Mechanical vibration of a cylindrically rolled-up cantilever shell in microelectromechanical and nanoelectromechanical systems

The mechanical vibration of a cylindrically rolled-up cantilever shell is studied for possible use as micro- and nano-electromechanical systems. The system is modeled as an isotropic open circular cylindrical shell of rectangular planform that is clamped along one straight edge and is free on the other three edges. The mechanical vibration is calculated using both numerical and analytical methods. The frequencies of the axial wave modes strongly increase when the curvature of the shell increases because the curvature induces in-plane extension. The frequencies of the bending in the circumference direction and twisting modes show weaker curvature dependence. Frequencies as a function of the curvature for the axial wave modes obey a scaling law different from that for the bending and twisting modes. Several possible electromechanical coupling mechanisms in micro- and nano-electromechanical systems are considered.