Theses and Dissertations

Date of Award


Document Type


Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Dr. Dumitru Caruntu

Second Advisor

Dr. Dorina Chipara

Third Advisor

Dr. Nazmul Islam


This work deals with the amplitude-frequency and amplitude-voltage responses of parametric and primary resonances of electrostatically actuated double-walled carbon nanotubes (DWCNTs). Nonlinear forces acting on the DWCNT are intertube van der Waals and electrostatic forces. Soft AC excitation and small viscous damping are assumed. In coaxial vibration, the outer and inner carbon nanotubes move together (in-phase), maintaining their geometric concentricity; while in noncoaxial vibration, the CNTs move in opposite direction (out-of-phase). Modal coordinate transformation is formulated. The Harmonic Balance Method (HBM) is used to find the free response solutions of the DWCNT. The Reduced Order Model (ROM) method is also used in this investigation. All ROMs using one through five modes of vibration (terms) are developed in terms of modal coordinates. ROM using one term is solved and frequency-amplitude response predicted by using the Method of Multiple Scales (MMS). All models and methods are in agreement at lower amplitudes for coaxial vibration, while in higher amplitudes only ROM with five terms provides reliable results. The effects of voltage, detuning frequency, and damping on the various resonance responses of electrostatically actuated DWCNTs are reported. A discussion of stability and bifurcation analysis is presented.


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