Quasi-3D Hyperbolic Shear Deformation Theory for the Free Vibration Study of Honeycomb Microplates with Graphene Nanoplatelets-Reinforced Epoxy Skins
Abstract
:1. Introduction
2. Theoretical Formulation
3. Governing Equations of the Problem
4. Analytical Solution Procedure
5. Numerical Results
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
References
- Maheri, M.R.; Adams, R.D. Steady-state flexural vibration damping of honeycomb sandwich beams. Compos. Sci. Technol. 1994, 52, 333–347. [Google Scholar] [CrossRef]
- Guo, Y.; Zhang, J. Shock Absorbing Characteristics and Vibration Transmissibility of Honeycomb Paperboard. Shock Vib. 2004, 11, 521–531. [Google Scholar] [CrossRef]
- Li, Y.; Jin, Z. Free flexural vibration analysis of symmetric rectangular honeycomb panels with SCSC edge supports. Compos. Struct. 2008, 83, 154–158. [Google Scholar] [CrossRef]
- Liu, J.; Cheng, Y.S.; Li, R.F.; Au, F.T.K. A semi-analytical method for bending, buckling, and free vibration analyses of sandwich panels with square-hoeycomb cores. Int. J. Struct. Stab. Dyn. 2010, 10, 127–151. [Google Scholar] [CrossRef] [Green Version]
- Burlayenko, V.N.; Sadowski, T. Influence of skin/core debonding on free vibration behavior of foam and honeycomb cored sandwich plates. Int. J. Non Linear Mech. 2010, 45, 959–968. [Google Scholar] [CrossRef]
- Katunin, A. Vibration-based spatial damage identification in honeycomb-core sandwich composite structures using wavelet analysis. Compos. Struct. 2014, 118, 385–391. [Google Scholar] [CrossRef]
- Mukhopadhyay, T.; Adhikari, S. Free-Vibration Analysis of Sandwich Panels with Randomly Irregular Honeycomb Core. J. Eng. Mech. 2016, 142, 06016008. [Google Scholar] [CrossRef]
- Duc, N.D.; Seung-Eock, K.; Tuan, N.D.; Tran, P.; Khoa, N.D. New approach to study nonlinear dynamic response and vibration of sandwich composite cylindrical panels with auxetic honeycomb core layer. Aerosp. Sci. Technol. 2017, 70, 396–404. [Google Scholar] [CrossRef]
- Piollet, E.; Fotsing, E.R.; Ross, A.; Michon, G. High damping and nonlinear vibration of sandwich beams with entangled cross-linked fibres as core material. Compos. Part B Eng. 2019, 168, 353–366. [Google Scholar] [CrossRef]
- Kumar, S.; Renji, K. Estimation of strains in composite honeycomb sandwich panels subjected to low frequency diffused acoustic field. J. Sound Vib. 2019, 449, 84–97. [Google Scholar] [CrossRef]
- Sobhy, M. Differential quadrature method for magneto-hygrothermal bending of functionally graded graphene/Al sandwich-curved beams with honeycomb core via a new higher-order theory. J. Sandw. Struct. Mater. 2020. [Google Scholar] [CrossRef]
- Li, Y.; Chen, Z.; Xiao, D.; Wu, W.; Fang, D. The Dynamic response of shallow sandwich arch with auxetic metallic honeycomb core under localized impulsive loading. Int. J. Impact Eng. 2020, 137, 103442. [Google Scholar] [CrossRef]
- Chen, D.; Yang, J.; Kitipornchai, S. Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams. Compos. Sci. Technol. 2017, 142, 235–245. [Google Scholar] [CrossRef] [Green Version]
- Karimiasl, M.; Ebrahimi, F.; Mahesh, V. On Nonlinear Vibration of Sandwiched Polymer- CNT/GPL-Fiber Nanocomposite Nanoshells. Thin-Walled Struct. 2020, 146, 106431. [Google Scholar] [CrossRef]
- Eyvazian, A.; Hamouda, A.M.; Tarlochan, F.; Mohsenizadeh, S.; Dastjerdi, A.A. Damping and vibration response of viscoelastic smart sandwich plate reinforced with non-uniform Graphene platelet with magnetorheological fluid core. Steel Compos. Struct. 2019, 33, 891–906. [Google Scholar]
