Piezo-viscoelastically damped nonlinear frequency response of functionally graded plates with a heated plate-surface

Abstract

A geometrically nonlinear frequency-domain analysis of functionally graded plates integrated with an active constrained layer damping (ACLD) arrangement is performed by developing an incremental nonlinear closed-loop dynamic finite element model of the overall plate. The active constraining layer is made of piezoelectric fiber reinforced composite (PFRC) and a heated substrate-plate surface is considered. The analysis is mainly for investigating the effect of temperature on the nonlinear vibration characteristics of the overall plate in the frequency domain and also, on the corresponding control authority of the PFRC constraining layer. A negative velocity feedback control strategy is utilized to achieve active damping. The temperature dependent material properties of the substrate plate are graded in the thickness direction according to a power law, and expressed in terms of the power law exponent and the constituent material (metal and ceramic) properties. Using the Golla-Hughes-McTavish method for modeling the viscoelastic material, the incremental nonlinear finite element equations of motion are derived in the frequency domain assuming periodic motion of the overall plate. An arc-length extrapolation solution technique is used in combination with a new strategy for determination of incremental arc-length. The numerical illustrations show a potential use of PFRC actuator in the ACLD arrangement and suggest an optimal thickness of viscoelastic layer for more effective use of PFRC. The analysis reveals the significant effects of initial thermal bending of the overall smart plate on its nonlinear dynamic behavior in the frequency domain. The effects of temperature, metal-volume fraction in substrate, fiber volume fraction in PFRC and the fiber orientation angle in the PFRC on the control authority of the ACLD layer are presented. For the use of the ACLD layer in the form of a patch, a new numerical strategy for determining its optimal location and optimal size for effective control is presented.

Keywords

Active constrained layer damping functionally graded (FG) plates nonlinear vibration control piezoelectric composite actuator

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References

Aboudi

(1998) Micromechanical prediction of the effective coefficients of thermo-piezoelectric multiphase composites. Journal of intelligent Material Systems and Structures 9(9): 713–722.

Aboudi

Pindera

Arnold

(1996) Thermoelastic theory for the response of materials functionally graded in two directions. International Journal of Solids and Structures 33(7): 931–966.

Arockiarajan

Sakthivel

(2012) Thermo-electro-mechanical response of 1–3–2 piezoelectric composites: effect of fiber orientations. Acta Mechanica 223(7): 1353–1369.

Bailey

Hubbard

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

Batra

Vel

(2001) Exact solution for thermoelastic deformations of functionally graded thick rectangular plates. American Institute of Aeronautics and Astronautics 40(7): 1421–1433.

Baz A (1993) Active constrained layer damping. In: DAMPING’93 Conference, San Francisco, CA, February 1993, pp. IBB 1–23.

Baz

(1995) Optimum design and control of active constrained layer damping. ASME Journal of Mechanical Design 117(B): 135–144.

Bent

Hagood

(1997) Piezoelectric fiber composites with interdigitated electrodes. Journal of Intelligent Material Systems and Structures 8(11): 903–919.

Chantalakhana

Stanway

(2001) Active constrained layer damping of clamped-clamped plate vibrations. Journal of Sound and Vibration 241(5): 755–777.

10.

Christensen

(1982) Theory of Viscoelasticity: An Introduction, 2nd edn. New York: Academic Press.

11.

Crawley

Luis

(1987) Use of piezoelectric actuators as elements of intelligent structures. American Institute of Aeronautics and Astronautics 25(10): 1373–1385.

12.

Feldman

Aboudi

(1997) Buckling analysis of functionally graded plates subjected to uniaxial loading. Composite Structures 38(1–4): 29–36.

13.

Golla

Hughes

(1985) Dynamics of viscoelastic structures – a time domain, finite element formulation. ASME Journal of Applied Mechanics 52(4): 897–906.

14.

Huang

Kuo

(1996) Micromechanics determination of the effective properties of piezoelectric composites containing spatially oriented short fibers. Acta Materialia 44(12): 4889–4898.

15.

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.

16.

