Investigation of boundary condition effects on the stability of FGP beams in thermal environment

• Autorzy: Nasirzadeh R. , Behjat B. , Kharazi M. , Khabazaghdam A.

Identyfikatory

DOI

10.15632/jtam-pl.55.3.1003

• Języki publikacji: EN

Abstrakty

EN

In this paper, stability and instability of Functionally Graded Piezoelectric (FGP) beams is investigated based on the Timoshenko beam theory. The material properties of the beam are considered to change gradually through thickness of the beam by a simple power law. By using the principle of minimum total potential energy, governing equations of the beam are derived. Stability behavior of the beam is predicted by solving the governing equations of the FGP beam. The results show that the homogeneity of boundary conditions plays a critical role in the stability of the FGP beam. While non-homogeneous boundary conditions lead to stable behavior of the FGP beam; homogeneous boundary conditions cause instability in the beam. By solving the eigenvalue equation of the FGP beam, the buckling load of the beam is obtained for the beams that have unstable behavior. Finally, the effects of various parameters on the buckling load of the unstable beam, such as power law index, temperature, applied voltage and aspect ratio are investigated, and the results are compared with the Euler-Bernoulli beam theory.

Słowa kluczowe

EN

FGP beam; stability; instability; buckling load; Timoshenko beam theory; non-homogeneous; homogeneous boundary conditions

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2017
• Tom: Vol. 55 nr 3
• Strony: 1003--1014
• Opis fizyczny: Bibliogr. 20 poz., rys., tab.

Twórcy

autor

Nasirzadeh R.

• Mechanical Engineering Faculty, Sahand University of Technology, Tabriz, Iran

autor

Behjat B.

• Mechanical Engineering Faculty, Sahand University of Technology, Tabriz, Iran

autor

Kharazi M.

• Mechanical Engineering Faculty, Sahand University of Technology, Tabriz, Iran

autor

Khabazaghdam A.

• Mechanical Engineering Faculty, Sahand University of Technology, Tabriz, Iran

Bibliografia

• 1. Ballas R.G., 2007, Piezoelectric Multilayer Beam Bending Actuators: Static and Dynamic Behavior and Aspects of Sensor Integration, Springer
• 2. Bathe K.J., 1996, Finite Element Procedures, Prentice Hall
• 3. Bodaghi M., Damanpack A.R., Aghdam M.M., Shakeri M., 2014, Geometrically non-linear transient thermo-elastic response of FG beams integrated with a pair of FG piezoelectric sensors, Composite Structures, 107, 48-59
• 4. Davoodinik A.R., Rahimi G.H., 2011, Large deflection of flexible tapered functionally graded beam, Acta Mechanica Sinica, 27, 5, 767-777
• 5. Doroushi A., Eslami M.R., Komeili, A., 2011. Vibration analysis and transient response of an FGPM beam under thermo-electro-mechanical loads using higher-order shear deformation theory, Journal of Intelligent Material Systems and Structures, 22, 3, 231-243
• 6. Esfahani S.E., Kiani Y., Eslami M.R., 2013, Non-linear thermal stability analysis of temperature dependent FGM beams supported on non-linear hardening elastic foundations, International Journal of Mechanical Sciences, 69, 10-20
• 7. Fallah A., Aghdam M.M., 2011, Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation, European Journal of Mechanics-A/Solids, 30, 4, 571-583
• 8. Fu Y., Wang J., Mao Y., 2012, Nonlinear analysis of buckling, free vibration and dynamic stability for the piezoelectric functionally graded beams in thermal environment, Applied Mathematical Modelling, 36, 9, 4324-4340
• 9. Kiani Y., Eslami M.R., 2010, Thermal buckling analysis of functionally graded material beams, International Journal of Mechanics and Materials in Design, 6, 3, 229-238
• 10. Komijani M., Kiani Y., Eslami M.R., 2013a, Non-linear thermoelectrical stability analysis of functionally graded piezoelectric material beams, Journal of Intelligent Material Systems and Structures, 24, 4, 399-410
• 11. Komijani M., Reddy J.N., Ferreira A.J.M., 2013b, Nonlinear stability and vibration of pre/post-buckled microstructure-dependent FGPM actuators, Meccanica, 49, 2729-2745
• 12. Li S.R., Batra R.C., 2013, Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler-Bernoulli beams, Composite Structures, 95, 5-9
• 13. Li S.R., Zhang J.H., Zhao Y.G., 2006, Thermal post-buckling of functionally graded material Timoshenko beams, Applied Mathematics and Mechanics, 27, 803-810
• 14. Nasirzadeh R., Behjat B., Kharazi M., 2014, Stability of FGP beams under thermo-electro-mechanical loading, International Journal of Material Science Innovations, 2, 6, 164-177
• 15. Pradhan S.C., Murmu T., 2009, Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method, Journal of Sound and Vibration, 321, 1, 342-362
• 16. Qin Q.H., 2013, Advanced Mechanics of Piezoelectricity, Springer
• 17. Wattanasakulpong N., Gangadhara Prusty B., Kelly D.W., 2011, Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams, International Journal of Mechanical Sciences, 53, 9, 734-743
• 18. Yang J.S., 2005, Introduction to the Theory of Piezoelectricity, Springer, New York
• 19. Ying J., Lu C.F., Chen W.Q., 2008, Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations, Composite Structures, 84, 3, 209-219.
• 20. Zhang D.G., 2013, Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory, Composite Structures, 100, 121-126

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)