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For the first time, this work employs analytic solutions to study static bending, as well as free and forced vibrations of organic nanobeams, including the impact of temperature. Calculation formulas are developed on the basis of the third-order shear strain theory of thickness. These formulas also account for the influence of the size effect by using nonlocal parameters. In contrast to the findings of earlier research on nanobeams, the nonlocal parameter in this investigation fluctuates with beam thickness. In addition to this, the viscous drag parameter of the beam is taken into consideration, which further complicates the calculation method, but this is also the new point of this work. The equation is developed using the potential work principle, and the Navier form solution is used to solve the resulting equilibrium equations. Nanobeams' natural frequency and static displacement have both real and complicated components …