Computers, Materials & Continua CMC, vol.62, no.3, pp.1001-1023, 2020 CMC. doi:10.32604/cmc.2020.08052 www.techscience.com/journal/cmc Free Vibration Analysis of FG-CNTRC Cylindrical Pressure Vessels Resting on Pasternak Foundation with Various Boundary Conditions Mohammad Arefi 1 , Masoud Mohammadi 1 , Ali Tabatabaeian 1 and Timon Rabczuk 2, * Abstract: This study focuses on vibration analysis of cylindrical pressure vessels constructed by functionally graded carbon nanotube reinforced composites (FG-CNTRC). The vessel is under internal pressure and surrounded by a Pasternak foundation. This investigation was founded based on two-dimensional elastic analysis and used Hamilton’s principle to drive the governing equations. The deformations and effective- mechanical properties of the reinforced structure were elicited from the first-order shear theory (FSDT) and rule of mixture, respectively. The main goal of this study is to show the effects of various design parameters such as boundary conditions, reinforcement distribution, foundation parameters, and aspect ratio on the free vibration characteristics of the structure. Keywords: FG-CNTRC cylindrical pressure vessel, first-ordershear deformation theory, free vibration, Pasternak’s foundation, rule of mixture. 1 Introduction Pressure vessels construct an essential part of industrial equipment. They are under high levels of stresses and temperatures. Also, one of the expensive tools in an industrial unit is the pressure vessel. These critical points caused researchers and companies to release analyzing approaches and design guidelines for pressure vessels. More recently, one of the popular subjects is to use of composite materials, especially functionally graded materials (FGMs), for fabricating pressure vessels and other industrial equipment [Miao, Chen, Wang et al. (2014)]. Functionally graded carbon nanotube reinforced composites (FG-CNTRCs) were comprehensively analyzed for various functions. They showed a strong bending performance and reducing effects on residual stresses [Arefi, Faegh and Loghman (2016)]. All of these studies expressed that addition of carbon nanotubes into the base material increases stiffness of the structure and decreases deflections. 1 Department of Solid Mechanic, Faculty of Mechanical Engineering, University of Kashan, Kashan 87317- 51167, Iran. 2 Duy Tan University, Institute of Research & Development, 3 Quang Trung, Danang, Vietnam. * Corresponding Author: Timon Rabczuk. Email: timon.rabczuk@uni-weimar.de.