Computer-aided generation of nonlinear reduced-order dynamic macromodels. II. Stress-stiffened case

Macromodels of Micro-Electro-Mechanical Systems (MEMS)

“…Reduced order modeling using modal basis functions was originally developed by [11][12][13] and has been continuously improved by several authors. The basis functions (,,) i xyz…”

“…In order to reduce the complexity of the fitting step, dominant and relevant modes are first characterized. Both the procedures in [13] and [17] can be partially automated and extended to include other conservative energy domains. Other algorithms have also been proposed for the approximation of dissipative energy terms [18,19].…”

“…The results are fitted with a rational fraction of multivariate polynomials using a nonlinear function fitting scheme. In order to model large-displacement behavior of the device, the strain energy is derived by fitting data from a set of full finite element simulations [13]. A similar procedure is proposed in [17].…”

“…The nonlinear energy terms, instead, are generally expressed as analytical functions of the modal coordinate. In [13] a single static full finite element simulation is used to determine the number of modal functions needed to capture the device behavior and their expected amplitude. Then this information is used to construct the electrostatic energy term.…”

MEMS Technologies for Energy Harvesting

“…Nonlinearity in springs appears for large deflections. For example, in the case of thin fixed-fixed beams, or tethers, it appears when the displacement of the proof mass is comparable or larger than the thickness of the springs, resulting in an increase of the strain energy due to stretching of the neutral surface, [34,35,36]. This is obviously an unwanted phenomenon in linear devices whereas it is a desired feature in those applications, such as energy harvesting, on which nonlinearity is sought as a means to increase bandwidth.…”