On the phase velocity simulation of the multi curved viscoelastic system via an exact solution framework

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ORIGINAL ARTICLE

On the phase velocity simulation of the multi curved viscoelastic system via an exact solution framework M. S. H. Al‑Furjan1,2 · Masoud Mohammadgholiha3 · Ibrahim M. Alarifi4 · Mostafa Habibi5,6 · Hamed Safarpour7  Received: 4 August 2020 / Accepted: 17 August 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020

Abstract The analysis of the wave propagation behavior of a sandwich structure with a soft core and multi-hybrid nanocomposite (MHC) face sheets is carried out in the framework of the higher-order shear deformation theory (HSDT). In order to take into account the viscoelastic influence, the Kelvin-Voight model is presented. In this paper, the constituent material of the core is made of an epoxy matrix which is reinforced by both macro- and nano-size reinforcements, namely carbon fiber (CF) and carbon nanotube (CNT). The effective material properties like Young’s modulus or density are derived utilizing a micromechanical scheme incorporated with the Halpin–Tsai model. Then, on the basis of an energy-based Hamiltonian approach, the equations of motion are derived. The detailed parametric study is conducted, focusing on the combined effects of the viscoelastic foundation, CNT’ weight fraction, core to total thickness ratio, small radius to total thickness ratio, and carbon fiber angle on the wave propagation behavior of sandwich structure. The results show that as well as increasing the phase velocity of the sandwich structure by increasing the wave number, this influence will be much more effective by increasing the damping factor. It is also observed that there is a critical value for the viscoelastic foundation that the relation between wave number and phase velocity will change from direct to indirect. The presented study outputs can be used in ultrasonic inspection techniques and structural health monitoring. Keywords  Kelvin-voight model · Multi-scale hybrid nanocomposite reinforcement · Elastic core · Doubly curved panel · Compatibility equations

1 Introduction A key issue in the various engineering fields is that the prediction of the properties, behavior, and performance of different systems is an important aspect [1–12]. It is well * Mostafa Habibi [email protected] * Hamed Safarpour [email protected] M. S. H. Al‑Furjan [email protected] Masoud Mohammadgholiha [email protected] Ibrahim M. Alarifi [email protected] 1



School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China



School of Materials Science and Engineering, State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou 310027, China

2

knowen that the compositionally structures have a intresting thermo-electro-mechanical property and this matter is being an esential fact to get the attention of all engineering fields of reaserches for having efficient productions with the aid of composite structure, especially carbon-based nanofillers 3



Department of Civil Engineering, K. N. Toosi University of Technology, Valiasr Street, P.O.