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Free Vibration Response of FG Porous Sandwich Micro-Beam with Flexoelectric Face-Sheets Resting on Modified Silica Aerogel Foundation

Ali Ghorbanpour Arani

Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

Institute of Nanoscience and Technology, University of Kashan, Kashan, Iran

E-mail Address: aghorban@kashanu.ac.ir

E-mail Address: a_ghorbanpour@yahoo.com

Corresponding author.

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Hassan Baba Akbar Zarei

Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

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, and

Pouya Pourmousa

Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

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https://doi.org/10.1142/S175882511950087XCited by:21 (Source: Crossref)

Abstract

The free vibration analysis of sandwich micro-beam (SMB) which is subjected to electrical field is investigated by adopting the Euler–Bernoulli beam theory (EBBT) and modified strain gradient theory (MSGT). SMB is made of three layers, including a functionally graded (FG) porous core and two flexoelectric face-sheets. The porosities are assumed to be distributed over the beam thickness based on the two distribution functions. Also, due to the electric properties of flexoelectric materials, face-sheets of SMB are subjected to the external electric field. The modified Silica Aerogel foundation model is employed to consider the effects of elastic foundation on SMB. The size-dependent governing equations of motion are derived using Hamilton’s principle and solved by Navier’s solution method for a case of simply supported SMB. The effects of various parameters, such as length to thickness ratio, porosity index, flexoelectric loadings (the load applied to the flexoelectric face-sheets caused by external electric field), small scale parameter and foundation parameters on dimensionless frequency of SMB, are assessed. The results of this work can be used for optimum design and control of micro-electro-mechanical devices.

Keywords:

