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**Reduced-order models for MEMS applications.**
*(English)*
Zbl 1142.74327

Summary: We review the development of reduced-order models for MEMS devices. Based on their implementation procedures, we classify these reduced-order models into two broad categories: node and domain methods. Node methods use lower-order approximations of the system matrices found by evaluating the system equations at each node in the discretization mesh. Domain-based methods rely on modal analysis and the Galerkin method to rewrite the system equations in terms of domain-wide modes (eigenfunctions). We summarize the major contributions in the field and discuss the advantages and disadvantages of each implementation. We then present reduced-order models for microbeams and rectangular and circular microplates. Finally, we present reduced-order approaches to model squeeze-film and thermoelastic damping in MEMS and present analytical expressions for the damping coefficients. We validate these models by comparing their results with available theoretical and experimental results.

### MSC:

74F15 | Electromagnetic effects in solid mechanics |

76D08 | Lubrication theory |

78A55 | Technical applications of optics and electromagnetic theory |

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\textit{A. H. Nayfeh} et al., Nonlinear Dyn. 41, No. 1--3, 211--236 (2005; Zbl 1142.74327)

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