This work investigates the thermo-mechanical vibration frequencies of an embedded composite nano-beam restrained with elastic springs at both ends. Composite nanobeam consists of a matrix and short fibers as reinforcement elements placed inside the matrix. An approach based on Fourier sine series and Stokes' transform is adopted to present a general solution that can examine the elastic boundary conditions of the short-fiber-reinforced nanobeam considered with the Halpin-Tsai model. In addition to the elastic medium effect considered by the Winkler model, the size effect is also considered on the basis of non- local strain gradient theory. After creating an eigenvalue problem that includes all the mentioned parameters, this problem is solved to examine the effects of fiber and matrix properties, size parameters, Winkler stiffness and temperature change. The numerical results obtained at the end of the study show that increasing the rigidity of the Winkler foundation, the ratio of fiber length to diameter and the ratio of fiber Young's modulus to matrix Young's modulus increase the frequencies. However, thermal loads acting in the positive direction and an increase in the ratio of fiber mass density to matrix mass density lead to a decrease in frequencies. In this study, it is clear from the eigenvalue solution calculating the frequencies of thermally loaded embbeded short-fiber-reinforced nanobeams that changing the stiffness of the deformable springs provides frequency control while keeping the other properties of the nanobeam constant.
Uzun et al. (Sun,) studied this question.