Investigating the Influence of Higher-Order Boundary Conditions on Free Vibrations of Bi-Directional Functionally Graded Thick Conical Micro-Shells

Document Type : Research Article

Authors

Department of Mechanical Engineering, Hakim Sabzevari University

Abstract

The present paper investigates the influence of higher-order boundary conditions caused by accounting for the small scales effect on free vibrations of bi-directional functionally graded thick conical micro-shells. The present model accounts for the gradation of the material length scale parameter as one of the micro-shell mechanical properties along with its thickness as well as its axial axis. The modified couple stress as well as the first-order shear deformable love shell theories together with the Ritz method are employed to obtain the eigenvalue eigenvector equations governing the free vibrations of the microstructure. These equations are solved for some different types of boundary conditions. The present findings are compared and successfully validated by the available results in the literature. The influences of small scales, higher-order boundary conditions, and power-law distribution indices in both the transversal and axial directions on free vibrations of conical micro-shells are then investigated. The results reveal that higher-order boundary conditions play a crucial role in the dynamics of conical micro-shells especially when these boundary conditions directly affect the eigenmodes which are dominant in the dynamics of the structure. In addition, it is observed that although the dynamics of the present conical micro-shell is affected by the power-law distribution indices in both the transversal and axial directions, it is more sensitive to the transversal one.

