Dynamic instability analysis of doubly clamped cylindrical nanowires in the presence of Casimir attraction and surface effects using modified couple stress theory

The dynamic instability of free-standing size-dependent nanowires by considering the Casimir force and surface effects is investigated in the following research work. The study is carried out for nanosystems with circular cross section and cylinder-plate geometry for which the governing equation of motion is derived based on the Gurtin-Murdoch model and modified couple stress theory. Two methods including the proximity force approximation for small separations and Dirichlet asymptotic approximation for large separations are utilized to formulate the Casimir attraction of a free-standing cylinder-plate geometry. To solve the complex nonlinear problem faced in this work, a stepwise numerical procedure is developed and the effects of length scale parameter, surface energy and vacuum fluctuations on the dynamic instability and adhesion time of nanowires are studied. Based on the obtained results, the phase portrait of Casimir-induced nanowires shows periodic and homoclinic orbits.