Document Type : Original Article

Authors

1 Department of Aerospace Engineering, Shahid Sattari Aeronautical University of Science and Technology, Tehran , Iran

2 Aerospace Faculty, Shahid Sattry Aeronautical University of Science and Technology

3 Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran

Abstract

In this paper, nonlinear vibration analysis of functionally graded piezoelectric (FGP) beam with porosities material is investigated based on the Timoshenko beam theory. Material properties of FG porous beam are described according to the rule of mixture which modified to approximate material properties with porosity phases. The Ritz method is used to obtain the governing equation which is then solved by a direct iterative method to determine the nonlinear vibration frequencies of FGP porous beam subjected to different boundary conditions. The effects of external electric voltage, material distribution profile, porosity volume fraction, slenderness ratios and boundary conditions on the nonlinear vibration characteristics of the FGP porous beam are discussed in detail. The results indicate that piezoelectric layers have significant effect on the nonlinear frequencies. Also it is found that the porosity has a considerable influence on the nonlinear frequency and these effects increased especially when the electric voltage is applied.

Keywords

Main Subjects

[1]   Koizumi M (1997) FGM activities in Japan. Composites Part B: Engineering 28 (1):1-4
[2]   Ebrahimi F (2013) Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment. Mechanics of Advanced Materials and Structures 20 (10):854-870
[3]   El-wazery M, El-Desouky A (2015) A review on functionally graded ceramic-metal materials. J Mater Environ Sci 6 (5):1369-1376.
[4]   Chmielewski M, Pietrzak K (2016) Metal-ceramic functionally graded materials–manufacturing, characterization, application. Bulletin of the Polish Academy of Sciences Technical Sciences 64 (1):151-160.
[5]   Kitipornchai S, Ke L, Yang J, Xiang Y (2009) Nonlinear vibration of edge cracked functionally graded Timoshenko beams. Journal of sound and vibration 324 (3):962-982
[6]   Ke L-L, Yang J, Kitipornchai S (2010) Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams. Composite Structures 92 (3):676-683
[7]   Akgöz B, Civalek Ö (2013) Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM). Composites Part B: Engineering 55:263-268
[8]   Pradhan K, Chakraverty S (2013) Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh–Ritz method. Composites Part B: Engineering 51:175-184
[9]   Ansari R, Gholami R, Sahmani S (2013) Size-dependent vibration of functionally graded curved microbeams based on the modified strain gradient elasticity theory. Archive of Applied Mechanics 83 (10)
[10]   Mashat DS, Carrera E, Zenkour AM, Al Khateeb SA, Filippi M (2014) Free vibration of FGM layered beams by various theories and finite elements. Composites Part B: Engineering 59:269-278
[11]   Hadji L, Daouadji T, Tounsi A, Bedia E (2014) A higher order shear deformation theory for static and free vibration of FGM beam. Steel and Composite Structures 16 (5):507-519
[12]   Sofiyev A (2015) On the vibration and stability of shear deformable FGM truncated conical shells subjected to an axial load. Composites Part B: Engineering 80:53-62
[13]   Chen, Y., Jin, G., Zhang, C., Ye, T., & Xue, Y (2018) Thermal vibration of FGM beams with general boundary conditions using a higher-order shear deformation theory Composites Part B: Engineering 153:376-386.
[14]   Zhang, K., Ge, M. H., Zhao, C., Deng, Z. C., & Xu, X. J (2019) Free vibration of nonlocal Timoshenko beams made of functionally graded materials by Symplectic method Composites Part B: Engineering 156:174-184.
[15]   Wattanasakulpong N, Ungbhakorn V (2014) Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerospace Science and Technology 32 (1):111-120
[16]   Ebrahimi F, Zia M (2015) Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities. Acta Astronautica 116:117-125
[17]   Chen D, Yang J, Kitipornchai S (2016) Free and forced vibrations of shear deformable functionally graded porous beams. International Journal of Mechanical Sciences 108:14-22
[18]   Shafiei N, Mousavi A, Ghadiri M (2016) On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams. International Journal of Engineering Science 106:42-56
[19]   Ebrahimi F, Ghasemi F, Salari E (2016) Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities. Meccanica 51 (1):223-249
[20]   Taya, M., Almajid, A. A., Dunn, M., & Takahashi, H (2003) Design of bimorph piezo-composite actuators with functionally graded microstructure Sensors and Actuators A: Physical 107(3):248-260.
[21]   She, G. L., Ren, Y. R., Yuan, F. G., & Xiao, W. S (2018) On vibrations of porous nanotubes International Journal of Engineering Science 125:23-35.
[22]   Li Y, Shi Z (2009) Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature. Composite Structures 87 (3):257-264
[23]   Armin A, Behjat B, Abbasi M, Eslami M (2010) Finite element analysis of functionally graded piezoelectric beams. Iran J Mech Eng (English) 11 (1):45-72
[24]   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
[25]   Ke L-L, Wang Y-S (2012) Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory. Smart Materials and Structures 21 (2):025018
[26]   Barati MR, Zenkour AM (2016) Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions. Journal of Vibration and Control:1077546316672788
[27]   Ebrahimi F, Salari E (2016) Thermal loading effects on electro-mechanical vibration behavior of piezoelectrically actuated inhomogeneous size-dependent Timoshenko nanobeams. Advances in Nano Research 4 (3):197-228
[28]   Ebrahimi, F., & Barati, M. R (2018) Vibration analysis of piezoelectrically actuated curved nanosize FG beams via a nonlocal strain-electric field gradient theory Mechanics of Advanced Materials and Structures 25(4):350-359.
[29]   Zhao, X., Iegaink, F. J. N., Zhu, W. D., & Li, Y. H (2019) Coupled thermo-electro-elastic forced vibrations of piezoelectric laminated beams by means of Green's functions International Journal of Mechanical Sciences.
[30]   Shen H-S (2005) Postbuckling of FGM plates with piezoelectric actuators under thermo-electro-mechanical loadings. International Journal of Solids and Structures 42 (23):6101-6121
[31]   Ke L-L, Yang J, Kitipornchai S, Xiang Y (2009) Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials. Mechanics of Advanced Materials and Structures 16 (6):488-502
[32]   Cowper, G. R. (1966) The shear coefficient in Timoshenko’s beam theory. Journal of applied mechanics 33(2):335-340.