A Variable Reduction Approach for Microbeams on Elastic Foundation

In this paper, the bending behavior of microbeams resting on elastic foundations is analyzed. Due to the widespread use of Micro-Electro-Mechanical Systems (MEMSs) in sensing and actuation applications, various approaches have been developed for modeling such beams. Numerous specialized analytical and numerical models exist for specific configurations of beams and elastic foundations. This work proposes a novel approach. Separate models for the beam and the elastic foundation are developed using the finite element method. These models are then coupled using a variable reduction technique, in which only the degrees of freedom of the beam are retained in the solving system. This approach enables the coupling of any beam and foundation model and allows for independent refinement of the foundation mesh without increasing the size of the solving system. This method is particularly effective for analyzing configurations where the substrate exhibits nonlinear or non-homogeneous characteristics, or where gaps are present between the beam and the substrate. The nonlocal effects due to the small scale of the beam are also considered. This paper focuses on both the static deformation and frequency response of the microbeam. The proposed approach is validated against previously published models. Compared with existing models, the method presented here offers a simpler and more flexible formulation, while allowing the inclusion of nonlinearities in both the beam and foundation, as well as the modeling of gaps.