Aero-thermoelastic stability and nonlinear flutter analysis of functionally graded panels

Abstract

Nonlinear flutter characteristics under the thermal load as well as aerodynamic heating on functionally graded material panels are investigated in the hypersonic flow. Mathematical models are defined such as power-law, sigmoid and exponential functionally graded materials by the volume fractions of the constituents. Further, third-order piston theory of aerodynamics and von Karman strain-displacement relationship is adopted in order to perform the aero-thermoelastic analysis. Applying the principle of virtual work, equations of motion are derived in the matrix form, and then finite element method is used to obtain the discretized equations. Then, the time domains analysis is performed using Newmark’s time integration method. To check the validity of the present formulation, numerical results are compared with the previous data in the literatures.

Keywords

Functionally graded materials third-order piston theory power-law functionally graded material sigmoid functionally graded material exponential functionally graded material

Get full access to this article

View all access options for this article.

References

Carnahan

Richards

. A modification to filtered-X LMS control for airfoil vibration and flutter suppression. J Vib Contr 2008; 14: 831–848.

Raja

Pashilkar

Sreedeep

. Flutter control of a composite plate with piezoelectric multilayered actuators. Aero Sci Tech 2006; 10: 435–441.

Kouchakzadeh

Rasekh

Haddadour

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

Sohn

Kim

. Nonlinear thermal flutter of functionally graded panel under a supersonic flow. Compos Struct 2009; 3: 380–387.

Prakash

Ganapathi

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

Cheng

Mei

. Finite element modal formulation for hypersonic panel flutter analysis with thermal effects. AIAA J 2004; 42: 687–695.

Song

. Active aeroelasic flutter analysis and vibration control of supersonic composite laminated plate. Compos Struct 2012; 94: 702–713.

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

Hirano

Yamada

. Multi-paradigm expert system architecture based upon the inverse design concept. Inter Work Artif Intel Indust Appl, Japan: Hitachi, 1988, pp. 25–27.

10.

Kapuria

Bhattacharyya

Kumar

. Bending and free vibration response of layered functionally graded beams: A theoretical model and its experimental validation. Compos Struct 2008; 82: 390–402.

11.

Delale

Erodogan

. The crack problem for a nonhomogeneous plane. J Appl Mech 1983; 50: 609–614.

12.

Jin

Batra

. Stresses intensity relaxation at the tip of an edge crack in a functionally graded material subjected to a thermal shock. J Therm Stres 1996; 19: 317–339.

13.

Javaheri

Eslami

. Thermal buckling of functionally graded plates. AIAA J 2002; 40: 162–169.

14.

Reddy

. Analysis of functionally graded plates. Inter J Numer Meth Eng 2000; 47: 663–684.

15.

Chung

Chi

. The residual stress of functionally graded materials. J Chin Inst Civil Hyd Eng 2001; 13: 1–9.

16.

Mollarzi

Foroutan

Dastjerdi

. Analysis of free vibration of functionally graded material (FGM) cylinders by a meshless method. J Compos Mater 2011; 46: 507–515.

17.

Lee

Kim

. Non-linear dynamic response of functionally graded panels under aerodynamic load. World Congr Advan Struct Eng Mech, Seoul: South Korea, 2011.

18.

Lee

Kim

. Thermal post-buckling characteristics of functionally graded plates under aerodynamic effects. In: Asian-Australian Conf Compos Mater, Taiwan, 2010, Taipei.

19.

Zienkiewicz

Taylor

Too

. Reduced integration technique in general analysis of plates and shells. Inter J Numer Meth Eng 1971; 3: 275–290.

20.

Dixon

Mei

. Finite element analysis of large-amplitude panel flutter of thin laminates. AIAA J 1993; 31: 701–707.

21.

Nguyen

Sab

Bonnet

. First-order shear deformation plate models for functionally graded materials. Compos Struct 2008; 83: 25–36.

22.

Efraim

Eisenberger

. Exact vibration analysis of variable thickness thick annular isotropic and FGM plates. J Sound Vib 2007; 299: 720–738.

23.

Reddy

Chin

. Thermomechanical analysis of functionally graded cylinders and plates. J Ther Stres 1998; 21: 593–629.

24.

Kim

Lomboy

Han

. Geometrically non-linear analysis of functionally graded material (FGM) plates and shells using a four-node quasi-conforming shell element. J Compos Mater 2008; 42: 485–511.