- Torabi, J.; Ansari, R. Numerical Phase-Field Vibration Analysis of Cracked Functionally Graded GPL-RC Plates. Mech. Based Des. Struct. Mach. 2020, 1–20. [Google Scholar] [CrossRef]
- Khoa, N.D.; Anh, V.M.; Duc, N.D. Nonlinear dynamic response and vibration of functionally graded nanocomposite cylindrical panel reinforced by carbon nanotubes in thermal environment. J. Sandw. Struct. Mater. 2019. [Google Scholar] [CrossRef]
- Ibrahim, H.H.; Tawfik, M.; Al-Ajmi, M. Thermal buckling and nonlinear flutter behavior of functionally graded material panels. J. Aircr. 2007, 44, 1610–1618. [Google Scholar] [CrossRef]
- Li, Y.; Li, F.; He, Y. Geometrically nonlinear forced vibrations of the symmetric rectangular honeycomb sandwich panels with completed clamped supported boundaries. Compos. Struct. 2011, 93, 360–368. [Google Scholar] [CrossRef]
- Mehar, K.; Panda, S.K. Thermal Free Vibration Behavior of FG-CNT Reinforced Sandwich Curved Panel Using Finite Element Method. Polym. Compos. 2017. [Google Scholar] [CrossRef]
- Nguyen, D.D.; Pham, C.H. Nonlinear dynamic response and vibration of sandwich composite plates with negative Poisson’s ratio in auxetic honeycombs. J. Sandw. Struct. Mater. 2017, 20, 692–717. [Google Scholar] [CrossRef]
- Tornabene, F.; Fantuzzi, N.; Bacciocchi, M.; Reddy, J.N. An equivalent layer-wise approach for the free vibration analysis of thick and thin laminated and sandwich shells. Appl. Sci. 2017, 7, 17. [Google Scholar] [CrossRef]
- Tornabene, F.; Fantuzzi, N.; Bacciocchi, M.; Viola, E.; Reddy, J.N. A numerical investigation on the natural frequencies of FGM sandwich shells with variable thickness by the local generalized differential quadrature method. Appl. Sci. 2017, 7, 131. [Google Scholar] [CrossRef] [Green Version]
- Jouneghani, F.Z.; Dimitri, R.; Tornabene, F. Structural response of porous FG nanobeams under hygro-thermo-mechanical loadings. Compos. Part B Eng. 2018, 152, 71–78. [Google Scholar] [CrossRef]
- Tornabene, F.; Brischetto, S. 3D capability of refined GDQ models for the bending analysis of composite and sandwich plates, spherical and doubly-curved shells. Thin Walled Struct. 2018, 129, 94–124. [Google Scholar] [CrossRef]
- Karimiasl, M.; Ebrahimi, F.; Mahesh, V. Nonlinear forced vibration of smart multiscale sandwich composite doubly curved porous shell. Thin Walled Struct. 2019, 143, 106152. [Google Scholar] [CrossRef]
- Nejati, M.; Ghasemi-Ghalebahman, A.; Soltanimaleki, A.; Dimitri, R.; Tornabene, F. Thermal vibration analysis of SMA hybrid composite double curved sandwich panels. Compos. Struct. 2019, 224, 111035. [Google Scholar] [CrossRef]
- Tornabene, F.; Fantuzzi, N.; Bacciocchi, M. Foam core composite sandwich plates and shells with variable stiffness: Effect of the curvilinear fiber path on the modal response. J. Sandw. Struct. Mater. 2019, 21, 320–365. [Google Scholar] [CrossRef]
- Hebali, H.; Tounsi, A.; Houari, A.M.S.; Bessaim, A.; Abbes, E. New Quasi-3D Hyperbolic Shear Deformation Theory for the Static and Free Vibration Analysis of Functionally Graded Plates. J. Eng. Mech. 2014, 140, 374–383. [Google Scholar] [CrossRef]
- Guerroudj, H.Z.; Yeghnem, R.; Kaci, A.; Zaoui, F.Z.; Benyoucef, S.; Tounsi, A. Eigenfrequencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory. Smart Struct. Syst. 2018, 22, 121. [Google Scholar]
- Amir, S.; Arshid, E.; Rasti-alhosseini, S.M.A.; Loghman, A. Quasi-3D tangential shear deformation theory for size-dependent free vibration analysis of three-layered FG porous micro rectangular plate integrated by nano-composite faces in hygrothermal environment. J. Therm. Stresses 2019, 43, 133–156. [Google Scholar] [CrossRef]
