Free Vibration Analysis of Functionally Graded Piezoelectric Material Beam by a Modified Mesh Free Method

Journal of Solid Mechanics

مقاله 10، دوره 11، شماره 1، خرداد 2019، صفحه 144-154   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/jsm.2019.664225

نویسندگان

M Foroutan^* ؛ Sh Sharafi؛ S Mohammadi

Department of Mechanical Engineering, Razi University, Kermanshah, Iran

چکیده

A mesh-free method based on moving least squares approximation (MLS)  and weak form of governing equations including two dimensional equations of motion and Maxwell’s equation is used to analyze the free vibration of functionally graded piezoelectric material (FGPM) beams. Material properties in beam are determined using a power law distribution. Essential boundary conditions are imposed by the transformation method. The mesh-free method is verified by comparison with a finite element method (FEM) which performed for FGPM beams. Comparisons showed that this model has a good accuracy. After validation of the presented model, a parametric study was carried out to investigate the effect of mechanical and electrical boundary conditions, slenderness ratio and distribution of constituent materials on natural frequencies of FGPM beams. It is concluded that slenderness   ratio has more significant effect on lower frequencies. On the other hand higher frequencies are affected by the volume fraction power index much more than lower frequencies.

کلیدواژه‌ها

Mesh-free method؛ Functionally graded piezoelectric beam؛ Free vibration؛ MLS shape function

مراجع

[1] Sharma P., Parashar S.K., 2016, Free vibration analysis of shear-induced flexural vibration of FGPM annular plate using Generalized Differential Quadrature method, Composite Structures 155: 213-222.
[2] Kruusing A., 2000, Analysis and optimization of loaded cantilever beam microactuators, Smart Materials and Structures 9(2): 186.
[3] Hauke T., 2000, Bending behavior of functionally gradient materials, Ferroelectrics 238(1): 195-202.
[4] Huang D., Ding H., Chen W., 2010, Static analysis of anisotropic functionally graded magneto-electro-elastic beams subjected to arbitrary loading, European Journal of Mechanics-A/Solids 29(3): 356-369.
[5] Li Y., Feng W., Cai Z., 2014, Bending and free vibration of functionally graded piezoelectric beam based on modified strain gradient theory, Composite Structures 115: 41-50.
[6] Wu C.-P., Syu Y.-S., 2007, Exact solutions of functionally graded piezoelectric shells under cylindrical bending, International Journal of Solids and Structures 44(20): 6450-6472.
[7] Li X.-F., Peng X.-L., Lee K.Y., 2010, The static response of functionally graded radially polarized piezoelectric spherical shells as sensors and actuators, Smart Materials and Structures 19(3): 035010.
[8] Hsu M.-H., 2005, Electromechanical analysis of piezoelectric laminated composite beams, Journal of Marine Science and Technology 13(2): 148-155.
[9] Razavi H., Babadi A.F., Beni Y.T., 2017, Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory, Composite Structures 160: 1299-1309.
[10] Zhang T., Shi Z., Spencer Jr B., 2008, Vibration analysis of a functionally graded piezoelectric cylindrical actuator, Smart Materials and Structures 17(2): 025018.
[11] Xiang H., Shi Z., 2009, Static analysis for functionally graded piezoelectric actuators or sensors under a combined electro-thermal load, European Journal of Mechanics-A/Solids 28(2): 338-346.
[12] Doroushi A., Eslami M., 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.
[13] Behjat B., Khoshravan M., 2012, Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates, Composite Structures 94(3): 874-882.
[14] Sedighi M., Shakeri M., 2009, A three-dimensional elasticity solution of functionally graded piezoelectric cylindrical panels, Smart Materials and Structures 18(5): 055015.
[15] Behjat B., 2009, Static, dynamic, and free vibration analysis of functionally graded piezoelectric panels using finite element method, Journal of Intelligent Material Systems and Structures 20(13): 1635-1646.
[16] Babaei M., Chen Z., 2009, The transient coupled thermo-piezoelectric response of a functionally graded piezoelectric hollow cylinder to dynamic loadings, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences.
[17] Liu G., Gu Y., 2005, An Introduction to Meshfree Methods and Their Programming, Springer, Dordrecht, Netherlands.
[18] Nayroles B., Touzot G., Villon P., 1992, Generalizing the finite element method: diffuse approximation and diffuse elements, Computational Mechanics 10(5): 307-318.
[19] Chuaqui T., Roque C., 2017, Analysis of functionally graded piezoelectric timoshenko smart beams using a multiquadric radial basis function method, Composite Structures 176: 640-653.
[20] Safaei B., Moradi-Dastjerdi R., Chu F., 2018, Effect of thermal gradient load on thermo-elastic vibrational behavior of sandwich plates reinforced by carbon nanotube agglomerations, Composite Structures 192: 28-37.
[21] Moradi-Dastjerdi R., Pourasghar A., 20216, Dynamic analysis of functionally graded nanocomposite cylinders reinforced by wavy carbon nanotube under an impact load, Journal of Vibration and Control 22(4): 1075-1062.
[22] Moradi-Dastjerdi R., Payganeh G., 2017, Thermoelastic dynamic analysis of wavy carbon nanotube reinforced cylinders under thermal loads, Steel and Composite Structures 25(3): 315-326.
[23] Reddy J., Chin C., 1998, Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses 21(6): 593-626.