Abstract
Transverse vibrations of a double-layered viscoelastic orthotropic graphene sheet system are investigated. The two sheets in the system are coupled by the visco-Pasternak medium. General governing equations for free and forced vibrations of the double-layered graphene sheet system with a high-order surface stress effect are formulated. Theoretical solutions for the damped vibrational frequency, damping ratio, and relative deflection of the two sheets with simply supported boundary conditions are obtained. The effects of the high-order surface stress on the damped frequency and damping ratio of the system for in-phase and out-of-phase free vibrations are discussed. The impacts of the high-order surface stress, structural damping, medium damping, Winkler modulus, and shear modulus of the medium on the relative deflection of the two sheets for forced vibrations are investigated. It is demonstrated that the high-order surface stress effects on the vibrational properties of the system are more significant than those of the conventional surface stress.
Similar content being viewed by others
REFERENCES
T. Natsuki, J. X. Shi, and Q. Q. Ni, “Vibration Analysis of Circular Double-Layered Graphene Sheets," J. Appl. Phys.111 (4), 044310 ( 2012).
S. A. H. Kordkheili and H. Moshrefzadeh-Sani, “Mechanical Properties of Double-Layered Graphene Sheets," Comput. Mater. Sci. 69, 335–343 (2013).
J. X. Shi, Q. Q. Ni, X. W. Lei, and T. Natsuki, “Study on Wave Propagation Characteristics of Double-Layer Graphene Sheets via Nonlocal Mindlin–Reissner Plate Theory. 1," J. Mech. Sci.84, 25–30 (2014).
N. Radic and D. Jeremic, “A Comprehensive Study on Vibration and Buckling of Orthotropic Double-Layered Graphene Sheets under Hygrothermal Loading with Different Boundary Conditions," Composites. Pt B: Eng. 128, 182–199 (2017).
Y. J. Su, H. Wei, R. G. Gao, et al., “Exceptional Negative Thermal Expansion and Viscoelastic Properties of Graphene Oxide Paper," Carbon 50 (8), 2804–2809 (2012).
S. H. Hashemi, H. Mehrabani, and A. Ahmadi-Savadkoohi, “Exact Solution for Free Vibration of Coupled double Viscoelastic Graphene Sheets by Visco-Pasternak Medium," Composites. Pt B: Eng.78, 377–383 (2015).
M. Hosseini, A. Jamalpoor, and M. Bahreman, “Small-Scale Effects on the Free Vibrational Behavior of Embedded Viscoelastic Double-Nanoplate-Systems under Thermal Environment," Acta Astronaut. 129, 400–409 (2016).
J. C. Liu, Y. Q. Zhang, and L. F. Fan, “Nonlocal Vibration and Biaxial Buckling of Double-Viscoelastic-FGM-Nanoplate System with Viscoelastic Pasternak Medium in Between," Phys. Lett. A381 (14), 1228–1235 (2017).
M. H. Jalaei and A. G. Arani, “Analytical Solution for Static and Dynamic Analysis of Magnetically Affected Viscoelastic Orthotropic Double-Layered Graphene Sheets Resting on Viscoelastic Foundation," Phys. B 530, 222–235 (2018).
M. Hosseini and A. Jamalpoor, “Analytical Solution for Thermomechanical Vibration of Double-Viscoelastic Nanoplate-Systems Made of Functionally Graded Materials," J. Thermal Stress.38 (12), 1428–1456 ( 2015).
A. Ghorbanpour-Arani and M. Shokravi, “Vibration Response of Visco-Elastically Coupled Double-Layered Visco-Elastic Graphene Sheet Systems Subjected to Magnetic Field via Strain Gradient Theory Considering Surface Stress Effects," Proc. Inst. Mech. Eng. Pt N: J. Nanoeng. Nanosyst. 229 (4), 180–190 (2014).
E. Allahyari and M. Fadaee, “Analytical Investigation on Free Vibration of Circular Double-Layer Graphene Sheets Including Geometrical Defect and Surface Effects," Composites. Pt B: Eng.85, 259–267 (2016).
F. Ebrahimi and S. H. S. Hosseini, “Surface Effects on Nonlinear Dynamics of NEMS Consisting of Double-Layered Viscoelastic Nanoplates," Europ. Phys. J. Plus 132, 172 (2017).
F. Liu, P. Rugheimer, E. Mateeva, et al., “Nanomechanics: Response of a Strained Semiconductor Structure," Nature 416, 498 (2002).
M. S. Chiu and T. Chen, “Effects of High-Order Surface Stress on Static Bending Behavior of Nanowires," Phys. E 44(3), 714–718 (2011).
M. Pang, Z. L. Li, and Y. Q. Zhang, “Size-Dependent Transverse Vibration of Viscoelastic Nanoplates Including High-Order Surface Stress Effect," Phys. B 545, 94–98 (2018).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 62, No. 1, pp. 147–158.https://doi.org/10.15372/PMTF20210116.
Rights and permissions
About this article
Cite this article
Pang, M., Fang, Y. & Zhang, Y.Q. FREE AND FORCED VIBRATIONS OF DOUBLE-LAYERED VISCOELASTIC ORTHOTROPIC GRAPHENE SHEETS WITH A HIGH-ORDER SURFACE STRESS EFFECT. J Appl Mech Tech Phy 62, 129–138 (2021). https://doi.org/10.1134/S0021894421010168
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894421010168