Smart control of cylindrical shells incorporating Murakami Zig-Zag function N. Mehadi Khan, R. Suresh Kumar ⇑ Department of Mechanical Engineering, National Institute of Technology Raipur, G. E. Road, Raipur, Chhattisgarh-492010, India ARTICLE INFO Keywords: Finite element method (FE) Smart damping Piezoelectric composite (PZC) Murakami zig‐zag function (MZZF) Cylindrical shells ABSTRACT The work is devoted towards incorporating the Murakami zig‐zag function (MZZF) for modelling the active constraining layer damping (ACLD) treatment of ‘N’ layered laminate cylindrical shells. The ACLD treatment in the patch form comprises of two material layers with the viscoelastic material layer constrained between the host shell and the smart 1–3 piezoelectric composite (PZC) material layer. The kinematics of deformation are derived successfully implementing the MZZF in the displacement fields. Virtual work principle has been employed for the finite element (FE) model to deduce governing equations of shell ACLD system in complete form. A feed‐back control system has been considered to arrive at closed loop governing equations of motion. Considering the above, a MATLAB code for the same is generated to emphasise on dynamics of the cylindrical shell ACLD system. Cylindrical shells with various lamination schemes have been considered to assess the validity and implementation of MZZF for ACLD treatment of shells. Also, the oblique orientation of the 1–3 PZC material layer and its effect on the damping behavior of the cylindrical shell has been thoroughly explored. 1. Introduction Composite materials in the layered form have been used exten- sively in almost all the engineering fields due to their excellent specific strength, ability to be tailormade and corrosion resistance. Due to the discontinuities between the individual layers of the laminates, the behavior of the same are anisotropic in nature. The low values of trans- verse to in‐plane modulus results in higher transverse shear resulting in the zig‐zag effect, which needs to be accounted for. The responses of the laminated cylindrical shells which differ from that of the plates have been accurately studied by many researchers by the use of differ- ent theories like the FSDT, HSDT and shell theories [1–6]. However, the inherent zig‐zag behavior of the structures composed of laminates is not taken care of using the FSDT and HSDT. Hence, the existing layer wise theories can be modified by incorporating the zig‐zag effect to accurately predict the behavior of the layered structures. Also, the zig‐zag effect considerations leads to many advantages like the degrees of freedom (DOF) become layer independent resulting in use of fewer numbers of variables and hence reduction in the overall computation time. To overcome these drawbacks, Murakami zig‐zag function (MZZF) has been proposed by Murakami [7] to acoount for these effects. Carrera and his team of researchers [8–13] employed this MZZF effectively in studying the behavior of plates and shells with laminates both statically and dynamically. Recently, Cinefra [14] investigated free vibration analysis of laminated composite shell struc- tures using trough the thickness variable kinematic model in the framework of Carrera unified formulation methods. The low damping nature of the layered structures poses a threat of vibration induced failures and hence to address this issue a concept called smart structure [15] has been developed. These type of struc- tures usually comprises of host mechanical member (either beam, plate or shell) embedded with smartness adding material like the piezoelectric material. When this smart material is supplied with con- trol voltage, the enhancement in damping of the entire structure is observed which makes the overall structure safe during operation [15,16]. Recently, Cinefra et al. [17] presented static response of com- posite laminates embedded with piezoelectric layers using Carrera Unified Formulation and applying refined plate models. Both equiva- lent single layer and layer wise approaches with axiomatic/asymptotic techniques were applied and governing equations were obtained con- sidering Navier‐type, closed‐form solutions. Cinefra and Carrera [18] presented finite element analysis of multi‐layered composite structures based on Carrera unified formulation undergoing thermal and elec- tromechanical loads. Static deflection and stresses evaluated using Mixed Interpolation of Tensorial Components (MITC) shell finite ele- ments for both thick and thin laminated structures. Zappino et al. [19] studied dynamic analysis of beam structures embedded with https://doi.org/10.1016/j.compstruct.2020.113044 Received 15 July 2020; Revised 19 September 2020; Accepted 24 September 2020 Available online xxxx 0263-8223/© 2020 Published by Elsevier Ltd. ⇑ Corresponding author. E-mail address: rskumar.me@nitrr.ac.in (R. Suresh Kumar). Composite Structures xxx (2020) 113044 Contents lists available at ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct Please cite this article in press as: Khan NM, Suresh Kumar R. Smart control of cylindrical shells incorporating Murakami Zig-Zag function. Compos Struct (2020), https://doi.org/10.1016/j.compstruct.2020.113044