Wave Propagation in Embedded Temperature-dependent Functionally Graded Nano-plates Subjected to Nonlinear Thermal Loading According to a Nonlocal Four-variable Plate Theory

Document Type : Research Article

Authors

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

Abstract

In this article, an analytical approach is used to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded nano-plate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nano-plate are graded using Mori-Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by means of Hamilton’s principle. Obtained frequencies are validated with those of previously published works. Moreover, effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter and gradient index on the wave propagation response of size-dependent functionally graded nano-plates have been investigated.

Keywords

Main Subjects

References

[1] V. Birman, L.W. Byrd, Modeling and analysis of functionally graded materials and structures, Applied mechanics reviews, 60(5) (2007) 195-216.
[2] N. Zhao, P.Y. Qiu, L.L. Cao, Development and application of functionally graded material, in: Advanced Materials Research, Trans Tech Publ, 2012, pp. 371-375.
[3] M. Shariyat, D. Asgari, M. AZADI, Nonlinear Transient Thermoelastic Analysis of a Thick FGM Cylinder with Temperature-Dependent Material Properties Using the Finite Element Method, (2010).
[4] A. Nosier, A. Ghaheri, Nonlinear forced vibrations of thin circular functionally graded plates, (2015).
[5] F. Ebrahimi, Effect of functionally graded microstructure on dynamic stability of piezoelectric circular plates, (2015).
[6] A. Moosaie, K.H. PANAHI, Exact solution of steady nonlinear heat conduction in exponentially graded cylindrical and spherical shells with temperature-dependent properties, (2016).
[7] N. Cheraghi, M. Lazgy Nazargah, An exact bending solution for functionally graded magneto-electro-elastic plates resting on elastic foundations with considering interfacial imperfections, Modares Mechanical Engineering, 15(12) (2016) 346-356.
[8] S. Iijima, Helical microtubules of graphitic carbon, nature, 354(6348) (1991) 56.
[9] Y. Zhang, G. Liu, J. Wang, Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression, Physical review B, 70(20) (2004) 205430.
[10] Q. Wang, Wave propagation in carbon nanotubes via nonlocal continuum mechanics, Journal of Applied physics, 98(12) (2005) 124301.
[11] Q. Wang, V. Varadan, Vibration of carbon nanotubes studied using nonlocal continuum mechanics, Smart Materials and Structures, 15(2) (2006) 659.
[12] A.C. Eringen, Linear theory of nonlocal elasticity and dispersion of plane waves, International Journal of Engineering Science, 10(5) (1972) 425-435.
[13] A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of applied physics, 54(9) (1983) 4703-4710.
[14] F. Yang, A. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39(10) (2002) 2731-2743.
[15] J. Reddy, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science, 45(2-8) (2007) 288-307.
[16] S. Pradhan, J. Phadikar, Nonlocal elasticity theory for vibration of nanoplates, Journal of Sound and Vibration, 325(1-2) (2009) 206-223.
[17] M. Aydogdu, A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration, Physica E: Low-dimensional Systems and Nanostructures, 41(9) (2009) 1651-1655.
[18] T. Murmu, S. Adhikari, Nonlocal transverse vibration of double-nanobeam-systems, Journal of Applied Physics, 108(8) (2010) 083514.
[19] C.W. Lim, C. Li, J.-L. Yu, Dynamic behaviour of axially moving nanobeams based on nonlocal elasticity approach, Acta Mechanica Sinica, 26(5) (2010) 755-765.
[20] L.-L. Ke, Y.-S. Wang, J. Yang, S. Kitipornchai, Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory, Acta Mechanica Sinica, 30(4) (2014) 516-525.
[21] Y.-Z. Wang, F.-M. Li, K. Kishimoto, Scale effects on flexural wave propagation in nanoplate embedded in elastic matrix with initial stress, Applied Physics A, 99(4) (2010) 907-911.
[22] Y.-Z. Wang, F.-M. Li, K. Kishimoto, Scale effects on the longitudinal wave propagation in nanoplates, Physica E: Low-dimensional Systems and Nanostructures, 42(5) (2010) 1356-1360.
[23] S. Narendar, S. Gopalakrishnan, Temperature effects on wave propagation in nanoplates, Composites Part B: Engineering, 43(3) (2012) 1275-1281.
[24] L. Zhang, J. Liu, X. Fang, G. Nie, Effects of surface piezoelectricity and nonlocal scale on wave propagation in piezoelectric nanoplates, European Journal of Mechanics-A/Solids, 46 (2014) 22-29.
[25] L. Zhang, J. Liu, X. Fang, G. Nie, Surface effect on size-dependent wave propagation in nanoplates via nonlocal elasticity, Philosophical Magazine, 94(18) (2014) 2009-2020.
