Spurred by the discovery of carbon nanotubes in 1991 and the succeeding neuropsychology revolution, there has been a marked increase in the volume of scientific and engineering literatures. Carbon nanotubes (CNTs) have aroused great interest in the scientific community because of their exceptional mechanical, electronic, electrochemical, and thermal properties. The CNTs hold exciting promise in useful potential applications, as electrodes in supercapacitors, as cable materials for space elevators, as structural elements in nanoscale devices and reinforcing element in superstrong and conducting nanocomposites. Particularly, great numbers of researchers dealt with various aspects of the vibratory behavior of carbon nanotubes and their composites in the last few years. Hence, understanding the mechanical and physical properties of CNTs is essential for their applications. The study of vibration in CNTs is a major topic of current interest, which is used to understand the dynamic behavior of CNTs. This study is concerned with the use of the nonlocal Euler-Bernoulli elastic beam model to analyze the vibrational behavior of CNTs under a thermal environment. Both Pasternak-type and Winkler-type models is used for simulating the interaction of the CNT and the elastic medium. The influence of nonlocal effects, thermal changes, Winkler constant and Pasternak shear modulus are obtained. Furthermore, different boundary conditions such as clamped-clamped, pinned-pinned, clamped-pinned end conditions have been used to calculate the vibrational natural frequencies of CNTs.

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