Article Journal of Vibration and Control 2019, Vol. 0(0) 1–17 © The Author(s) 2019 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/1077546319889857 journals.sagepub.com/home/jvc Free vibration analysis of hybrid laminated composite cylindrical shells reinforced with shape memory alloy fibers Morteza Nekouei 1 , Mehdi Raghebi 1  and Meisam Mohammadi 2 Abstract In the present paper, vibration behavior of hybrid laminated composite cylindrical shells reinforced with shape memory alloy fibers is investigated. Material properties of shape memory alloy fibers and composites are accurately considered temperature dependent. Thermo-mechanical properties of shape memory alloy fibers with uniform temperature change are calculated using Brinson’ s one-dimensional constitutive law. Love’ s first approximation and first-order shear de- formation theory of shells with the von K´ arm´ an type of geometrical non-linearity are used in conjunction with Hamilton’ s principle for deriving the equations of motion. The generalized differential quadrature method is employed to solve the coupled partial differential equations. The effects of pre-strain, volume fraction, phase transformation, location of shape memory alloy fibers, boundary conditions and temperature on the fundamental frequency of the hybrid laminated composite cylindrical shells are studied. Results indicate that a small amount of shape memory alloy fibers significantly increases the fundamental frequency and vibration control of the hybrid laminated composite reinforced with shape memory alloy hybrid laminated composite cylindrical shells. Keywords Hybrid laminated composite cylindrical shells, shape memory alloy fibers, Brinson constitutive model, free vibration, temperature dependency, generalized differential quadrature method 1. Introduction Shape memory alloys (SMAs) are a special category of smart materials that are capable of remembering their original shape under thermal and/or mechanical loadings via solid-to-solid phase transformation between austenite (at high temperature and low stress) and martensite (at low temperature and high stress). Two unique mechanical be- haviors of SMAs result from this transformation: the shape memory effect, which is the ability to recover a large re- sidual strain via heating in martensite to austenite phase transformation, and the pseudo-elastic effect, which is the ability to achieve a very large strain during the loading- unloading cycle that is fully recovered in a hysteresis loop at a sufficiently high temperature. These exciting properties enable SMA to be used as actuators, couplers and vibration dampers in the civil structure (Song et al., 2006) and aerospace (Hartl and Lagoudas, 2007). Also, Nitinol (NiTi), the most popular SMA, is biocompatible, leading to the application of SMAs in biomedical, assistive, and re- habilitation devices (Nematollahi et al., 2019). Since their discovery (Buehler et al., 1963), SMAs have been increasingly admitted as an engineering solution for various problems. Therefore, numerous research efforts have focused on development of new alloys such as high- temperature SMAs, magnetic SMAs and shape memory polymers or creation of hybrid materials that combine the characteristics of existing materials. The latter possibility holds more excitement with respect to SMAs by combining one (or more) SMA phases with other materials, novel material systems with both specific effective thermo-elastic and transformation behaviors may be created. Such a con- cept incorporates materials using SMAs as reinforcement in composites. Efforts into this area started when Rogers and Robertshaw (1988) first embedded Nitinol wires in a lam- inated polymer matrix composite. Subsequently, empirical 1 Department of Mechanical Engineering, University of Birjand, Iran 2 Department of Mechanical Engineering, Vali-e-Asr University of Rafsanjan, Iran Received: 12 May 2019; accepted: 17 September 2019 Corresponding author: Mehdi Raghebi, Department of Mechanical Engineering, University of Birjand, University Blvd., Birjand, Southern Khorasan, Iran. Email: raghebi@birjand.ac.ir