BEM modeling of damping forces on MEMS with thin plates

An incompressible fluid Stokes flow model is often useful for the determination of damping forces on Micro-Electro-Mechanical (MEM) structures. Such structures in the shape of thin beams and plates are of primary interest in this work. Two difficulties arise with the standard Boundary Element Method (BEM) analysis of this problem. The first is that the usual Stokes kernel is singular; the second is numerical ill conditioning of the stiffness matrix owing to the plates being thin. A novel approach is proposed in this paper to take care of both these problems in a simple and effective manner. Sample numerical results for some simple illustrative problems are given in this paper.