Dynamic analysis of restrained short‐fiber‐reinforced and functionally graded nanobeams via stress‐driven model

Abstract In this work, the lateral dynamic response of two types of restrained composite nanobeams is studied. One of these nanobeams consists of a functionally graded composite material, while the other is in the form of a matrix reinforced with short fibers. These composite nanobeams rest on deformable springs. In the dynamic problem, stress‐driven theory is considered to highlight the small‐scale effect. To provide the general solution for calculating the free lateral vibration frequencies of the composite nanobeams, Fourier sine series and Stokes’ transform are utilized. The effects of damping on the dynamic behavior of nanobeams are also demonstrated using the Kelvin–Voigt viscoelastic model. After the mathematical steps, a general eigenvalue problem is derived that includes small‐scale, elastic spring, and damping effects. The validation of the model and the effects of various parameters on the free lateral vibration frequencies of the restrained composite nanobeams are presented in tables and graphs.