization. Eng Optimiz 2007; 39: 287–305.