Nonlinear Structural Mechanics of Micro-and Nanosystems

In the nanoscale, when trying to fabricate straight clamped-clamped single-walled CNT transistors, the outcome comes as nonperfectly straight beam with an initial curvature, also called slack. Hence, we can see that understanding the dynamics of arches serve both the micro-and nanoworlds. The dynamic behavior of CNTs also is greatly needed. Researchers have several reported unexplained and unjustified phenomena for electrically actuated slacked CNTs. These include multiple resonances, frequency crossing, frequency avoiding of crossing (veering), undistinguished resonances whether they are out-of-plane or in-plane, unexplained low values of quality factor, etc. A robust model of these complicated structures can reveal many of their dynamical related issues. In the first part of this chapter, we summarize the main contributions in the area of modeling the structural mechanics of carbon nanotubes used as NEMS devices. We also address the need to add the slack effect when modeling CNTs. Then, we introduce general concepts (essentially reduced-order modeling and perturbation technique) in modeling the nonlinear structural mechanics problems of beams under several loading conditions (mainly electric actuation). We also include derivation of the equations of motion of MEMS arches along with discussing some conditions for applicability of the continuum theory in modeling the mechanical behavior of CNTs. In the second part of this chapter, we present an investigation into modeling and analyzing the nonlinear structural mechanics of electrically actuated carbon nanotube resonators. We investigate in details the nonlinear structural mechanics of such devices including the effect of their initial curvature (level of slack). We present a framework and a platform to properly understand the dynamics of these complicated systems by explaining and revealing the meaning of their various detected resonance