Keywords

Main Subjects

References

[1] J. Awrejcewicz, A.V. Krysko, M.V. Zhigalov, V.A. Krysko, Size-Dependent Theories of Beams, Plates and Shells, in: J. Awrejcewicz, A.V. Krysko, M.V. Zhigalov, V.A. Krysko (Eds.) Mathematical Modelling and Numerical Analysis of Size-Dependent Structural Members in Temperature Fields: Regular and Chaotic Dynamics of Micro/Nano Beams, and Cylindrical Panels, Springer International Publishing, Cham, 2021, pp. 25-78.
[2] F. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct., 39 (2002) 2731-2743.
[3] Z. Li, Y. He, J. Lei, S. Guo, D. Liu, L. Wang, A standard experimental method for determining the material length scale based on modified couple stress theory, Int. J. Mech. Sci., 141 (2018) 198-205.
[4] A.R. Askari, M. Tahani, Presenting a size-dependent electro-mechanical model for rectangular plates-based resonant micro-sensors based on modified couple stress theory, J. Modares Mechanical Engineering, 14(8) (2014) 121-130. (In persian)
[5] A. Bakhsheshy, K. Khorshidi, Free vibration of functionally graded rectangular nanoplates in thermal environment based on the modified couple stress theory, J. Modares Mechanical Engineering, 14(15) (2015) 323-330. (In persian)
[6] S.J.-T. OmidDezyani, R., M. Abedi, H. Afrasiab, Vibration analysis of a microplate in contact with a fluid based on the modified couple stress theory, J. Modares Mechanical Engineering, 17(2) (2017) 47-57. (In persian)
[7] s. salehi, O. Rahmani, S.A. Hoseini, Free and forced vibration analysis of Kelvin-Voigt viscoelastic rectangular nanoplate based on the modified couple stress theory, Amirkabir Journal of Mechanical Engineering, 52(1) (2020) 173-186. (In persian)
[8] H. Zeighampour, Y.T. Beni, A shear deformable cylindrical shell model based on couple stress theory, Arch. Appl. Mech., 85(4) (2015) 539-553.
[9] Y. Tadi Beni, F. Mehralian, H. Zeighampour, The modified couple stress functionally graded cylindrical thin shell formulation, Mech. Adv. Mater. Struc., 23(7) (2016) 791-801.
[10] K.S. Al-Basyouni, A. Tounsi, S.R. Mahmoud, Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position, Compos. Struct., 125 (2015) 621-630.
[11] M. Tahani, R.C. Batra, A.R. Askari, Size-dependent free vibrations of electrostatically predeformed functionally graded micro-cantilevers, IOP Conference Series: Materials Science and Engineering, 87(1) (2015) 012117.
[12] Y. Tadi Beni, F. Mehralian, H. Razavi, Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory, Compos. Struct., 120 (2015) 65-78.
[13] H. Zeighampour, M. Shojaeian, Size-dependent vibration of sandwich cylindrical nanoshells with functionally graded material based on the couple stress theory, J. Braz. Soc. Mech. Sci., 39(7) (2017) 2789-2800.
[14] M. Ghadiri, H. SafarPour, Free vibration analysis of size-dependent functionally graded porous cylindrical microshells in thermal environment, J. Therm. Stresses, 40(1) (2017) 55-71.
[15] M. Ghadiri, H. Safarpour, Free Vibration Analysis of a Functionally Graded Cylindrical Nanoshell Surrounded by Elastic Foundation Based on the Modified Couple Stress Theory, Amirkabir Journal of Mechanical Engineering, 49(4) (2018) 721-730. (In persian)
[16] H. Razavi, A.F. Babadi, Y. Tadi Beni, Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory, compos. Struct., 160 (2017) 1299-1309.
[17] S. Zeng, B.L. Wang, K.F. Wang, Analyses of natural frequency and electromechanical behavior of flexoelectric cylindrical nanoshells under modified couple stress theory, J. Vib. Control, 25(3) (2018) 559-570.
[18] Y. Wang, K. Xie, T. Fu, W. Zhang, A unified modified couple stress model for size-dependent free vibrations of FG cylindrical microshells based on high-order shear deformation theory, Eur. Phys. J. Plus, 135(1) (2020) 71.
[19] J. Ehyaei, H. Safarpour, E. Shahabinejad, Vibration analysis of a double layer microshell utilizing a modified couple stress theory, Iranian Journal of Mechanical Engineering Transactions of the ISME, 21(1) (2020) 21-44.
[20] S.-S. Yu, W.-T. Zheng, Effect of N/B doping on the electronic and field emission properties for carbon nanotubes, carbon nanocones, and graphene nanoribbons, Nanoscale, 2(7) (2010) 1069-1082.
[21] R. Majidi, K.G. Tabrizi, Study of neon adsorption on carbon nanocones using molecular dynamics simulation, Physica B: Condensed Matter, 405(8) (2010) 2144-2148.
[22] Y.-G. Hu, K.M. Liew, X. He, Z. Li, J. Han, Free transverse vibration of single-walled carbon nanocones, Carbon, 50(12) (2012) 4418-4423.
[23] J. Yan, K.M. Liew, L. He, Ultra-sensitive analysis of a cantilevered single-walled carbon nanocone-based mass detector, Nanotechnology, 24(12) (2013) 125703.
[24] W.-J. Chang, T.-H. Fang, H.-L. Lee, Y.-C. Yang, Vibration sensitivity of the scanning near-field optical microscope with a tapered optical fiber probe, Ultramicroscopy, 102(2) (2005) 85-92.
[25] I.-C. Chen, L.-H. Chen, X.-R. Ye, C. Daraio, S. Jin, C.A. Orme, A. Quist, R. Lal, Extremely sharp carbon nanocone probes for atomic force microscopy imaging, Applied Physics Letters, 88(15) (2006) 153102.
[26] Q. Fan, Z. Wang, Y. Cui, Optimal design of an antireflection coating structure for enhancing the energy-conversion efficiency of a silicon nanostructure solar cell, RSC advances, 8(61) (2018) 34793-34807.
[27] M. Toma, A. Belu, D. Mayer, A. Offenhäusser, Flexible gold nanocone array surfaces as a tool for regulating neuronal behavior, Small, 13(24) (2017) 1700629.
[28] L. Qian, R. Batra, Design of bidirectional functionally graded plate for optimal natural frequencies, Journal of Sound and Vibration, 280(1-2) (2005) 415-424.
[29] B. Saleh, J. Jiang, R. Fathi, T. Al-hababi, Q. Xu, L. Wang, D. Song, A. Ma, 30 Years of functionally graded materials: An overview of manufacturing methods, Applications and Future Challenges, Composites Part B: Engineering,  (2020) 108376.
[30] H. Zeighampour, Y. Tadi Beni, Analysis of conical shells in the framework of coupled stresses theory, Int. J. Eng. Sci., 81 (2014) 107-122.
[31] H. Zeighampour, Y.T. Beni, F. Mehralian, A shear deformable conical shell formulation in the framework of couple stress theory, Acta Mech., 226(8) (2015) 2607-2629.
[32]   Y. Tadi Beni, F. Mehralian, The effect of small scale on the free vibration of functionally graded truncated conical shells, J. Mech. Mater. Struct., 11(2) (2016) 91-112.
[33]   Y. Yuan, K. Zhao, Y. Han, S. Sahmani, B. Safaei, Nonlinear oscillations of composite conical microshells with in-plane heterogeneity based upon a couple stress-based shell model, Thin-Walled Structures, 154 (2020) 106857.
[34]   H. Yaghoobi, A. Fereidoon, R. Shahsiah, Thermal Buckling of Axially Functionally Graded Thin Cylindrical Shell, J. Therm. Stresses, 34(12) (2011) 1250-1270.
[35]   J.N. Reddy, Theory and Analysis of Elastic Plates and Shells, 2nd ed., Taylor & Francis, Philadelphia, 2007.
[36]   J.N. Reddy, Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons, New York, 2002.
[37]   K. Lam, L. Hua, Influence of boundary conditions on the frequency characteristics of a rotating truncated circular conical shell, Journal of Sound and Vibration, 223(2) (1999) 171-195.
[38]   T. Irie, G. Yamada, K. Tanaka, Natural frequencies of truncated conical shells, Journal of Sound and Vibration, 92(3) (1984) 447-453.
[39]   F.-M. Li, K. Kishimoto, W.-H. Huang, The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh–Ritz method, Mechanics Research Communications, 36(5) (2009) 595-602.
[40]   M. Rahaeifard, M.H. Kahrobaiyan, M. Asghari, M.T. Ahmadian, Static pull-in analysis of microcantilevers based on the modified couple stress theory, Sensor Actuat. A-Phys. , 171 (2011) 370-374.
Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 10
January 2022
Pages 5085-5104

Files

Share

How to cite

Statistics