Frequency tuning of weakly and strongly coupled micromechanical beams
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ORIGINAL ARTICLE
Frequency tuning of weakly and strongly coupled micromechanical beams P. Manoj Kumar1 • Akarapu Ashok1 • Prem Pal2 • Ashok Kumar Pandey1 Received: 12 May 2020 / Revised: 18 August 2020 / Accepted: 30 August 2020 Institute of Smart Structures & Systems, Department of Aerospace Engineering, Indian Institute of Science, Bangalore 2020
Abstract Mechanical coupling forms the basis for many exciting applications in tuning the frequencies of multi-degrees of freedom systems starting from coupling the motion of fire-flies to MEMS arrays. In this paper, the influence of the weak and strong coupling between two micromechanical cantilever beams is performed using the experimental and analytical studies. To do the study, the two types of coupled micromechanical beams are taken, namely, a weakly coupled beams and a strongly coupled beams. While the weakly coupled beams are coupled along their lengths through a coupling beam of constant length and width, two strongly coupled beams are coupled through beams of varying length and constant width with one end of its length fixed at fixed portion of cantilever beam. Here, we fabricated both types of coupled beams through microfabrication process. After measuring their in-phase and out-of-phase frequencies with varying coupling parameters, the influence of coupling parameters on these two modes is investigated. It is found that one of the modes consist of a transverse mode and another a kind of torsional mode which lead to out-of-phase mode. After finding this interesting observation, further analysis is done using the corresponding analytical models of transverse and torsional modes. Furthermore, the generalized analytical models are developed to capture the effects of coupling in weakly and strongly coupled beams as a function of coupling element dimensions. Keywords MEMS resonators Mechanical coupling Frequency tunning
Introduction Electromechanical or mechanical coupling have been the subject of serious investigation to achieve desired bandwidth and sensitivity of various microelectromechanical system (MEMS) and nanoelectromechanical systems (NEMS) in the field of mass detection (Wang et al. 2015; Spletzer et al. 2006), high frequency resonators (Verbridge et al. 2007; Buks and Roukes 2002; Pandey 2013; Kambali et al. 2015; Weinstein et al. 2007; Verbiest et al. 2016; Ashok et al. 2018), optomechanical cavity Zaitsev et al. (2011), energy harvesters (Sriramdas and Pratap 2017;
P. Manoj Kumar and Akarapu Ashok contributed equally to this work. & Ashok Kumar Pandey [email protected] 1
Mechanical and Aerospace Engineering, IIT Hyderabad, Kandi 502285, India
2
Department of Physics, IIT Hyderabad, Kandi 502285, India
Sahoo and Pandey 2018; Vijayan et al. 2015), etc. To achieve the effective coupling, one need to understand the modeling of mechanical coupling through a simple structure. In this paper, we deal with two mechanically coupled micromechanical cantilever beams with weak and strong coupling, respect
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