- Benahmed, A.; Houari, A.M.S.; Benyoucef, S.; Belakhdar, K.; Tounsi, A. A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation. Geomech. Eng. 2017, 12, 9–34. [Google Scholar] [CrossRef]
- Ebrahimi, F.; Karimiasl, M.; Mahesh, V. Vibration analysis of magneto-flexo-electrically actuated porous rotary nanobeams considering thermal effects via nonlocal strain gradient elasticity theory. Adv. Nano Res. 2019, 7, 223–231. [Google Scholar]
- Torabi, K.; Afshari, H.; Aboutalebi, F.H. Vibration and flutter analyses of cantilever trapezoidal honeycomb sandwich plates. J. Sandw. Struct. Mater. 2019, 21. [Google Scholar] [CrossRef]
- Arshid, E.; Amir, S.; Loghman, A. Static and Dynamic Analyses of FG-GNPs Reinforced Porous Nanocomposite Annular Micro-Plates Based on MSGT. Int. J. Mech. Sci. 2020, 180, 105656. [Google Scholar] [CrossRef]
- Mohammad-Rezaei Bidgoli, E.; Arefi, M. Free vibration analysis of micro plate reinforced with functionally graded graphene nanoplatelets based on modified strain-gradient formulation. J. Sandw. Struct. Mater. 2019. [Google Scholar] [CrossRef]
- Amir, S.; Arshid, E.; Ghorbanpour Arani, M.R. Size-Dependent Magneto-Electro-Elastic Vibration Analysis of FG Saturated Porous Annular/ Circular Micro Sandwich Plates Embedded with Nano-Composite Face sheets Subjected to Multi-Physical Pre Loads. Smart Struct. Syst. 2019, 23, 429–447. [Google Scholar]
- Arshid, E.; Khorshidvand, A.R. Thin-Walled Structures Free vibration analysis of saturated porous FG circular plates integrated with piezoelectric actuators via differential quadrature method. Thin Walled Struct. 2018, 125, 220–233. [Google Scholar] [CrossRef]
- Amir, S.; Soleymani-Javid, Z.; Arshid, E. Size-dependent free vibration of sandwich micro beam with porous core subjected to thermal load based on SSDBT. Appl. Math. Mech. 2019, 99, e201800334. [Google Scholar] [CrossRef]
- Arshid, E.; Khorshidvand, A.R.; Khorsandijou, S.M. The Effect of Porosity on Free Vibration of SPFG Circular Plates Resting on visco-Pasternak Elastic Foundation Based on CPT, FSDT and TSDT. Struct. Eng. Mech. 2019, 70, 97–112. [Google Scholar]
- Kiani, Y.; Dimitri, R.; Tornabene, F. Free vibration of FG-CNT reinforced composite skew cylindrical shells using the Chebyshev-Ritz formulation. Compos. Part B Eng. 2018, 147, 169–177. [Google Scholar] [CrossRef]
- Amir, S.; BabaAkbar-Zarei, H.; Khorasani, M. Flexoelectric vibration analysis of nanocomposite sandwich plates. Mech. Based Des. Struct. Mach. 2020, 48, 146–163. [Google Scholar] [CrossRef]
- Liu, Y.; Liu, W.; Gao, W.; Zhang, L.; Zhang, E. Mechanical responses of a composite sandwich structure with Nomex honeycomb core. J. Reinf. Plast. Compos. 2019, 38, 601–615. [Google Scholar] [CrossRef]
- Lin, H.G.; Cao, D.Q.; Xu, Y.Q. Vibration, Buckling and Aeroelastic Analyses of Functionally Graded Multilayer Graphene-Nanoplatelets-Reinforced Composite Plates Embedded in Piezoelectric Layers. Int. J. Appl. Mech. 2018, 10, 1850023. [Google Scholar] [CrossRef]
- Thai, C.H.; Ferreira, A.J.M.; Tran, T.D.; Phung-Van, P. A size-dependent quasi-3D isogeometric model for functionally graded graphene platelet-reinforced composite microplates based on the modified couple stress theory. Compos. Struct. 2020, 234, 111695. [Google Scholar] [CrossRef]
- Dindarloo, M.H.; Li, L.; Dimitri, R.; Tornabene, F. Nonlocal Elasticity response of Doubly-Curved Nanoshells. Symmetry 2020, 12, 466. [Google Scholar] [CrossRef] [Green Version]
