Study of a Beam FGM under Loading Electrostatic
Journal of Advanced Research in Fluid Mechanics and Thermal Sciences
Volume 17 No. 1, January 2016, Pages 1-17
H. M. Berrabah1,3,*, N. Z. Sekrane1,2, B. E. Adda1,2
1Département de Génie Civil, Centre Universitaire de Relizane, Relizane, Algérie
2Département de Génie Civil, Université Djillali Liabes, Sidi Bel Abbes, Algérie
3Laboratoire des Matériaux et Hydrologie, Sidi Bel Abbes, Algérie
*Corresponding author: email@example.com
FGM, beam, electric potential, piezothermoelastic, elasticity, thermal material parameters
Based on the theory of elasticity, some exact solutions of functionally gradient piezothermoelastic cantilevers under different coupled loadings are obtained. As an application, these solutions have been successfully used to identify the gradient piezoelectric parameter and the thermal material coefficients. Besides, some numerical results have been carried out for the cantilever under two different kinds of loadings. It is found that the tip deflection of the cantilever agrees very well with the experimental and theoretical findings provided by other investigations. The present study also shows that the linear change of thermal material parameters does not influence the distribution of the stress and induction of the cantilever. But it influences the components of strain and electric field strength as well as the displacement and electric potential of the cantilever. The analytical expressions have been derived for the through thickness stresses of a composite active FGM beam subjected to electrical excitation. The structure is comprised of a substrate, an electro-elastically graded layer and an active layer. Continuous gradation of the volume fraction in the FGM layer is modelled in the form of an mth power polynomial of the coordinate axis in thickness direction of the beam. A numerical scheme of discretizing the continuous FGM layer (in sub-layers) and treating the beam as a discretely graded structure has also been developed. Appropriate expressions for the solution have been derived for the case of continuous power law gradation (mth power) of the FGM layer. The discretized FGM layer scheme has been shown to yield results that practically match those predicted analytically by the closed-form model.
CITE THIS ARTICLE
Berrabah, H. M., et al. “Study of a Beam FGM under Loading Electrostatic.” Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 17.1 (2016): 1-17.
Berrabah, H. M., Sekrane, N. Z., & Adda, B. E. (2016). Study of a Beam FGM under Loading Electrostatic. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 17(1), 1-17.
Berrabah, H. M., N. Z. Sekrane, and B. E. Adda. “Study of a Beam FGM under Loading Electrostatic.” Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 17, no. 1 (2016): 1-17.
Berrabah, H.M., Sekrane, N.Z. and Adda, B.E., 2016. Study of a Beam FGM under Loading Electrostatic. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 17(1), pp.1-17.
Berrabah, HM, Sekrane, NZ, Adda, BE. Study of a Beam FGM under Loading Electrostatic. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences. 2016;17(1):1-17.
 P. Bouchilloux, K. Uchino, Combined Finite Element Analysis – Genetic Algorithm Method for the Design of Ultrasonic Motors, Journal of Intelligent Materials Systems and Structures 14 (2003) 657–667.
 P. Jane, B. Chris Rhys, Characterization of Mulyi-layer Actuators, Ferroelectrics 273 (2002) 255–260.
 Q. Jinhao, T. Junji, U. Toshiyuki, M. Teppei, T. Hirofumi, D. Hejun, Fabrication and High Durability of Functionally Gradient Piezoelectric Bending Actuators, Smart Materials and Structures 12 (2003) 115–121.
 S. Raja, K. Rohwer, M. Rose, Piezothermoelastic Modeling and Active Vibration Control of Laminated Composite Beams, Journal of Intelligent Material Systems and Structures 10 (1999) 890–899.
 J.N. Reddy, Z. Q. Cheng, Three-Dimensional Solutions of Smart Functionally Graded Plates, Journal of Applied Mechanics 68 (2001) 234-241.
 A.J. Ruys, E.B. Popov, D. Sun, J.J. Russell, C.C.J. Murray, Functionally graded electrical/thermal ceramic systems, Journal of the European Ceramic Society21 (2001) 2025-2029.
 M.J. Schult, M.J. Sundaresan, M. Jason, D. Clayton, R. Sadler, B. Nagel, Piezoelectric Materials at Elevated Temperature, Journal of Intelligent Materials Systems and Structures 14(2003) 693–705.
 Z.F. Shi, General Solution of a Density Functionally Gradient Piezoelectric Cantilever and its Applications, Smart Materials and Structures 11(2002) 122–129.
 Z.F. Shi, Y. Chen, Functionally Graded Piezoelectric Cantilever Beam Under Load. Archive of Applied Mechanics 74 (2004) 237–247.
 J. Sirohi, I. Chopra, Fundamental Behavior of Piezoceramic Sheet Actuators, Journal of Intelligent Material Systems and Structures 11 (2000) 47–61.
 J. Sirohi, I. Chopra, Fundamental Understanding of Piezoelectric Strain Sensors, Journal of Intelligent Material Systems and Structures, 11 (2000) 246–257.
 J. Sirohi, I. Chopra, Design and Development of a High Pumping Frequency Piezoelectric-hydraulic Hybrid Actuator, Journal of Intelligent Materials Systems and Structures 14 (2003) 135–147.
 I. Tamura, Y. Tomota, M. Ozawa, Strength and ductility of Fe-Ni-C alloys composed of austenite and martensite with various strength, Proceedings of the 3rd International Conference on Strength of Metals and Alloys (1973) 611-615.
 X.G. Tian, Y.P. Shen, Finite Element Analysis of Thermo-mechanical Behaviour of Piezoelectric Structures under Finite Deformation, Acta mechanica solida sinica, 24 (2003) 169–178.
 C. Va´ zquez, K. Uchino,Novel Piezoelectric-based Power Supply for Driving Piezoelectric Actuators Designed for Active Vibration Damping Applications, Journal of Electroceramics 7 (2001) 197–210.
 J. Vendlinski, D. Brei, Dynamic Behavior of Telescopic Actuators, Journal of Intelligent Materials Systems and Structures 14 (2003) 577–586.
 B. Victor, Thermal Effects on Measurements of Dynamic Processes in Composite Structures using Piezoelectric Sensors, Smart Materials and Structures 5 (1996) 379–385.
 W. Voigt, Über die Beziehung Zwischen den Beiden Elasticitats-Constanten Isotroper Korper, Annalen der Physik and Chemie 38 (1889) 573-587.
 F. Weileun, Determination of the Elastic Modulus of Thin Film Materials Using Selfdeformed Micromachined Cantilevers, Journal of Micromechanics and Microengineering 9 (1999) 230–235.
 Z. Zhong, E.T. Shang, Three Dimensional Exact Analysis of Functionally Gradient Piezothermoelectric Material Rectangular Plate, Acta mechanical sinica 35 (2003) 542–552.
 X.H. Zhu, Q. Wang, Z.Y. Meng, A Functionally Gradient Piezoelectric Actuator Prepared by Powder Metallurgical Process in PNN-PZ-PT System, Journal of Materials Science Letters 14 (1995) 516–518.
 X. Zhu, J. Xu, Z. Meng, Z. Jianming, S. Zhou, Q. Li, Z. Liu, N. Ming, Microdisplacement characteristics and microstructures of functionally graded piezoelectric ceramic actuator, Materials and Design 21 (2001) 561.