Frequency simulation of viscoelastic multi-phase reinforced fully symmetric systems
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ORIGINAL ARTICLE
Frequency simulation of viscoelastic multi‑phase reinforced fully symmetric systems M. S. H. Al‑Furjan1,2 · Mostafa Habibi3,4 · Jing Ni1 · Dong won Jung5 · Abdelouahed Tounsi6 Received: 27 July 2020 / Accepted: 8 October 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Honeycomb structures have the geometry of the lattice network 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 multiscale hybrid nanocomposite (MHC) face sheets rested on an elastic foundation. 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 quad‑ rature method (GDQM). Afterward, a parametric study is done to present the effects of the orientation of fibers ( 𝜃f ∕𝜋 ) in the epoxy matrix, Winkler–Pasternak constants ( Kw and Kp ), thickness to length ratio of the honeycomb network ( th ∕lh ), the weight fraction of CNTs, value fraction of carbon fibers, angle of honeycomb networks, and inner to outer radius ratio on the frequency of the sandwich disk. The results show that it is true that the roles of Kw and Kp are the same as an enhancement, but the impact of Kw could be much more considerable than the effect of Kp on the stability of the structure. Additionally, when the angle of the fibers is close to the horizon, the frequency of the system improves. Keywords Sandwich disk · Honeycomb core · Elastic foundation · GDQM · Imperfection multiscale hybrid laminated nanocomposite · Frequency characteristic * Mostafa Habibi [email protected] * Dong won Jung [email protected] * Abdelouahed Tounsi [email protected] M. S. H. Al‑Furjan [email protected] Jing Ni [email protected] 1
School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China
2
State Key Laboratory of Silicon Materials, School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China
3
Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
4
Faculty of Electrical‑Electronic Engineering, Duy Tan University, Da Nang 550000, Vietnam
5
Departement of Mechanical Engineering, Jeju National University, Jeju 690‑756, South Korea
6
Yonsei Frontier Lab, Yonsei University, Seoul, South Korea
List of symbols h, Ri, and Ro Thickness, the inner and outer radius of the disk, respectively CNTs Carbon nanotubes F and NCM Fiber and nanocomposite matrix, respectively 𝜌, E, 𝜈 and G The density, Young’s modu‑ lus, Poisson’s ratio, and shear parameter, respectively VNCM, VF Volume fractions of the nanocomposite matrix and fiber, respectively lCNT, tCNT, dCNT, ECNT and VCNT The length,
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