Partitioning design space for linear tuning of natural frequencies in planar dynamic MEMS structures

One of the critical design considerations in dynamic microelectromechanical systems (MEMS) devices is the structural natural frequency of the sensing or actuation element. Most dynamic MEMS devices employ planar geometry using an assembly of beams and plates for the structural elements. Most often the goal is to place the first resonant frequency at a desired value. Since the frequency depends on mass and stiffness of the structure, designing for frequency usually requires FEM analysis of the structure. FEM calculations are intensive, depend on many subtle modelling assumptions, and require huge number of simulations to build intuition. Since the design space for such structures is fairly high dimensional, tuning the frequency of the first-cut design can be a fairly intensive optimization computation. Here, we present a lumped parameter spring-mass model for a typical microstructure consisting of a plate and beams and show how the higher dimensional geometric design space can be partitioned to effect desired frequency changes in the structure linearly with the chosen design variables. In particular, four sets of design variables are considered and their effective range and sensitivity for linear tuning of the natural frequency is presented. We include the effect of residual stress on stiffness and show how the values of residual stress affect the tuning of the natural frequency with respect to the selected design variables. All results are compared with FEM calculations and a table is presented for cross comparison of efficacy of the different design variables. The goal is to present a simple analysis that can be easily followed by MEMS designers with any background and build their intuition for such designs.