The Effects of Various Boundary Conditions on Thermal Buckling of Functionally Graded Beamwith Piezoelectric Layers Based on Third order Shear Deformation Theory

Authors: O. Miraliyari

Abstract:

This article attempts to analyze functionally graded beam thermal buckling along with piezoelectric layers applying based on the third order shearing deformation theory considering various boundary conditions. The beam properties are assumed to vary continuously from the lower surface to the upper surface of the beam. The equilibrium equations are derived using the total potential energy equations, Euler equations, piezoelectric material constitutive equations and third order shear deformation theory assumptions. In order to fulfill such an aim, at first functionally graded beam with piezoelectric layers applying the third order shearing deformation theory along with clamped -clamped boundary conditions are thoroughly analyzed, and then following making sure of the correctness of all the equations, the very same beam is analyzed with piezoelectric layers through simply-simply and simply-clamped boundary conditions. In this article buckling critical temperature for functionally graded beam is derived in two different ways, without piezoelectric layer and with piezoelectric layer and the results are compared together. Finally, all the conclusions obtained will be compared and contrasted with the same samples in the same and distinguished conditions through tables and charts. It would be noteworthy that in this article, the software MAPLE has been applied in order to do the numeral calculations.

Keywords: Thermal buckling, functionally graded beam, piezoelectric layer, various boundary conditions.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1333867

References:

[1] C. Edvard, D.L Javier, "Use of Piezoelectric Actuators as Element of Inteligent Structure", AIAA journal, Vol 25, No10, 1373-1385, 1387.
[2] J.A Fabunni, Forced Vibration of a single State axial Compressor Rotor , Journal Engineering for Power , Vol .102,No.2,33-328,1980.
[3] W.G Cady, "Piezoelectricity", McGraw Hill, New York Dover Press publication,New York,1964.
[4] H.F Triesten, Linear Piezoelectric plate Vibration, Plenum Press,New York , 1969.
[5] H.S Tzou, Piezoelectric Shells Distributed Sensing and Control of Continua, Kluwer Acad. Pud., Boston/ Dordrecht,1993.
[6] J.N Reddy on Laminated Composite Plate with Integrated Sensors and Actuators, Engineering Structures, Vol.21, 568-593, 1999.
[7] D.A Saravanos, et al, Layerwise Mechanics and Finite Element for the Dynamic Analisis of Piezoelectric composite Plate INt.j. Solids structure vol. 34(3), 359-378, 1997.
[8] P Heyliger, and Brooks, S., Exact Solution for Laminated Piezoelectric Plates in Cylinrical bending J App.Mech., Vol 63.
[9] H Kawai ,The Piezoelectric of poly (vinylidene floride) Japanes J.App Vol
[10] D.O Brush, B .O Almort, Buckling of Bars, Plates and shells. Mc Graw Hill, New york, 1975.
[11] A.R.de Faria. On buckling Enhancemented Beams with Piezoelectric Actuators via Stress Stiffening, composite Structures 65 (2004)187 -192, December 2003.
[12] T.S Barret.et al, Active Vibration Control of Rotating Machinary Using Piezoelectric Actatures Incorporating Flexible Casting Effect ,J.eng.Gas turbines Power ,117(1),176-187,1995. G. R. Faulhaber, "Design of service systems with priority reservation," in Conf. Rec. 1995 IEEE Int. Conf. Communications, pp. 3-8.