- Karimi, M.; Khorshidi, K.; Dimitri, R.; Tornabene, F. Size-dependent hydroelastic vibration of FG microplates partially in contact with a fluid. Compos. Struct. 2020, 244, 112320. [Google Scholar] [CrossRef]
- Khorasani, M.; Eyvazian, A.; Karbon, M.; Tounsi, A.; Lampani, L.; Sebaey, T.A. Magneto-electro-elastic vibration analysis of modified couple stress-based three-layered micro rectangular plates exposed to multi-physical fields considering the flexoelectricity effects. Smart Struct. Syst. 2020, 26, 331–343. [Google Scholar]
- Arshid, E.; Kiani, A.; Amir, S. Magneto-electro-elastic vibration of moderately thick FG annular plates subjected to multi physical loads in thermal environment using GDQ method by considering neutral surface. Mater. Des. Appl. 2019. [Google Scholar] [CrossRef]
- Amir, S.; Khorasani, M.; BabaAkbar-Zarei, H. Buckling analysis of nanocomposite sandwich plates with piezoelectric face sheets based on flexoelectricity and first-order shear deformation theory. J. Sandw. Struct. Mater. 2020, 22, 2186–2209. [Google Scholar] [CrossRef]
Total GPLs Content (Percentage) | λU | λL | λP |
---|---|---|---|
0 | 0 | 0 | 0 |
1/3 | 1/3 | 2/3 | 1 |
1 | 1 | 2 | 3 |
a/h | lm/h | |||||||
---|---|---|---|---|---|---|---|---|
0.0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 | |||
5 | Epoxy | Present | 0.2145 | 0.2322 | 0.2786 | 0.3319 | 0.4143 | 0.4815 |
Ref. [45] | 0.2148 | 0.2301 | 0.2708 | 0.3271 | 0.3920 | 0.4615 | ||
Uniform | Present | 0.4460 | 0.4820 | 0.5794 | 0.7114 | 0.8622 | 1.0220 | |
Ref. [45] | 0.4468 | 0.4789 | 0.5639 | 0.6813 | 0.8164 | 0.9613 | ||
10 | Epoxy | Present | 0.0586 | 0.0632 | 0.0752 | 0.0918 | 0.1109 | 0.1315 |
Ref. [45] | 0.0586 | 0.0629 | 0.0745 | 0.0905 | 0.1091 | 0.1290 | ||
Uniform | Present | 0.1219 | 0.1314 | 0.1564 | 0.1910 | 0.2308 | 0.2736 | |
Ref. [45] | 0.1219 | 0.1310 | 0.1551 | 0.1885 | 0.2271 | 0.2686 |
ω (MHz) | ||||
---|---|---|---|---|
(m, n) | ||||
MCST | (1, 1) | 0.1789 | 0.1762 | 0.1728 |
(2, 1) | 0.3821 | 0.3691 | 0.3542 | |
(2, 2) | 0.5113 | 0.4940 | 0.4758 | |
CET | (1, 1) | 0.1678 | 0.1633 | 0.1577 |
(2, 1) | 0.3555 | 0.3376 | 0.3166 | |
(2, 2) | 0.4545 | 0.4310 | 0.4064 |
ω (MHz) | ||||
---|---|---|---|---|
(m, n) | Uniform (λU = 1) | Parabolic (λP = 1) | Linear (λL = 2) | Epoxy |
(1, 1) | 0.1745 | 0.1637 | 0.2115 | 0.1044 |
(2, 1) | 0.3584 | 0.3368 | 0.4246 | 0.2192 |
(2, 2) | 0.4832 | 0.4521 | 0.5670 | 0.2950 |
(3, 1) | 0.5849 | 0.5505 | 0.6799 | 0.3656 |
(3, 2) | 0.6794 | 0.6378 | 0.7860 | 0.4287 |
(3, 3) | 0.8131 | 0.7606 | 0.9387 | 0.5016 |
Sample Availability: Samples of the compounds are not available from the authors. |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Arshid, H.; Khorasani, M.; Soleimani-Javid, Z.; Dimitri, R.; Tornabene, F. Quasi-3D Hyperbolic Shear Deformation Theory for the Free Vibration Study of Honeycomb Microplates with Graphene Nanoplatelets-Reinforced Epoxy Skins. Molecules 2020, 25, 5085. https://doi.org/10.3390/molecules25215085
Arshid H, Khorasani M, Soleimani-Javid Z, Dimitri R, Tornabene F. Quasi-3D Hyperbolic Shear Deformation Theory for the Free Vibration Study of Honeycomb Microplates with Graphene Nanoplatelets-Reinforced Epoxy Skins. Molecules. 2020; 25(21):5085. https://doi.org/10.3390/molecules25215085
Chicago/Turabian StyleArshid, Hossein, Mohammad Khorasani, Zeinab Soleimani-Javid, Rossana Dimitri, and Francesco Tornabene. 2020. "Quasi-3D Hyperbolic Shear Deformation Theory for the Free Vibration Study of Honeycomb Microplates with Graphene Nanoplatelets-Reinforced Epoxy Skins" Molecules 25, no. 21: 5085. https://doi.org/10.3390/molecules25215085