Controlling the deformation in elastic and viscoelastic structures due to temperature and moisture changes using piezoelectric actuators

Abstract

We study the placement of surface-bonded piezoelectric actuators to control or minimize the deformation due to changes in temperature and moisture content in linear elastic and linear viscoelastic cantilever beams. The effect of unsteady heat and moisture diffusion phenomena on the response characteristics of the elastic and viscoelastic beams, such as displacement, stress, and strain fields, is examined based on which the magnitude of external actuating voltage to minimize deformation is predicted. This is followed by a comparative study of the field variables in cases of actuated and unactuated beams. Finite difference method is used to solve the field equations numerically. The numerical results are corroborated by comparing the results with analytical and experimental results that are available. Relatively smaller magnitude of external actuating voltage is necessary to minimize bending in the viscoelastic structure compared to the elastic structure due to the phenomenon of stress relaxation.

Keywords

Hygrothermal expansion piezoelectric actuators coupled heat conduction moisture diffusion

Get full access to this article

View all access options for this article.

References

Ahmed

Upadhyay

(2006) Electro-thermo-elastic formulation for the analysis of smart structures. Smart Materials and Structures 2: 401–406.

Atkin

Crane

(1976) Continuum theory of mixtures—basic theory and historical development. Quarterly Journal of Mechanics and Applied Mathematics 29: 209–244.

Avdelidis

Almond

Dobbinson

. (2004) Aircraft composites assessment by means of transient thermal NDT. Progress in Aerospace Sciences 40: 143–162.

Bouadi

Sun

(1989) Hygrothermal effects on the stress field of laminated composites. Journal of Reinforced Plastics and Composites 1: 40–54.

Bowen

(1982) Compressible porous media models by use of the theory of mixtures. International Journal of Engineering Science 20: 697–735.

Crawley

Anderson

(1990) Detailed models of piezoceramic actuation of beams. Journal of Intelligent Material Systems and Structures 1: 4–25.

Crawley

De Luis

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

Flaggs

Crossman

(1981) Analysis of the viscoelastic response of composite laminates during hygrothermal exposure. Journal of Composite Materials 15: 21–40.

Harper

(2002) Handbook of Plastics, Elastomers, and Composites. New York: McGraw-Hill Professional.

10.

Kutz

(2005) Mechanical Engineers’ Handbook. New York: John Wiley and Sons, Inc.

11.

Leaderman

and Textile Foundation (eds) (1943) Elastic and Creep Properties of Filamentous Materials and Other High Polymers. Washington, DC: Textile Foundation, pp. 238–251.

12.

Lee

Saravanos

(1996) Coupled layerwise analysis of thermopiezoelectric composite beams. AIAA Journal 34: 1231–1237.

13.

Muliana

Rajagopal

(2011) Changes in the response of viscoelastic solids due to changes in their internal structure. Acta Mechanica 217(3–4): 297–316.

14.

Muliana

Rajagopal

Subramanian

(2009) Degradation of an elastic composite cylinder due to diffusion of fluid. Journal of Composite Materials 43: 1225–1249.

15.

Rajagopal

Wineman

(2010) Application of viscoelastic clock models in biomechanics. Acta Mechanica 213: 255–266.

16.

Rajagopal

Tao

(1995) Mechanics of Mixtures. Singapore: World Scientific.

17.

Ramachandra

(2011) Controlling deformation in elastic and viscoelastic beams due to temperature and moisture changes using piezoelectric actuators. Thesis, Texas A&M University, College Station, TX, USA.

18.

Schwarzl

Starverman

(1952) Time-temperature dependence of linear viscoelastic behavior. Journal of Applied Physics 23: 838–843.

19.

Sih

Michopoulos

Chou

(eds) (1986) Hygrothermoelasticity. Dordrecht: Kluwer Academic Publishers.

20.

Sih

Ogawa

Chou

(1981) Two-dimensional transient hygrothermal stresses in bodies with circular cavities: moisture and temperature coupling effects. Journal of Thermal Stresses 4: 193–222.

21.

Sih

Shih

Chou

(1980) Transient hygrothermal stresses in composites: coupling of moisture and heat with temperature varying diffusivity. International Journal of Engineering Science 1: 19–42.

22.

Song

Zhou

Binienda

(2004) Thermal deformation compensation of a composite beam using piezoelectric actuators. Smart Materials and Structures 13: 30–37.

23.

Springer

(1988) Environmental Effects on Composite Materials, vol. 3. Lancaster, PA: Technomic Publishing Company.

24.

Tiersten

(1971) On the non-linear equations of electro-thermo-elasticity. International Journal of Engineering Science 9: 587–604.

25.

Truesdell

(1957a) Sulle basi della termomeccanica I. Rendiconti Lincei 8: 22–38.

26.

Truesdell

(1957b) Sulle basi della termomeccanica II. Rendiconti Lincei 8: 158–166.

27.

Weitsman

(1987) Coupled damage and moisture-transport in fiber-reinforced, polymeric composites. International Journal of Solids and Structures 23: 1003–1025.

28.

Weitsman

(2001) Effects of fluids on polymeric composites—a review. Polymer Matrix Composites 2: 369–401.

29.

Weitsman

Cai

(1994) Non-Fickian moisture diffusion in polymer composites. Journal of Composite Materials 28: 130–154.

30.

Wineman

Rajagopal

(2000) Mechanical Response of Polymers: An Introduction. New York: Cambridge University Press.

31.

Wright

(1981) The effect of diffusion of water into epoxy resins and their carbon-fibre reinforced composites. Composites 12: 201–205.

32.

Yang

(2005) An Introduction to the Theory of Piezoelectricity. New York: Springer.

33.

Zhou

Tiersten

(1994) An elastic analysis of laminated composite plates in cylindrical bending due to piezoelectric actuators. Smart Materials and Structures 3: 255–265.