References

Al Rjoub, Y. S. and Hamad, A. G. [2017] “ Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method,” KSCE Journal of Civil Engineering 21, 792–806. Crossref, Web of Science, Google Scholar
Amir, S., Mohammad-Rezaei Bidgoli, E. and Arshid, E. [2018a] “ Size-dependent vibration analysis of a three-layered porous rectangular nano plate with piezo-electromagnetic face sheets subjected to pre loads based on SSDT,” Mechanics of Advanced Material and Structure, pp. 1–15, https://doi.org/10.1080/15376494.2018.1487612. Crossref, Web of Science, Google Scholar
Amir S., Khorasani M. and BabaAkbar-Zarei M. [2018b] “ Buckling analysis of nanocomposite sandwich plates with piezoelectric face sheets based on flexoelectricity and first-order shear deformation theory,” Journal of Sandwich Structure and Materials, pp. 1–24, https://doi.org/10.1177/1099636218795385. Web of Science, Google Scholar
Amir S., BabaAkbar-Zarei H. and Khorasani, M. [2019a] “ Flexoelectric vibration analysis of nanocomposite sandwich plates,” Mechanics Based Design of Structure and Machine, pp. 1–18, https://doi.org/10.1080/15397734.2019.1624175. Web of Science, Google Scholar
Amir S., Arshid E., Ghorbanpour Arani, M. R. [2019b] “ 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 Structures and Systems 23(5), 429–447. Web of Science, Google Scholar
Aydogdu, M. and Taskin, V. [2007] “ Free vibration analysis of functionally graded beams with simply supported edges,” Materials & Design 28, 1651–1656. Crossref, Web of Science, Google Scholar
Barati, M. R. [2017] “ On non-linear vibrations of flexoelectric nanobeams,” International Journal of Engineerng and Science 121, 143–153. Crossref, Web of Science, Google Scholar
Baroudi S., Najar, F. and Jemai, A. [2017] “ Static and dynamic analytical coupled field analysis of piezoelectric flexoelectric nanobeams: A strain gradient theory approach,” International Journal of Science and Research 135, 110–124. Google Scholar
Bozhevolnaya, E. and Sun, J. Q. [2004] “ Free vibration analysis of curved sandwich beams,” Journal of Sandwich Structure and Material 6, 47–73. Crossref, Web of Science, Google Scholar
Chen, D., Yang, J. and Kitipornchai, S. [2015] “ Elastic buckling and static bending of shear deformable functionally graded porous beam,” Composite Structure 133, 54–61. Crossref, Web of Science, Google Scholar
Chen, D., Kitipornchai, S. and Yang, J. [2016] “ Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core,” Thin-Walled Structure 107, 39–48. Crossref, Web of Science, Google Scholar
Ebrahimi, F. and Barati, M. R. [2017] “ Surface effects on the vibration behavior of flexoelectric nanobeams based on nonlocal elasticity theory,” The European Physical Journal Plus 132, 19. Crossref, Web of Science, Google Scholar
Ebrahimi, F. and Karimiasl, M. [2018] Nonlocal and surface effects on the buckling behavior of flexoelectric sandwich nanobeams. Materials and Structure 25(11), 943–952. Web of Science, Google Scholar
Fattahian, D. S. and Tadi, B. Y. [2017] “ Electro-mechanical free vibration of single-walled piezoelectric/flexoelectric nano cones using consistent couple stress theory,” International Journal of Mechanical Science 128–129, 125–139. Crossref, Web of Science, Google Scholar
Ghorbanpour Arani, A. and Amir, S. [2013] “ Electro-thermal vibration of visco-elastically coupled BNNT systems conveying fluid embedded on elastic foundation via strain gradient theory,” Physica B 419, 1–6. Crossref, Web of Science, Google Scholar
Ghorbanpour Arani, A. and Zamani, M. H. [2017] “ Investigation of electric field effect on size-dependent bending analysis of functionally graded porous shear and normal deformable sandwich nanoplate on silica Aerogel foundation,” Journal of Sandwich Structures & Materials, https://doi.org/10.1177/1099636217721405. Web of Science, Google Scholar
Ghorbanpour Arani, A. and Zamani, M. H. [2018] “ Bending analysis of agglomerated carbon nanotube-reinforced beam resting on two parameters modified Vlasov model foundation,” Indian Journal of Physics 92(6), 767–777. Crossref, Web of Science, Google Scholar
Ghorbanpour Arani, A., BabaAkbar-Zarei, H., Pourmousa, P. and Eskandari, M. [2018] “ Investigation of free vibration response of smart sandwich micro-beam on Winkler–Pasternak substrate exposed to multi physical fields,” Microsystem Technologies 24(7), 3045–3060. Crossref, Web of Science, Google Scholar
Joseph, R. P., Zhang, C., Wang, B. L. and Samali, B. [2018] “ Fracture analysis of flexoelectric double cantilever beams based on the strain gradient theory,” Composite Structures 202, 1322–1329. Crossref, Web of Science, Google Scholar
Lei, J. and Liu, Z. [2018a] “ A novel constitutive model for the mechanical properties of silica aerogels,” Journal of Applied Physics 124, 025102–025106. Crossref, Web of Science, Google Scholar
