Supersonic flutter and vibration analyses of a functionally graded porous-nanocomposite sandwich microbeam

Subject Areas : Applied Mechanics

Mohammad Hossein Hashempour ¹ , Ali Ghorbanpour Arani ^{2 *} , Zahra Khoddami Maraghi ³ , Iman Dadoo ⁴ , Saeed Amir ⁵

1 - Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
2 - Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran.
3 -
4 - Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran
5 - Mechanical Engineering Faculty, University of Kashan

Received: 2024-07-06 Accepted : 2024-12-01 Published : 2025-07-25

Keywords: Free vibration, Flutter, supersonic fluid flow, Sandwich microbeam, Composite materials, Porous core.,

Abstract :

The present study investigates free vibration and flutter instability analyses of a sandwich microbeam subjected to supersonic fluid flow. The microbeam comprises functionally graded (FG) porosity cores, with top and bottom sheets reinforced by carbon nanotubes (CNTs). Mechanical properties of FG porous-nanocomposite sandwich microbeam are determined using the rule of mixture and the Ashleby-Mori-Tanaka method. Euler-Bernoulli, Timoshenko, and Reddy beam theories are used while the modified couple stress theory (MCST) accounts for size effects. linearized piston theory and Pasternak foundation is considered to model supersonic fluid flow and elastic medium. In the analysis of free vibrations, natural frequencies and corresponding mode shapes are extracted and in flutter analysis, the variations in natural frequencies with respect to the aerodynamic pressure of the fluid flow are plotted to calculate the critical pressure. A parametric study is conducted to investigate the impact of various characteristics include the geometric properties porosity and distribution pattern of pores, mass fraction, type and distribution pattern of CNTs, length scale parameter, and boundary conditions. Based on the results, it can be concluded that using CNTs with smaller chiral indices leads to a maximum increase in the microbeam's natural frequencies and achieves the highest aeroelastic stability. The findings of this research can be utilized in the design and analysis of microturbines as well as equipment used in biomechanical engineering.

References:


