Vibration analysis and optimization of functionally graded carbon nanotube reinforced doubly-curved shallow shells
Zakia Hammou,Zakia Guezzen,Fatima Z. Zradni,Zouaoui Sereir,Abdelouahed Tounsi,Yamna Hammou
Abstract
In the present paper an analytical model was developed to study the non‐linear vibrations of Functionally Graded Carbon Nanotube (FG-CNT) reinforced doubly-curved shallow shells using the Multiple Scales Method (MSM). The nonlinear partial differential equations of motion are based on the FGM shallow shell hypothesis, the non‐linear geometric Von-Karman relationships, and the Galerkin method to reduce the partial differential equations associated with simply supported boundary conditions. The novelty of the present model is the simultaneous prediction of the natural frequencies and their mode shapes versus different curvatures (cylindrical, spherical, conical, and plate) and the different types of FG-CNTs. In addition to combining the vibration analysis with optimization algorithms based on the genetic algorithm, a design optimization methode was developed to maximize the natural frequencies. By considering the expression of the non-dimensional frequency as an objective optimization function, a genetic algorithm program was developed by valuing the mechanical properties, the geometric properties and the FG-CNT configuration of shallow double curvature shells. The results obtained show that the curvature, the volume fraction and the types of NTC distribution have considerable effects on the variation of the Dimensionless Fundamental Linear Frequency (DFLF). The frequency response of the shallow shells of the FG-CNTRC showed two types of nonlinear hardening and softening which are strongly influenced by the change in the fundamental vibration mode. In GA optimization, the mechanical properties and geometric properties in the transverse direction, the volume fraction, and types of distribution of CNTs have a considerable effect on the fundamental frequencies of shallow double-curvature shells. Where the difference between optimized and not optimized DFLF can reach 13.26%.
Zakia Hammou — Physical chemistry Department, Chemistry Faculty, University of Science and Technology of Oran, USTO, Oran, Algeria
Zakia Guezzen — Composite Structures and Innovative Materials Laboratory, Mechanical Engineering Faculty, University of Science and Technology of Oran, BP 1505 El M'naouer, USTO, Oran, Algeria
Fatima Z. Zradni — Oorganic Synthesis, Physico-chemistry, Biomolecular and Environment Laboratory, Chemical Engineering Department, Chemistry Faculty, University of Science and Technology of Oran, USTO, Oran, Algeria
Zouaoui Sereir — Composite Structures and Innovative Materials Laboratory, Mechanical Engineering Faculty, University of Science and Technology of Oran, BP 1505 El M'naouer, USTO, Oran, Algeria
Abdelouahed Tounsi — YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea 5Material and Hydrology Laboratory, University of SidiBel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Yamna Hammou — Maritime Sciences and Engineering Laboratory, Mechanical Engineering Faculty, University of Science and Technology of Oran, BP 1505 El M'naouer, USTO, Oran, Algeria
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