Lei, J. and Liu, Z. [2018b] “ The structural and mechanical properties of graphene aerogels based on Schwarz-surface-like graphene models,” Carbon 130, 741–748. Crossref, Web of Science, Google Scholar
Li, A., Zhou, S., Zhou, S. and Wang, B. [2014] “ Size-dependent analysis of a three-layer microbeam including electromechanical coupling,” Composite Structure 116, 120–127. Crossref, Web of Science, Google Scholar
Li, X. and Luo, Y. [2017] “ Flexoelectric effect on vibration of piezoelectric microbeams based on a modified couple stress theory,” Hindawi Shock and Vibration 2017, 7. Web of Science, Google Scholar
Liang, X., Yang, W., Hu, S. and Shen, S. [2016] “ Buckling and vibration of flexoelectric nanofilms subjected to mechanical loads,” Journal of Physical D: Applied Physics 49, 115307. Crossref, Web of Science, Google Scholar
Majdoub, M. S., Sharma, P. and Cagin, T. [2008] “ Dramatic enhancement in energy harvesting for a narrow range of dimensions in piezoelectric nanostructures,” Physical Review B 78(12), 121407. Crossref, Web of Science, Google Scholar
Malekzadeh, P and Shojaee, M. [2015] “ A two-variable first-order shear deformation theory coupled with surface and nonlocal effects for free vibration of nanoplates,” Journal of Vibration and Control 21(14), 2755–2772. Crossref, Web of Science, Google Scholar
Marynowski, K. [2012] “ Dynamic analysis of an axially moving sandwich beam with viscoelastic core,” Composite Structure 94, 2931–2936. Crossref, Web of Science, Google Scholar
Miandoab, E. M., Yousefi-Koma, A. and Pishkenari, H. N. [2015] “ Nonlocal and strain gradient based model for electrostatically actuated silicon nano-beams,” Microsystem Technologies 21(2), 457–464. Crossref, Web of Science, Google Scholar
Navarro, P., Abrate, S., Aubry, J., Marguet, S., Ferrero, J. F. [2013] “ Analytical modeling of indentation of composite sandwich beam,” Composite Structure 100, 79–88. Crossref, Web of Science, Google Scholar
Refaeinejad, V., Rahmani, O. and Hosseini, S. A. H. [2017] “ An analytical solution for bending, buckling, and free vibration of FG nanobeam lying on Winkler-Pasternak elastic foundation using different nonlocal higher order shear deformation beam theories,” Scientia Iranica 24(3), 1635–1653. Crossref, Web of Science, Google Scholar
Saraswathy, B., Kumar, R. R. and Mangal, L. [2012] “ Dynamic analysis of honeycomb sandwich beam with multiple debonds,” Mechanical Engineering 2012, 1–7. Google Scholar
Shafiei, N., Mousavi, A. and Ghadiri, M. [2016] “ On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams,” International Journal of Engineering Science 106, 42–56. Crossref, Web of Science, Google Scholar
Shen, S. and Kuang, Z. B. [1999] “ An active control model of laminated piezothermoelastic plate,” International Journal of Solid Structure 36(13), 1925–1947. Crossref, Web of Science, Google Scholar
Simssek, M. [2010] “ Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories,” Nuclear Engineering and Design 240, 697–705. Crossref, Web of Science, Google Scholar
Sneha Rupa, N. and Ray, M. C. [2017] “ Analysis of flexoelectric response in nanobeams using nonlocal theory of elasticity,” International Journal of Mechanics and Materials in Design 13(3), 453–467. Crossref, Web of Science, Google Scholar
Vallabhan, C. V. G., Straughan, W. T. and Das, Y. C. [1991] “ Refined model for analysis of plates on elastic foundations,” Journal of Engineering Mechanics 117(12), 2830–2843. Crossref, Web of Science, Google Scholar
Wang, K. F. and Wang, B. L. [2017] “ Non-linear flexoelectricity in energy harvesting,” International Journal of Engineering Science 116, 88–103. Crossref, Web of Science, Google Scholar
Wang, W., Li, P., Jin, F. and Wang, J. [2016] “ Vibration analysis of piezoelectric ceramic circular nanoplates considering surface and nonlocal effects,” Composite Structure 140, 758–775. Crossref, Web of Science, Google Scholar
Zenkour, A. M. [2017] “ Nonlocal thermoelasticity theory without energy dissipation for nano-machined beam resonators subjected to various boundary conditions,” Microsystem Technologies 23(1), 55–65. Crossref, Web of Science, Google Scholar
Zhang, R., Liang, X. and Shen, S. [2016] “ A Timoshenko dielectric beam model with flexoelectric effect,” Meccanica 51(5), 1181–1188. Crossref, Web of Science, Google Scholar
Zhang, Z., Yan, Z. and Jiang, L. [2014] “ Flexoelectric effect on the electroelastic responses and vibrational behaviors of a piezoelectric nanoplate,” Journal of Applied Physics 116, 014307–014311. Crossref, Web of Science, Google Scholar
Zheng, S., Zhao, X. and Hongtao, W. [2019] “ Theoretical and finite element modeling of piezoelectric nanobeams with surface and flexoelectricity effects,” Mechanics of Advanced Materials and Structure 26(15), 1261–1270. Crossref, Web of Science, Google Scholar