Abstract
Laminated composites are extensively employed in many aerospace structures due to their excellent mechanical properties. In this paper, a size-dependent model on the basis of the nonlocal strain gradient theory is adopted to reveal the vibration behavior of laminated nanoplate with piezo-magnetic face sheets in its upper and lower surfaces. The governing equations are derived by employing the Hamilton’s principle and Mindlin plate theory. The validation of the present study is carried out by comparison with two previous works and good agreements are achieved. By comparing the vibrational frequencies of composite laminated core sandwich nanoplate with and without the piezo-magnetic face sheets, it is demonstrated that the upper and lower piezo-magnetic face sheets will extensively enhance the vibrational frequencies of laminated core sandwich nanoplates. Furthermore, a comprehensive numerical investigation is performed to examine the influence of the cross-ply laminated type, external electric and magnetic potentials, thickness ratio, size scale parameters, as well as aspect and width-to-thickness ratios on the vibration of the laminated core piezo-magnetic sandwich nanoplate. It is expected that the current work can provide some helpful guidelines for employing the piezo-magnetic surfaces as sensors and actuators to control their vibration behaviors of composite laminated nanostructures.










Similar content being viewed by others
References
Canales FG, Mantari JL (2018) Free vibration of thick isotropic and laminated beams with arbitrary boundary conditions via unified formulation and Ritz method. Appl Math Model 61:693–708
Houmat A (2018) Three-dimensional free vibration analysis of variable stiffness laminated composite rectangular plates. Compos Struct 194:398–412
Shi P, Dong C, Sun F, Liu W, Hu Q (2018) A new higher order shear deformation theory for static, vibration and buckling responses of laminated plates with the isogeometric analysis. Compos Struct 204:342–358
Amabili M (2018) Nonlinear vibrations and stability of laminated shells using a modified first-order shear deformation theory. Eur J Mech A Solids 68:75–87
Sayyad AS, Ghugal YM (2017) Bending, buckling and free vibration of laminated composite and sandwich beams: a critical review of literature. Compos Struct 171:486–504
Wang L, Yang J, Li YH (2020) Nonlinear vibration of a deploying laminated Rayleigh beam with a spinning motion in hygrothermal environment. Eng Comput. https://doi.org/10.1007/s00366-020-01035-6
Hajmohammad MH, Azizkhani MB, Kolahchi R (2018) Multiphase nanocomposite viscoelastic laminated conical shells subjected to magneto-hygrothermal loads: dynamic buckling analysis. Int J Mech Sci 137:205–213
Shen H-S, Xiang Y (2018) Postbuckling behavior of functionally graded graphene-reinforced composite laminated cylindrical shells under axial compression in thermal environments. Comput Methods Appl Mech Eng 330:64–82
Chai Y, Song Z, Li F (2018) Investigations on the aerothermoelastic properties of composite laminated cylindrical shells with elastic boundaries in supersonic airflow based on the Rayleigh-Ritz method. Aerosp Sci Technol 82–83:534–544
Xie F, Qu Y, Zhang W, Peng Z, Meng G (2019) Nonlinear aerothermoelastic analysis of composite laminated panels using a general higher-order shear deformation zig-zag theory. Int J Mech Sci 150:226–237
Zhang LW, Xiao LN (2017) Mechanical behavior of laminated CNT-reinforced composite skew plates subjected to dynamic loading. Compos B Eng 122:219–230
Xie F, Qu Y, Guo Q, Zhang W, Peng Z (2019) Nonlinear flutter of composite laminated panels with local non-smooth friction boundaries. Compos Struct 223:110934
Chen C, Shi Y, Zhang YS, Zhu J, Yan Y (2006) Size dependence of Young’s modulus in ZnO nanowires. Phys Rev Lett 96:075505
Vijayaraghavan V, Zhang L (2018) Effective mechanical properties and thickness determination of boron nitride nanosheets using molecular dynamics simulation. Nanomaterials 8:546
Eringen AC (1972) Theory of micromorphic materials with memory. Int J Eng Sci 10:623–641
Eringen AC (1972) Nonlocal polar elastic continua. Int J Eng Sci 10:1–16
Lyu Z, Yang Y, Liu H (2020) High-accuracy hull iteration method for uncertainty propagation in fluid-conveying carbon nanotube system under multi-physical fields. Appl Math Model 79:362–380
Wang Y, Xie K, Fu T (2020) Size-dependent dynamic stability of a FG polymer microbeam reinforced by graphene oxides. Struct Eng Mech 73:685–698