[26] J. Zang, B. Fang, Y.-W. Zhang, T.-Z. Yang, D.-H. Li, Longitudinal wave propagation in a piezoelectricnanoplate considering surface effects and nonlocal elasticity theory, Physica E: Low-dimensional Systems and Nanostructures, 63 (2014) 147-150.
[27] G. Varzandian, S. Ziaei, Analytical Solution of Non-Linear Free Vibration of Thin Rectangular Plates with Various Boundary Conditions Based on Non-Local nanoplate considering surface effects and nonlocal elasticity theory, Physica E: Low-dimensional Systems and Nanostructures, 63 (2014) 147-150.
[27] G. Varzandian, S. Ziaei, Analytical Solution of Non-Linear Free Vibration of Thin Rectangular Plates with Various Boundary Conditions Based on Non-Local Theory, Mechanical Engineering, 48(4) (2017).
[28] A. Kaghazian, H.R. Foruzande, A. Hajnayeb, H. Mohammad Sedighi, nonlinear free vibrations analysis of a piezoelectric bimorph nanoactuator using nonlocal elasticity theory, Modares Mechanical Engineering, 16(4) (2016) 55-66.
[29] R. Nazemnezhad, K. Kamali, Investigation of the inertia of the lateral motions effect on free axial vibration of nanorods using nonlocal Rayleigh theory, Modares Mechanical Engineering, 16(5) (2016) 19-28.
[30] Z. Su, L. Ye, Y. Lu, Guided Lamb waves for identification of damage in composite structures: A review, Journal of sound and vibration, 295(3-5) (2006) 753-780.
[31] R.F. Bunshah, J.M. Blocher, Deposition technologies for films and coatings: developments and applications, Noyes Data, 1982.
[32] P. Patel, D. Almond, Thermal wave testing of plasma-sprayed coatings and a comparison of the effects of coating microstructure on the propagation of thermal and ultrasonic waves, Journal of Materials science, 20(3) (1985) 955-966.
[33] S. Natarajan, S. Chakraborty, M. Thangavel, S. Bordas, T. Rabczuk, Size-dependent free flexural vibration behavior of functionally graded nanoplates, Computational Materials Science, 65 (2012) 74-80.
[34] F. Ebrahimi, E. Salari, Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments, Composite Structures, 128 (2015) 363-380.
[35] F. Ebrahimi, E. Salari, S.A.H. Hosseini, Thermomechanical vibration behavior of FG nanobeams subjected to linear and non-linear temperature distributions, Journal of Thermal Stresses, 38(12) (2015) 1360-1386.
[36] R. Ansari, M. Ashrafi, T. Pourashraf, S. Sahmani, Vibration and buckling characteristics of functionally graded nanoplates subjected to thermal loading based on surface elasticity theory, Acta Astronautica, 109 (2015) 42-51.
[37] I. Belkorissat, M.S.A. Houari, A. Tounsi, E. Bedia, S. Mahmoud, On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model, Steel Compos. Struct, 18(4) (2015) 1063-1081.
[38] M.R. Nami, M. Janghorban, M. Damadam, Thermal buckling analysis of functionally graded rectangular nanoplates based on nonlocal third-order shear deformation theory, Aerospace Science and Technology, 41 (2015) 7-15.
[39] H.-T. Thai, D.-H. Choi, A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation, Composites Part B: Engineering, 43(5) (2012) 2335-2347.
[40] H.-T. Thai, T. Park, D.-H. Choi, An efficient shear deformation theory for vibration of functionally graded plates, Archive of Applied Mechanics, 83(1) (2013) 137-149.
[41] F. Kaviani, H. Mirdamadi, Static Analysis of Bending, Stability, and Dynamic Analysis of Functionally Graded Plates by a Four-Variable Theory.
[42] S.A. Yahia, H.A. Atmane, M.S.A. Houari, A. Tounsi, Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories, Structural Engineering and Mechanics, 53(6) (2015) 1143-1165.
[43] A. Ghorbanpour Arani, M. Jamali, A. Ghorbanpour-Arani, R. Kolahchi, M. Mosayyebi, Electro-magneto wave propagation analysis of viscoelastic sandwich nanoplates considering surface effects, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231(2) (2017) 387-403.
[44] M.R. Barati, A.M. Zenkour, H. Shahverdi, Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory, Composite Structures, 141 (2016) 203-212.
[45] Y.-W. Zhang, J. Chen, W. Zeng, Y.-Y. Teng, B. Fang, J. Zang, Surface and thermal effects of the flexural wave propagation of piezoelectric functionally graded nanobeam using nonlocal elasticity, Computational Materials Science, 97 (2015) 222-226.
[46] L. Li, Y. Hu, L. Ling, Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory, Composite Structures, 133 (2015) 1079-1092.
Amirkabir Journal of Mechanical Engineering
Volume 50, Issue 5
January and February 2019
Pages 973-988

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