1. Eroğlu M., Esen İ., Koç M.A., 2024, Thermal vibration and buckling analysis of magneto-electro-elastic functionally graded porous higher-order nanobeams using nonlocal strain gradient theory, Acta Mech, https://doi.org/10.1007/s00707-023-03793-y.
2. Addou F. Y., Bourada F., Tounsi A., Bousahla A. A., Tounsi A., Benrahou K. H., Albalawi H., 2024, Effect of porosity distribution on flexural and free vibrational behaviors of laminated composite shell using,
Archiv.Civ.Mech.Eng ,https://doi.org/10.1007/s43452-024-00894-w.
3. Van N. T. H., van Minh P., Duc N. D., 2024,Finite-element modeling for static bending and free vibration analyses of double-layer non-uniform thickness FG plates taking into account sliding interactions, Archives of Civil and Mechanical Engineering , https://doi.org/10.1007/s43452-024-00914-9.
4. Civalek Ö., Ersoy H., Uzun B.,Ersoy H.,Yayli M. Ö., 2023, Dynamics of a FG porous microbeam with metal foam under deformable boundaries, Acta Mech, https://doi.org/10.1007/s00707-023-03663-7.
5. Ghorbanpour-Arani A., Khoddami Maraghi Z., Ghorbanpour Arani A., 2023, The Frequency Response of Intelligent Composite Sandwich Plate Under Biaxial In-Plane Forces. Journal of Solid Mechanics, https://doi.org/10.22034/jsm.2020.1895607.1563.
6. Gia Phi B., Van Hieu D., Sedighi H.M., Sofiyev A.H., 2022, Size-dependent nonlinear vibration of functionally graded composite micro-beams reinforced by carbon nanotubes with piezoelectric layers in thermal environments, Acta Mech,https://doi.org/10.1007/s00707-022-03224-4.
7. Wu X.W., Zhu L.F., Wu Z.M., Ke L.L., 2022, Vibrational power flow analysis of Timoshenko microbeams with a crack, Composite Structures, http://.org/10.1016/j.compstruct.2022.115483.
8. Wang Y.Q., Zhao H.L., Ye C., Zu J.W., 2022, A porous microbeam model for bending and vibration analysis based on the sinusoidal beam theory and modified strain gradient theory. International Journal of Applied Mechanics,https://doi.org/10.1142/S175882511850059.
9. Karamanli A., Vo T.P., 2021, Bending, vibration, buckling analysis of bi-directional FG porous microbeams with a variable material length scale parameter, Applied Mathematical Modelling, http://doi.org/10.1016/j.apm.2020.09.058.
10. Arshid E., Amir S., 2021, Size-dependent vibration analysis of fluid-infiltrated porous curved microbeams integrated with reinforced functionally graded graphene platelets face sheets considering thickness stretching effect, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, https://doi.org/10.1177/1464420720985556.
11. Tlidji Y., Benferhat R., Tahar H.D., 2021, Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity, Structural Engineering and Mechanics, An Int'l Journal, https://doi.org/10.12989/sem.2021.77.2.217.
12. Haghparast E., Ghorbanpour-Arani A ., Ghorbanpour Arani A ., 2020, Effect of Fluid–Structure Interaction on Vibration of Moving Sandwich Plate with Balsa Wood Core and Nanocomposite Face Sheets, International Journal of Applied Mechanics, https://doi.org/10.1142/S1758825120500787.
13. Enayat S., Hashemian M., Toghraie D., Jaberzadeh E., 2020,A comprehensive study for mechanical behavior of functionally graded porous nanobeams resting on elastic foundation, Journal of the Brazilian Society of Mechanical Sciences and Engineering, https://doi.org/10.1007/s40430-020-02474-4.
14. Ghorbanpour Arani A., Soleymani T., 2019, Size-dependent vibration analysis of a rotating MR sandwich beam with varying cross section in supersonic airflow. International Journal of Mechanical Sciences, https://doi.org/10.1016/j.ijmecsci.2018.11.024.
15. Amir S., Soleimani Javid Z., Arshid E., 2019, Size‐dependent free vibration of sandwich micro beam with porous core subjected to thermal load based on SSDBT, ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik,https://doi.org/10.1002/zamm.201800334.
16. Wang Y.Q., Zhao H.L., Ye C., Zu J.W., 2018,A porous microbeam model for bending and vibration analysis based on the sinusoidal beam theory and modified strain gradient theory, International Journal of Applied Mechanics , https://doi.org/10.1142/S175882511850059.
17. Ghorbanpour Arani A., Soleymani T., 2019, Size-dependent vibration analysis of an axially moving sandwich beam with MR core and axially FGM faces layers in yawed supersonic airflow, European Journal of Mechanics-A/Solids, http://doi.org/10.1016/j.euromechsol.2019.05.007.
18. Nasr Esfahani M., Hashemian M., Aghadavoudi F., 2022, The vibration study of a sandwich conical shell with a saturated FGP core. Scientific Reports , https://doi.org/10.1038/s41598-022-09043-w.
19. Adab N., Arefi M., 2023,Vibrational behavior of truncated conical porous GPL-reinforced sandwich micro/nano-shells, Engineering with Computers. https://doi.org/10.1007/s00366-021-01580-8.
20. Chen D., Kitipornchai S., Yang J., 2016, Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core, Thin-Walled Structures , https://doi.org/10.1016/j.tws.2016.05.025.
21. Şimşek M., Reddy J.N., 2013, Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory. International Journal of Engineering Science , https://doi.org/10.1016/j.ijengsci.2012.12.002.
22. Reddy J.N., 2017,Energy principles and variational methods in applied mechanics, John Wiley & Sons, Hoboken, New Jersey, United States.
23. Khoddami Maragh Z., Amir S., Arshid E., 2024,On the natural frequencies of smart circular plates with magnetorheological fluid core embedded between magneto strictive patches on Kerr elastic substance, Mechanics Based Design of Structures and Machines , https://doi.org/10.1080/15397734.2022.2156885.
24. Tornabene F., Bacciocchi M., Fantuzzi N., Reddy J.N., 2019,Multiscale approach for three‐phase CNT/polymer/fiber laminated nanocomposite structures, Polymer composites,https://doi.org/10.1002/pc.24520.
25. Sadd M.H., 2009, Elasticity theory, applications, and numerics, Elsevier, Cambridge, Massachusetts, United States.
26. Rajesh K., Saheb K.M., 2017, Free vibrations of uniform timoshenko beams on pasternak foundation using coupled displacement field method, Archive of Mechanical Engineering, https://doi.org/ 10.1515/meceng-2017-0022.
27. Soltan Arani A.H., Ghorbanpour Arani A., Khoddami Maraghi Z., 2024,Nonlocal quasi-3d vibration/analysis of three-layer nanoplate surrounded by Orthotropic Visco-Pasternak foundation by considering surface effects and neutral surface concept, Mechanics Based Design of Structures and Machines , http://doi.org/10.1080/15397734.2024.2348103.
28. Ashley H., Zartarian G., 1956, Piston theory-a new aerodynamic tool for the aeroelasticity, Journal of the aeronautical sciences , https://doi.org/10.2514/8.3740.
29. Ghorbanpour Arani A., Kiani F., 2019, Afshari H.: Aeroelastic Analysis of Laminated FG-Cntrc Cylindrical Panels Under Yawed Supersonic Flow, International Journal of Applied Mechanics , https://doi.org/10.1142/S1758825119500522.
30. Hosseini M., Ghorbanpour Arani A., Karamizadeh M.R., Afshari H., Niknejad S., 2019, Aeroelastic analysis of cantilever non-symmetric FG sandwich plates under yawed supersonic flow, Wind and Structures, https://doi.org/10.12989/was.2019.29.6.457.
31. Bellman R., Casti J., 1971, Differential quadrature and long-term integration, Journal of mathematical analysis and Applications, https://doi.org/10.1016/0022-247X(71)90110-7.
32. Bellman R., Kashef B., Casti J., 1972, Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. Journal of computational physics, https://api.semanticscholar.org/CorpusID:122053474.
33. Bert C.W., Malik M., 1956, Differential quadrature method in computational mechanics: a review, Applied Mechanics Reviews,DOI:10.1115/1.3101882.
34. Jahangiri S., Ghorbanpour Arani A., Khoddami Maraghi Z., 2024,Dynamics of a rotating ring-stiffened sandwich conical shell with an auxetic honeycomb core, Applied Mathematics and Mechanics , https://doi.org/10.1007/s10483-024-3124-7.
35. Chen D., Yang J., Kitipornchai S., 2016, Free and forced vibrations of shear deformable functionally graded porous beams, International journal of mechanical sciences, https://doi.org/10.1016/j.ijmecsci.2016.01.025.
36. Khoddami Maraghi Z., 2019, Flutter and divergence instability of nanocomposite sandwich plate with magneto strictive face sheets, Journal of Sound and Vibration ,http://doi.org/10.1016/j.jsv.2019.06.002.