Wang Y, Zhou A, Xie K, Fu T, Shi C (2020) Nonlinear static behaviors of functionally graded polymer-based circular microarches reinforced by graphene oxide nanofillers. Results Phys 16:102894
Liu H, Zhang Q, Ma J (2021) Thermo-mechanical dynamics of two-dimensional FG microbeam subjected to a moving harmonic load. Acta Astronaut 178:681–692
Zhang Q, Liu H (2020) On the dynamic response of porous functionally graded microbeam under moving load. Int J Eng Sci 153:103317
Toupin RA (1962) Elastic materials with couple-stresses. Arch Ration Mech Anal 11:385–414
Arani AG, Jafari GS (2015) Nonlinear vibration analysis of laminated composite Mindlin micro/nano-plates resting on orthotropic Pasternak medium using DQM. Appl Math Mech 36:1033–1044
Kolahchi R, Zarei MS, Hajmohammad MH, Naddaf Oskouei A (2017) Visco-nonlocal-refined Zigzag theories for dynamic buckling of laminated nanoplates using differential cubature-Bolotin methods. Thin-Walled Struct 113:162–169
Preethi K, Raghu P, Rajagopal A, Reddy JN (2017) Nonlocal nonlinear bending and free vibration analysis of a rotating laminated nano cantilever beam. Mech Adv Mater Struct 25:439–450
Sahmani S, Fattahi AM, Ahmed NA (2018) Analytical mathematical solution for vibrational response of postbuckled laminated FG-GPLRC nonlocal strain gradient micro-/nanobeams. Eng Comput 35:1173–1189
Lim CW, Zhang G, Reddy JN (2015) A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J Mech Phys Solids 78:298–313
Lu L, Guo X, Zhao J (2017) A unified nonlocal strain gradient model for nanobeams and the importance of higher order terms. Int J Eng Sci 119:265–277
Liu H, Wu H, Lyu Z (2020) Nonlinear resonance of FG multilayer beam-type nanocomposites: effects of graphene nanoplatelet-reinforcement and geometric imperfection. Aerosp Sci Technol 98:105702
Wu H, Liu H (2020) Nonlinear thermo-mechanical response of temperature-dependent FG sandwich nanobeams with geometric imperfection. Eng Comput. https://doi.org/10.1007/s00366-020-01005-y
Arefi M, Kiani M, Rabczuk T (2019) Application of nonlocal strain gradient theory to size dependent bending analysis of a sandwich porous nanoplate integrated with piezomagnetic face-sheets. Compos Part B 168:320–333
Ebrahimi F, Barati MR, Dabbagh A (2016) A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates. Int J Eng Sci 107:169–182
Sahmani S, Aghdam MM (2017) Nonlinear instability of axially loaded functionally graded multilayer graphene platelet-reinforced nanoshells based on nonlocal strain gradient elasticity theory. Int J Mech Sci 131–132:95–106
Zeighampour H, Tadi Beni Y, Botshekanan Dehkordi M (2018) Wave propagation in viscoelastic thin cylindrical nanoshell resting on a visco-Pasternak foundation based on nonlocal strain gradient theory. Thin-Walled Struct 122:378–386
Moayedi H, Ebrahimi F, Habibi M, Safarpour H, Foong LK (2020) Application of nonlocal strain–stress gradient theory and GDQEM for thermo-vibration responses of a laminated composite nanoshell. Eng Comput. https://doi.org/10.1007/s00366-020-01002-1
Liu H, Liu H, Yang J (2018) Vibration of FG magneto-electro-viscoelastic porous nanobeams on visco-Pasternak foundation. Compos Part B 155:244–256
Liu H, Lv Z (2018) Uncertain material properties on wave dispersion behaviors of smart magneto-electro-elastic nanobeams. Compos Struct 202:615–624
Li C, Li P, Zhang Z, Wen B (2020) Optimal locations of discontinuous piezoelectric laminated cylindrical shell with point supported elastic boundary conditions for vibration control. Compos Struct 233:111575
Shariati A, Hosseini SHS, Ebrahimi F, Toghroli A (2020) Nonlinear dynamics and vibration of reinforced piezoelectric scale-dependent plates as a class of nonlinear Mathieu-Hill systems: parametric excitation analysis. Eng Comput. https://doi.org/10.1007/s00366-020-00942-y
Lal A, Shegokar NL, Singh BN (2017) Finite element based nonlinear dynamic response of elastically supported piezoelectric functionally graded beam subjected to moving load in thermal environment with random system properties. Appl Math Model 44:274–295
Abad F, Rouzegar J (2017) An exact spectral element method for free vibration analysis of FG plate integrated with piezoelectric layers. Compos Struct 180:696–708
Zhao X, Iegaink FJN, Zhu WD, Li YH (2019) Coupled thermo-electro-elastic forced vibrations of piezoelectric laminated beams by means of Green’s functions. Int J Mech Sci 156:355–369
