Contents lists available at ScienceDirect Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws Full length article Large amplitude vibration of viscoelastically damped multiscale composite doubly curved sandwich shell with fexible core and MR layers Mahsa Karimiasl, Farzad Ebrahimi ∗ Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Qazvin, Iran ARTICLEINFO Keywords: Nonlinear vibration behavior Multiscale composite doubly curved shell Flexible core MR TSDT HPM applied magnetics voltage ABSTRACT Thisisthefrstresearchonthenonlinearvibrationofsmartviscoelasticcompositedoublycurvedsandwichshell with fexible core and MR layers with diferent distribution patterns. By using Reddy's third order shear de- formationtheory(TSDT),thestrainsandstressesareobtained.Thissmartmodelincludingmultiscalecomposite layers, fexible core and magnetorheological layer (MR). According to the Halpin-Tsai model three-phase composites layers have been considered. The governing equations of the multiscale doubly curved shell have beenderivedbyimplementingtheHamilton'sprinciple.Forinvestigatingcorrectnessandaccuracy,thispaperis validated by other previous studies. The results of this work are validated through the comparison with the results available researches. Finally, the infuence of diferent parameters such as temperature rise, various distributionspattern,magneticfelds,andcurvatureratiosonnonlinear frequencyresponseareinvestigatedin the details. The results presented that the multiscale doubly curved sandwich shell with fexible core show a complex behavior. 1. Introduction Vibrationandsuppressionofnoiseisamajorconcerninmanyload- bearing structures such as aerospace, marine vehicles and automotive. However, the vibration can be suppressed by vibration isolator by shifting the natural frequency, the sandwich structures with damping layers can be efectively used to overcome this issue for wide fre- quencies. Amongst these structures, sandwich cylindrical shells or pa- nels are widely used for many applications such as pressurized gas tanks, boilers and aircraft fuselage. Recently, using smart sandwich shells are signifcant because of its applicable in construction. Magnetorheological layers (MR) are one of the intelligent materials; furthermore,ithasbeenfoundthatnonlinearforcedvibrationofsmart compositestructureshasalotofapplicationsindiferentindustrialsuch as automotive, robotics, civil structures, aircraft and spacecraft, etc. One of the most signifcant forms of smart structures is their applica- tion, employing MR and fexible core in smart structures. The in- telligenceofthesmartstructureswillmakesense,weightsavings,some controloverdirectionalityinactuationandtheresultingMRefects.In recent years, it has been found that nonlinear vibration of smart com- posite structures has many applications in various industrial applica- tions such as automotive, robotics. The primary studies on MR fuids have been discovered by Jacob Rabinow(1984).Gargetal.[1]studiedthefreevibrationofcomposite doubly curved sandwich shells. In frame work Sander's theory they considered a parabolic distribution of transverse shear strains through the shell thickness. According to the frst shear deformation theory (FSDT), the thermally postbuckled plates has been studied by Lee and Lee [2].Vibration of sandwich shells made of thin layers and a mod- erately thick core are investigated by Singh [3]. He obtained natural frequencies by implementing used Rayleigh–Ritz method. The non- linear vibration of composite shells in hygrothermal environments is investigated by Naidu et al. [4]. The chaotic and nonlinear dynamics orthotropic functionally graded material (FGM) rectangular plate sub- jected to the thermal environment via third order shear deformation theory has been presented by Zhang et al. (2009). In continue, Zhang et al. (2011) presented the nonlinear dynamics of FGM circular cy- lindrical shell subjected to thermal environment based on frst order shear deformation shell theory (FSDT) and von- Karman geometric nonlinearity.Ebrahimietal.[5]investigateddynamicbehaviorofnon- homogenous piezoelectric nanobeams under magnetic feld. Ebrahimi et al. [6] presented buckling analysis of nonlocal third-order shear deformable piezoelectric nanobeams embedded in elastic medium. Nonlinear vibration of cylindrical shell in frame work higher order sheardeformationtheoryarepresentedbyAmabilietal.[7].Continued from previous work, large amplitude forced vibrations of rectangular https://doi.org/10.1016/j.tws.2019.04.020 Received5October2018;Receivedinrevisedform17March2019;Accepted15April2019 ∗ Corresponding author. E-mail address: febrahimy@eng.ikiu.ac.ir (F. Ebrahimi). Thin-Walled Structures 144 (2019) 106128 0263-8231/ © 2019 Elsevier Ltd. All rights reserved. T