Modelling a micro-cantilever vibrating in vacuum,gas or liquid under thermal base excitation |
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| Affiliation: | 1. Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, 1, Academician Zuev Square, 634021 Tomsk, Russia;2. Laboratory of Molecular Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, 1, Academician Zuev Square, 634021 Tomsk, Russia;3. Laboratory of Atmospheric Absorption Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, 1, Academician Zuev Square, 634021 Tomsk, Russia;1. Federal University of Uberlândia, Av. João Naves de Ávila, n. 2121, Uberlândia, MG, Brazil;2. Technological Institute of Aeronautics, Praça Marechal Eduardo Gomes, 50, São José dos Campos, SP, Brazil;1. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;2. Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, China;1. Air Force Research Laboratory, 3550 Aberdeen Ave SE, Kirtland Air Force Base, NM 87117, United States;2. Leidos, 2109 Air Park Rd SE, Albuquerque, NM 87106, United States |
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| Abstract: | The dynamic behaviour of a micro-cantilever that is transversely excited at its base is investigated in this paper. The base actuation is provided by thermal cycles via taking the advantage of thermal expansion. The Euler–Bernoulli equation along with corresponding boundary conditions is used to model the continuous cantilever beam. The resultant boundary value problem takes into account the thermal expansion and stiffness of the actuator at the base as well as the effect of the surrounding gas or liquid. A closed-form analytical model is developed to compute natural frequencies, mode shapes, and harmonic response of the vibrating cantilever, in addition to an integral function for quality factor. The model is validated via a finite element (FE) analysis using ANSYS commercial package. This validation shows that the proposed model can properly predict the cantilever's vibrating behaviour. |
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| Keywords: | Micro-electro-mechanical systems (MEMS) Micro-cantilever beam Harmonic response Thermal excitation Fluid dynamics |
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