Vol.:(0123456789) 1 3 Journal of Vibration Engineering & Technologies (2022) 10:2151–2161 https://doi.org/10.1007/s42417-022-00499-8 ORIGINAL PAPER De‑coupling the Eigenmodes of SMA‑reinforced Bimorph Composites using Multi‑objective Optimization Rupal Srivastava 1  · Bishakh Bhattacharya 2 Received: 13 July 2021 / Revised: 22 February 2022 / Accepted: 18 March 2022 / Published online: 29 April 2022 © Krishtel eMaging Solutions Private Limited 2022, corrected publication 2022 Abstract Introduction Autonomous shape and vibration control of a structure expand its utility, thereby increasing the need for adaptive composites in the feld of aerodynamics, civil, space, and mechanical engineering. One way to achieve this is by reinforcing composites with smart materials like shape memory alloy (SMA) wires or ribbons, piezoelectric (PZT) materi- als, and magnetostrictive materials. Objectives In this study, the authors optimize the numerically solved bending behavior of SMA fber-reinforced E-glass fber-Silicone matrix composite upon thermal actuation. The study is shown for four cases (a) single layer of SMA embedded unimorph, (b) two-layers of SMA embedded bimorph, (c) single layer SMA embedded bimorph with a honeycomb core, and (d) single layer SMA embedded bimorph with an auxetic core. The vibration responses of these cases upon analysis show that the frst three eigenmodes of the unimorph and the bimorph SMA composite include bending and torsion modes and the corresponding eigenfrequencies are signifcantly close in magnitude for the Austenite fnish ( A f ) temperature. In other words, the frst natural frequency displays complex eigenmodes. A multi-objective optimization approach for SMA hybrid composite plates for de-coupling eigenfrequencies is proposed in this study. Methods The Non-dominated Sorting Genetic Algorithm (NSGA-II) is used to minimize the eigenfrequency corresponding to the frst bending eigenmode and maximize the eigenfrequency corresponding to the frst twisting eigenmode, thus increas- ing the efective diference between the two eigenfrequencies. The authors also simultaneously maximize the defection of the structures in order to obtain a considerable morphing observation. The present investigations involve determining the best laminate confguration relying on SMA fber angle orientation and SMA ply thickness as the variables. Results A complex mode or a combination of two modes at the frst eigenfrequency or complex modes can cause failure of the structure, making decoupling an essential requirement. The algorithm proposed can also be used to interchange the eigenmodes of their corresponding eigenfrequencies, thus allowing the frst natural frequency to give a twisting or torsional eigenmode and the consecutive natural frequency that of a bending mode. This technique can be used to avoid Phugoid motion-based failure in an aircraft by continuously controlling and interchanging the eigenmodes of its wings. Keywords Shape memory alloys · Adaptive composites · NSGA II · Multiobjective optimization · De-coupled eigenfrequency · Structural optimization Introduction Adaptive composites are becoming increasingly popular due to their superior adaptive characteristics, like variable stif- ness, making it amenable to tailoring structural, damping, and vibration responses. Exceptional variations in such composites’ mechanical and vibration response can be achieved by altering the lay-up, the volume fraction of fbers, fber-angle orientation, and ply thickness. Thus, adaptive composites ofer the prospect to create an extensive set of various structural output tailored for specifc needs. Several smart materials are being used as * Bishakh Bhattacharya bishakh@iitk.ac.in Rupal Srivastava rupal.srivastava@tus.ie 1 Confrm Smart Manufacturing, Science Foundation Ireland, Technological University of the Shannon: MM, Athlone, Ireland 2 Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, India