بررسی ارتعاش آزاد و پاسخ استاتیکی تیر مدرج هدفمند پیزوالکتریک براساس نظریه الاستیسیته دوبعدی

[1]                 Li Y S ., Feng W J and Cai Z Y., Bending and free vibration of functionally graded piezoelectric beam based on modified strain gradient theory. Composite Structures, Vol 115, pp. 41- 50, 2014.

[2]                 Lezgy-Nazargaha M., Vidal P and Polit O., An efficient finite element model for static and dynamic analyses of functionally graded piezoelectric beams. Composite Structures, Vol 104, pp. 71- 84, 2013.

[3]                 Kruusing A., Analytical and Optimization of Loaded Cantilever Beam Microactuators. Smart Materials and Structures, Vol 9, pp. 186- 196, 2000.

[4]                 Hauke T., Kouvatov A., Steinhausen R., Seifert W and Beige. Bending Behavior of Functionally Gradient Materials. Ferroelectrics, Vol 238, pp.195- 202, 2000.

[5]                 Lee H J., Layerwise Laminate Analysis of Functionally Graded Piezoelectric Bimorph Beams. Journal of Intelligent Material Systems and Structures, Vol 16, pp. 365- 371, 2005.

[6]                 Hsu M H., Electromechanical Analysis of Piezoelectric Laminated Composite Beams. Journal of Marine Science Technology, Vol 13, pp 148- 155, 2005.

[7]                 Liu T T and Shi Z F., Bending Behavior of Functionally Gradient Piezoelectric Cantilever. Ferroelectrics, Vol 308, pp. 43- 51, 2004.

[8]                 Shi Z F, Bending Behavior of Piezoelectric Curved Actulator. Smart Materials and Structures, Vol 14, pp. 835- 842, 2005.

[9]                 Xiang H J and Shi Z F., Static Analysis for Functionally Graded Piezoelectric Actuators or Sensors under a Combined Electro-thermal Load. European Journal of Mechanics - A/Solids, Vol 28, pp. 338 -346, 2009.

[10]             Huang D J., Ding H J and Chen W Q., Static Analysis of Anisotropic Functionally Graded Magneto-Electro-Elastic Beams Subjected to Arbitrary Loading. European Journal of Mechanics - A/Solids, Vol 29, pp. 356- 369, 2010.

[11]             Doroushi A., Eslami M. R and Komeili A., Vibration analysis and transient response of an FGPM beam under thermo-electro-mechanical loads using higher-order shear deformation theory. J Intell Mater Syst Struct, Vol 22, p231–43, 2011.

[12]             Komijani M, Reddy J. N, Eslami M. R., Nonlinear analysis of microstructure-dependent functionally graded piezoelectric material actuators. Journal of the Mechanics and Physics of Solids, Vol 63, pp. 214- 227, 2014.

[13]             S.Abrate., Impact on composite structures. Cambridge university press, USA, 1998.

[14]             Reddy J. N., An Introduction to the Finite Element Method. McGraw-Hill Education, USA, 2006.

[15]             Alshorbagy Amal E., Eltaher M A and Mahmoud F F., Free vibration characteristics of a functionally graded beam by finite element method. Applied Mathematical Modelling, Vol 35, pp. 412- 425, 2011.

[16]              Yang J and Xiang H J., Thermo-electro-mechanical characteristics of functionally graded piezoelectric actuators. Smart Materials and Structures, Vol 16, pp. 784- 797, 2007.

[17]             Komeili A., Akbarzadeh A H and Doroushi A., and Eslami M. R. Static Analysis of Functionally Graded Piezoelectric Beams under Thermo-Electro-Mechanical Loads. Advances in Mechanical Engineering, 2011.

[18]             Li Yang., shi zhifei. Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature. Composite Structures, Vol 87, pp.257- 264, 2009.

[19]             Rahmani O., Pedram O. Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory. International Journal of Engineering Science, Vol 77, pp.55- 70, 2014.

[20]             Y.S. Li., Pan E. Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory. International Journal of Engineering Science, Vol 97, pp.40- 59, 2015.

Lin C., Muliana A. Nonlinear Electro-mechanical Responses of Functionally Graded Piezoelectric
Beams. Composites: Part B, 2015.