Dynamics and vibration analysis of an electrostatically actuated FGM microresonator involving flexural and torsional modes

• Published in: International journal of mechanical sciences Vol. 148; pp. 422 - 441
• Main Authors: Shoghmand, A., Ahmadian, M.T.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2018
• Subjects: Functionally graded material; MEMS; Microresonator; Modal interactions; Natural frequencies; Pull-in voltages; Microresonator; MEMS; Pull-in voltages; Modal interactions; Functionally graded material; Natural frequencies
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2018.08.003

•A nonlinear pedal like FGM microresonator under electrostatic actuation is modeled.•Both softening-type and hardening-type behaviors are observed in the system.•Pull-in voltages are calculated for various FG material profiles and gap distances.•Internal resonance of 1:2 ratio between the two modes of the system is studied.•Using FG material provides a wider frequency bandwidth during design process. In this paper a nonlinear pedal like microresonator made of Functionally Graded material is introduced and modeled. Using Lagrangian formulation nonlinear equations of motion of the system are derived and the natural frequencies and mode shapes are extracted by linear analysis. The effects of various parameters such as geometry, FG material index and DC voltages on the natural frequencies and mode shapes are investigated. Static pull-in voltages of the system are obtained and it is found that depending on the type of actuation, both softening and hardening behaviors can be observed in the system. The results are compared with previous studies and finite element method where a good agreement is achieved. A two-mode reduced order model along with first-order averaging technique is implemented to derive the asymptotic dynamic equations of motion. The effects of different parameters including AC actuation level, damping and material power index on the dynamic response of the system are studied around resonance conditions. It is observed that when the system parameters are adjusted properly, the directly excited in-plane mode, in turn excites the out-of-plane torsional mode of the structure through internal resonance of 1:2 ratio within a specific frequency bandwidth. A wide range of frequency will be available by changing only the power index of the material and the system can be manipulated to be used in various MEMS applications such as mass sensors and RF filter-mixer devices. [Display omitted]