This study simulates the vibrations of a single-walled CNT (SWCNT) and multi-walled CNTs (MWCNTs) resting on an elastic foundation using a hinged-hinged nonlinear multi-layered-beam with a tuned mass damper (as a nano-particle) installed on the beam. The beam is supported by cubic nonlinear springs to simulate the CNTs resting on an elastic matrix. We obtained the equations of motion for the nonlinear beam using Newton’s 2nd law with Euler’s angle transformation and Taylor series expansion. The frequency in each vibration mode of a SWCNT and MWCNTs resting on a nonlinear elastic matrix was analyzed by using the method of multiple scales (MOMS) to examine the possibility of internal resonance (I.R.). This study provides a novel concept of applying a nano-particle on the top layer of the CNTs to serve as a tuned mass damper (TMD). Our results indicate that internal resonance is possible in SWCNTs resting on an elastic matrix with a level of elasticity. However, van der Waals’ forces rule out the possibility of internal resonance in MWCNTs. Furthermore, vibration reduction can be achieved in both SWCNTs and MWCNTs through the placement of nano-particle in the correct location.
Keywords: Internal Resonance, Nonlinear Vibrations, Tuned Mass Damper, Carbon Nanotubes
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