**ABSTRACT**

In this work, analytical investigations of the combined effects surface elasticity, initial stress, residual surface tension and nonlocality on the nonlinear vibration of single-walled carbon conveying nanotube resting on linear and nonlinear elastic foundation and operating in a thermo-magnetic environment. The developed equation is solved using Galerkin’s decomposition and regular perturbation methods. Parametric studies are presented using the approximate analytical solutions. The results revealed that the ratio of the nonlinear to linear frequencies increases with the negative value of the surface stress while it decreases with the positive value of the surface stress. At any given value of nonlocal parameters, the surface effect reduces for increasing in the length of the nanotube. ratio of the frequencies decreases with increase in the strength of the magnetic field, nonlocal parameter and the length of the nanotube. The natural frequency of the nanotube gradually approaches the nonlinear Euler–Bernoulli beam limit at high values of nonlocal parameter and nanotube length. nonlocal parameter reduces the surface effects on the ratio of the frequencies. Increase in temperature change at high temperature causes decrease in the frequency ratio. However, at room or low temperature, the frequency ratio of the hybrid nanostructure increases as the temperature change increases. Also, the ratio of the frequencies at low temperatures is lower than at high temperatures. The present work will assist in the control and design of carbon nanotubes operating in thermo-magnetic environment and resting on elastic foundations.

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