Kalamkarov

Savi

(2012) Micromechanical modeling and effective properties of the smart grid reinforced composites. Journal of Brazilian Society of Mechanical Science and Engineering XXXIV: 343–351.

17.

Koizumi

(1993) Concept of FGM. Ceramics Transactions on Functionally Graded Materials 34: 3–10.

18.

Lau

Cheung

Chen

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

19.

Loy

Lam

Reddy

(1999) Vibration of functionally graded cylindrical shells. International Journal of Mechanical Sciences 41(3): 309–324.

20.

Mallik

Ray

(2003) Effective coefficients of piezoelectric fiber reinforced composites. American Institute of Aeronautics and Astronautics 41(4): 704–710.

21.

Mian

Spencer

AJM

(1998) Exact solutions for functionally graded and laminated elastic materials. Journal of the Mechanics and Physics of Solids 46(12): 2283–2295.

22.

Miller SE and Hubbard JE (1987) Observability of a Bernoulli-Euler beam using PVF₂ as a distributed sensor. MIT Draper Laboratory Report, 1 July 1987.

23.

Noda

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

24.

Panda

Ray

(2008) Active constrained layer damping of geometrically nonlinear vibrations of functionally graded plates using piezoelectric fiber reinforced composites. Smart Materials and Structures 17(2): 1–15.

25.

Park

Baz

(1999) Vibration control of bending modes of plates using active constrained layer damping. Journal of Sound and Vibration 227(4): 711–734.

26.

Praveen

Reddy

(1998) Nonlinear transient thermoelastic analysis of functionally graded ceramic metal plates. International Journal of Solids and Structures 35(33): 4457–4476.

27.

Ray

(2006) Hybrid damping of smart functionally graded plates using piezoelectric fiber reinforced composites. IEEE Transactions, Ultrasonic Ferroelectric Frequency Control 53(11): 2152–2165.

28.

Ray

Batra

(2007) Vertically reinforced 1-3 composites for active damping of functionally graded plates. American Institute of Aeronautics and Astronautics 45(7): 1179–1183.

29.

Ray

Baz

(1999) Optimization of energy dissipation of active constrained layer damping treatments of plates. Journal of Sound and Vibration 208(3): 391–406.

30.

Ray

Mallik

(2004) Active constrained layer damping of laminated composite beams using piezoelectric fiber reinforced composite layer. Smart Materials and Structures 13(1): 146–152.

31.

Reibero

Petyt

(1999) Nonlinear vibration analysis of plates by hierarchical finite element and continuation methods. International Journal of Mechanical Sciences 41(4--5): 437–459.

32.

Rongong

Wright

Wynne

(1997) Modelling of a hybrid constrained layer/piezoceramic approach to active damping. ASME Journal of Vibration and Acoustics 119(1): 120–130.

33.

Sankar

(2001) An elasticity solution for functionally graded beams. Composite Science and Technology 61(5): 689–696.

34.

Sarvanan

Ganesan

Ramamurti

(2001) Semianalytical finite element analysis of active constrained layer damping in cylindrical shells of revolution. Composite Structures 79(11): 1131–1145.

35.

Shen

(2002) Nonlinear bending response of functionally graded plates subjected to transverse loads and in thermal environments. International Journal of Mechanical Sciences 44(3): 561–584.

36.

Shi

Hua

Sol

(2004) The finite element analysis and experimental study of beams with active constrained layer damping treatment. Journal of Sound and Vibration 278(1–2): 343–363.

37.

Shu

Della

(2008) The performance of 1–3 piezoelectric composites with a porous non-piezoelectric matrix. Acta Materialia 56(4): 754–761.

38.

Smith

Auld

(1991) Modeling 1-3 composite piezoelectrics: thickness mode oscillations. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 38(1): 40–47.

39.

Tiersten

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

40.

Venkatesh

Kar-Gupta

(2013) Electromechanical response of (2–2) layered piezoelectric composites. Smart Materials and Structures 22(2): 02530351–02503514.

41.

Woo

Meguid

(2001) Nonlinear analysis of functionally graded plates and shallow shells. International Journal of Solids and Structures 38(42--43): 7409–7421.