Harmonically exited nonlinear vibration of heated functionally graded plates integrated with piezoelectric composite actuator

Abstract

A nonlinear frequency response analysis of a smart functionally graded plate operating under a heated substrate plate surface is presented. The analysis is mainly for investigating the effect of temperature on the harmonically exited nonlinear vibration characteristics of smart functionally graded plates and also on the corresponding control authority of piezoelectric fiber–reinforced composite actuator bonded to the substrate plate surface. A negative velocity feedback control strategy is utilized so as to achieve smart damping. The temperature-dependent material properties of the ceramic metal–based functionally graded plate are graded in the thickness direction. Based on the von Karman nonlinear strain–displacement relations and assuming periodic motion, a nonlinear dynamic incremental finite element model of the overall smart functionally graded plate is developed. An arc-length extrapolation technique with a new strategy for determining the arc length is used for numerical solutions. The analysis reveals significant effects of temperature and metal volume fraction in substrate on the structural dynamic behavior of the overall plate. The analysis also reveals the effects of temperature, metal volume fraction in substrate, fiber volume fraction in piezoelectric fiber–reinforced composite, and fiber orientation in piezoelectric fiber–reinforced composite on the smart damping. For using the piezoelectric fiber–reinforced composite actuator in the form of a patch, its optimal location and size are numerically determined.

Keywords

Functionally graded plates piezoelectric fiber–reinforced composite actuator nonlinear vibration control smart damping

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References

Aboudi

Pindera

(1996) Thermoelasticity theory for the response of materials functionally graded in two directions. International Journal of Solids and Structures 33(7): 936–966.

Alibeigloo

(2010) Exact solution for thermo-elastic response of functionally graded rectangular plates. Composite Structures 92(1): 113–121.

Alijani

Nejad

Amabili

(2011) Nonlinear vibrations of FGM rectangular plates in thermal environment. Nonlinear Dynamics 66(3): 251–270.

Bailey

Hubbard

(1985) Distributed piezoelectric polymer active vibration control of a cantilever beam. Journal of Guidance, Control, and Dynamics 8(5): 605–611.

Behjat

Khoshravan

(2012) Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates. Composite Structures 94(3): 874–882.

Cheung

Chen

Lau

(1990) Application of the incremental harmonic balance method to cubic nonlinearity. Journal of Sound and Vibration 140(2): 273–286.

Crawley

Luis

(1987) Use of piezoelectric actuators as elements of intelligent structures. AIAA Journal 25(10): 1373–1385.

Ebrahimi

Rastgoo

(2008) An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory. Thin-Walled Structures 46(12): 1402–1408.

Ebrahimi

Rastgoo

(2009a) Nonlinear vibration of smart circular functionally graded plates coupled with piezoelectric layers. International Journal of Material Design 5(2): 157–165.

10.

Ebrahimi

Rastgoo

(2009b) Temperature effects on nonlinear vibration of FGM plates coupled with piezoelectric actuators. Journal of Solid Mechanics 1(4): 271–288.

11.

Fakhari

Ohadi

Yousefian

(2011) Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layers in thermal environment. Composite Structures 93(9): 2310–2321.

12.

Huang

Shen

(2004) Nonlinear vibration and dynamic response of functionally graded plates in thermal environments. International Journal of Solids and Structures 41(9–10): 2403–2427.

13.

Koizumi

(1993) Concept of FGM. Ceramic Transactions 34(4): 3–10.

14.

Kou

(2009) Three-dimensional vibration analysis of functionally graded material plates in thermal environment. Journal of Sound and Vibration 324(3–5): 733–750.

15.

Liew

. (2001) Active control of FGM plates subjected to a temperature gradient: modeling via finite element method based on FSDT. International Journal of Numerical Methods in Engineering 52(11): 1253–1271.

16.

Mallik

Ray

(2003) Effective coefficients of piezoelectric fiber reinforced composites. AIAA Journal 41(4): 704–710.

17.

Matsunaga

(2009) Stress analysis of functionally graded plates subjected to thermal and mechanical loadings. Composite Structures 87(4): 344–357.

18.

Miller

Hubbard

(1987) Observability of a Bernoulli-Euler beam using PVF2 as a distributed sensor. In Proceedings of : 6th VPI & SU/AIAA Symposium on Dynamic and Control of Large Structures, June, 1987.

19.

Noda

(1999) Thermal stresses in functionally graded materials. Journal of Thermal Stresses 22(4–5): 477–512.

20.

Ootao

Tanigawa

(2001) Control of the transient thermoelastic displacement of functionally graded rectangular plate bonded to a piezoelectric plate due to nonuniform heating. Acta Mechanica 148(1–4): 17–33.

21.

Praveen

Reddy

(1998) Nonlinear transient thermo elastic analysis of functionally graded ceramic metal plates. International Journal of Solids and Structures 35(33): 4457–4467.

22.

Ray

Sachade

(2006) Finite element analysis of smart functionally graded plates. International Journal of Solids and Structures 43(18–19): 5468–5484.

23.

Reddy

Ray

(2007) Optimal control of smart functionally graded plates using piezoelectric fiber reinforced composites. Journal of Vibration and Control 13(6): 795–814.

24.

Ribeiro

Petyt

(2000) Nonlinear free vibration of isotropic plates with internal resonance. International Journal of Non-linear Mechanics 35(2): 263–278.

25.

Shakeri

Mirzaeifar

(2009) Static and dynamic analysis of thick functionally graded plates with piezoelectric layers using layerwise finite element model. Mechanics of Advanced Materials and Structure 16(8): 561–575.

26.

Tierstien

(1969) Linear Piezoelectric Plate Vibrations. New York: Plenum Press.

27.

Vel

Batra

(2004) Three-dimensional exact solution for the vibration of functionally graded rectangular plates. Journal of Sound and Vibration 272(3–5): 703–730.

28.

Woo

Meguid

(2001) Nonlinear analysis of functionally graded plates and shallow shell. International Journal of Solids and Structures 38(42): 7409–7421.

29.

Xia

Shen

(2009) Nonlinear vibration and dynamic response of FGM plates with piezoelectric fiber reinforced composite actuators. Composite Structures 90(2): 254–262.

30.

Yang

Shen

(2002) Vibration characteristics and transient response of shear deformable functionally graded plates in thermal environments. Journal of Sound and Vibration 255(3): 579–602.

31.

Yiqi

(2010) Nonlinear dynamic response and active vibration control for piezoelectric functionally graded plate. Journal of Sound and Vibration 329(11): 2015–2028.

32.

Zhao

Lee

Liew

(2009) Mechanical and thermal buckling analysis of functionally graded plates. Composite Structures 90(2): 161–171.