Zhang P, Qi C, Fang H, Ma C, Huang Y (2019) Semi-analytical analysis of static and dynamic responses for laminated magneto-electro-elastic plates. Compos Struct 222:110933
Arani AG, Zamani MH (2018) Nonlocal free vibration analysis of FG-porous shear and normal deformable sandwich nanoplate with piezoelectric face sheets resting on silica aerogel foundation. Arab J Sci Eng 43:4675–4688
Yang WD, Fang CQ, Wang X (2017) Nonlinear dynamic characteristics of FGCNTs reinforced microbeam with piezoelectric layer based on unifying stress-strain gradient framework. Compos B Eng 111:372–386
Ninh DG, Bich DH (2018) Characteristics of nonlinear vibration of nanocomposite cylindrical shells with piezoelectric actuators under thermo-mechanical loads. Aerosp Sci Technol 77:595–609
Zhu C-S, Fang X-Q, Liu J-X, Li H-Y (2017) Surface energy effect on nonlinear free vibration behavior of orthotropic piezoelectric cylindrical nano-shells. Eur J Mech A Solids 66:423–432
Zeng S, Wang BL, Wang KF (2019) Nonlinear vibration of piezoelectric sandwich nanoplates with functionally graded porous core with consideration of flexoelectric effect. Compos Struct 207:340–351
Arefi M, Kiani M, Zenkour AM (2020) Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak’s foundation via MCST. J Sandwich Struct Mater 22:55–86
Arefi M, Zenkour AM (2016) A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment. J Sandwich Struct Mater 18:624–651
Mohammadimehr M, Akhavan Alavi SM, Okhravi SV, Edjtahed SH (2017) Free vibration analysis of micro-magneto-electro-elastic cylindrical sandwich panel considering functionally graded carbon nanotube–reinforced nanocomposite face sheets, various circuit boundary conditions, and temperature-dependent material properties using high-order sandwich panel theory and modified strain gradient theory. J Intell Mater Syst Struct 29:863–882
Liu H, Lyu Z (2020) Modeling of novel nanoscale mass sensor made of smart FG magneto-electro-elastic nanofilm integrated with graphene layers. Thin-Walled Struct 151:106749
Ke L-L, Wang Y-S, Yang J, Kitipornchai S (2014) Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory. Acta Mech Sin 30:516–525
Arefi M, Zamani MH, Kiani M (2020) Smart electrical and magnetic stability analysis of exponentially graded shear deformable three-layered nanoplate based on nonlocal piezo-magneto-elasticity theory. J Sandwich Struct Mater 22:599–625
Arefi M, Kiani M, Zamani MH (2018) Nonlocal strain gradient theory for the magneto-electro-elastic vibration response of a porous FG-core sandwich nanoplate with piezomagnetic face sheets resting on an elastic foundation. J Sandwich Struct Mater 22(7):2157–2185
Ebrahimi F, Dabbagh A (2017) On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory. Compos Struct 162:281–293
Ma LH, Ke LL, Reddy JN, Yang J, Kitipornchai S, Wang YS (2018) Wave propagation characteristics in magneto-electro-elastic nanoshells using nonlocal strain gradient theory. Compos Struct 199:10–23
Gholami R, Ansari R, Gholami Y (2018) Numerical study on the nonlinear resonant dynamics of carbon nanotube/fiber/polymer multiscale laminated composite rectangular plates with various boundary conditions. Aerosp Sci Technol 78:118–129
Xiang R, Pan Z-Z, Ouyang H, Zhang L-W (2020) A study of the vibration and lay-up optimization of rotating cross-ply laminated nanocomposite blades. Compos Struct 235:111775
Bouazza M, Kenouza Y, Benseddiq N, Zenkour AM (2017) A two-variable simplified nth-higher-order theory for free vibration behavior of laminated plates. Compos Struct 182:533–541
Ke L-L, Wang Y-S (2014) Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory. Physica E 63:52–61
He D, Yang W, Chen W (2017) A size-dependent composite laminated skew plate model based on a new modified couple stress theory. Acta Mech Solida Sin 30:75–86
Acknowledgements
The financial support from the National Postdoctoral Program for Innovative Talents in China under the Grant Number BX201900024 is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendices
Appendix A: Reduced material parameters of piezo-magnetic face sheets
Appendix B: Rigidity coefficients
Appendix C: Elements in stiffness and mass matrices
where
Rights and permissions
About this article
Cite this article
Liu, H., Zhang, Q., Yang, X. et al. Size-dependent vibration of laminated composite nanoplate with piezo-magnetic face sheets. Engineering with Computers 38, 3007–3023 (2022). https://doi.org/10.1007/s00366-021-01285-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00366-021-01285-y