Maximization of Natural Frequencies for Functionally Graded Rectangular Plates

Abstract:

In this paper optimal design of free vibrations for functionally graded plates is studied using the analytical methods. The analytical methods can be employed for the solution of six of 21 arbitrary boundary conditions (the combinations of clamped, simply supported and free). The influence of various models of porosity and forms of different reinforcements with nanoplatelets and carbon nanotubes are investigated, including variations of stiffness/density along the thickness of a plate. The analysis is carried out for the classical plate theory. Parametric studies illustrate the possibility of increasing natural frequencies and the necessity of implementing the optimization techniques to find the best solutions from the engineering point of view.

• Periodical: Key Engineering Materials (Volume 891)
• Pages: 116-121
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.891.116
• Online since: July 2021
• Authors: Aleksander Muc*
• Keywords: Functionally Graded Materials (FGM), Natural Frequencies, Optimization, Rectangular Plates

References

[1] Bendsøe, M.P., Sigmund O., Topology Optimization. Theory, Methods and Applications, Springer-Verlag, Berlin, (2004).

[2] Pedersen P., Design for minimum stress concentration – some practical aspects, Structural Optimization (Rozvany, G.I.N., Karihaloo, B.L., eds), Kluwer, Dordrecht, 1988, pp.225-232.

DOI: 10.1007/978-94-009-1413-1_29

[3] Muc, A., Gurba, W., Genetic algorithms and finite element analysis in optimization of composite structures (2001) Composite Structures, 54 (2-3), pp.275-281.

DOI: 10.1016/s0263-8223(01)00098-8

[4] Muc, A., Optimal design of composite multilayered plated and shell structures (2007) Thin-Walled Structures, 45 (10-11), pp.816-820.

DOI: 10.1016/j.tws.2007.08.042

[5] Muc, A., Ulatowska, A., Local fibre reinforcement of holes in composite multilayered plates, (2012) Composite Structures, 94 (4), pp.1413-1419.

DOI: 10.1016/j.compstruct.2011.11.017

[6] Muc, A., Effectiveness of optimal design with respect to computational models for laminated composite structures weakened by holes, (1998) Structural Optimization, 16 (1), pp.58-67.

DOI: 10.1007/bf01214000

[7] Muc, A., Design of blended/tapered multilayered structures subjected to buckling constraints (2018) Composite Structures, 186, pp.256-266.

DOI: 10.1016/j.compstruct.2017.12.001

[8] Muc, A., Kędziora, P., Optimal design of smart laminated composite structures, (2010) Materials and Manufacturing Processes, 25 (4), pp.272-280.

DOI: 10.1080/10426910903426463

[9] Kędziora, P., Muc, A., Optimal shapes of PZT actuators for laminated structures subjected to displacement or eigenfrequency constraints, (2012) Composite Structures, 94 (3), pp.1224-1235.

DOI: 10.1016/j.compstruct.2011.11.019

[10] Muc, A., Kędziora, P., Stawiarski, A., Buckling enhancement of laminated composite structures partially covered by piezoelectric actuators, (2019) European Journal of Mechanics, A/Solids, 73, pp.112-125.

DOI: 10.1016/j.euromechsol.2018.07.002

[11] Trung Thanh Tran, Quoc-Hoa Pham, Trung Nguyen-Thoi, Static and free vibration analyses of functionally graded porous variable-thickness plates using an edge-based smoothed finite element method, Defence Technology, https://doi.org/10.1016 /j. dt. 2020.06.001.

DOI: 10.1016/j.dt.2020.06.001

[12] M.T. Song, J. Yang, S. Kitipornchai, Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates, (2017) Int. J. Mech. Sci. 131 p.345–355.

DOI: 10.1016/j.ijmecsci.2017.07.017

[13] Z.X. Lei, L.W. Zhang, K.M. Liew, Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method, (2015) Composite Structures, 127, p.245–259.

DOI: 10.1016/j.compstruct.2015.03.019

[14] Leissa AW, Free vibrations of rectangular plates, Journal of Sound and Vibration (1973) 31(3), pp.257-293.

DOI: 10.1016/s0022-460x(73)80371-2