Application of singular elements for fully Lagrangian modeling of dynamics of MEMS with thin beams

The problem of coupled electro-mechanical vibration of a thin micro-electro-mechanical system (MEMS) beam has been recently addressed by Ghosh and Mukherjee (2009) [1]. A singularity in charge density and force usually arises at the corners of a free edge in such beams. This is of little consequence in clamped–clamped beams (addressed in [1], Ghosh and Mukherjee, 2009) because the edges are restrained. For cantilevered beams, however, such singularities on its free edge deserve attention. The present paper addresses the above problem for a cantilevered beam. The boundary element next to the free edge of the beam is treated as singular. Numerical results for static deflections as well as vibrations of the cantilevered beams from the two methods (singular element and nonsingular elements analogous to [1], Ghosh and Mukherjee, 2009) are compared and discussed.