Influence of in-plane loading on the vibrations of the fully symmetric mechanical systems via dynamic simulation and gen
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ORIGINAL ARTICLE
Influence of in‑plane loading on the vibrations of the fully symmetric mechanical systems via dynamic simulation and generalized differential quadrature framework M. S. H. Al‑Furjan1,2 · Mahmoud Fereidouni3 · Mostafa Habibi4,5 · Raneen Abd Ali6 · Jing Ni1 · Mehran Safarpour7 Received: 3 August 2020 / Accepted: 12 September 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Honeycomb structures are one type of structure that has the geometry of a honeycomb to allow the minimization of the amount of used material to reach minimal material cost and minimal weight. In this regard, this article deals with the frequency analysis of imperfect honeycomb core sandwich disk with multi-scale hybrid nanocomposite (MHC) face sheets. The honeycomb core is made of aluminum due to its low weight and high stiffness. The rule of the mixture and modified Halpin–Tsai model are engaged to provide the effective material constant of the composite layers. By employing Hamilton’s principle, the governing equations of the structure are derived and solved with the aid of the generalized differential quadrature method. Afterward, a parametric study is carried out to investigate the effects of the thickness to length ratio of the honeycomb core, honeycomb core thickness to inner radius ratio, value fraction of carbon fibers, radius ration of the disk, the angle of honeycomb network, the weight fraction of CNTs, and tensile and compressive in-plane force on the frequency of the sandwich disk with honeycomb core and MHC. The results show that the critical fiber angle is 𝜃f ∕𝜋 = 0.5 for C–C and C–S boundary conditions. Another consequence is that when the structure is fixed with S–S boundary conditions, for p = 500 and p = 1000 , as well as the critical dimensionless angle for fibers is 0.5, there are two more range for critical fiber angle in which they are 0.275 ≤ 𝜃f ∕𝜋 ≤ 0.375 and 0.23 ≤ 𝜃f ∕𝜋 ≤ 0.39 , respectively. Additionally, the range of the critical dimensionless angle for fibers increases by increasing the applied load. Some new results related to dynamic behavior of an MHC are also presented, which can serve as benchmark solutions for future investigations. Keywords Dynamics · Sandwich disk · Honeycomb core · FG · In-plane pressure · GDQM · Multi-scale hybrid nanocomposite
2
M. S. H. Al‑Furjan [email protected]
School of Materials Science and Engineering, State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou 310027, China
3
Mahmoud Fereidouni [email protected]
Faculty of Aerospace Engineering, K.N. Toosi University of Technology, Tehran, Iran
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Raneen Abd Ali [email protected]
Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
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Jing Ni [email protected]
Faculty of Electrical–Electronic Engineering, Duy Tan University, Da Nang 550000, Vietnam
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College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
7
Department of Mecha
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