Nonlinear Free Vibrations of a Carbon Nanobeam Carrying an Elastically Mounted Concentrated Mass

Abstract

In the present study, the interaction of nonlocal parameters with linear mode shapes and nonlinear forced frequency response of Rayleigh nanobeam system connected to a suspended mass-spring-damper is examined. For this purpose, the dimensionless vibration equations governing the system based on the theory of displacement elasticity are extracted using the power series and the Green function concept considering the Kelvin-Voigt viscoelastic damping. Also, the method of multiple scales is considered to derive the equations of motion. Then, the forced response of the system under the extensive uniform harmonic external force is analyzed around the first natural frequency and the occurrence of the initial resonance. In order to examine the frequency response, nonlocal parameter, and system parameters, a degree of freedom is considered. Thus, the modal interaction occurs through the initial resonance. To validate the results of this study, the natural frequencies of the system with the results of the previous research are also compared with a beam without a mass-spring-damper and based on the same assumptions. Accordingly, it is revealed that increasing the mass-spring-damper leads to changing the amplitude in the nanobeam oscillation. The novelty of the paper lies in the combination of a continuous system with a discontinuous system by nanomaterials in the form of free and forced vibrations. A detalied look at the literature reveals that the analysis of free and forced vibrations using nonlocal theories is presented for the first time here.