Size-dependent dynamics of a FG Nanobeam near nonlinear resonances induced by heat |
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| Institution: | 1. Department of Mechanical Engineering, Urmia University, Urmia, Iran;2. Urmia University of Technology, Urmia, Iran;3. College of Engineering, Swansea University, Bay Campus, Fabian Way, Swansea, SA1 8EN United Kingdom;4. South Ural State University, Chelyabinsk, Russian Federation;1. College of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou, Zhejiang, 325035, China;2. School of Surveying and Geospatial Engineering, College of Engineering, University of Tehran, Tehran, Iran;3. Department of Computer Science, School of Computing, National University of Singapore, Singapore, Singapore;4. Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam;1. Young Researchers and Elite Club, Islamshahr Branch, Islamic Azad University, Islamshahr, Iran;2. Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran;3. Institute of Nanoscience & Nanotechnology University of Kashan, Kashan, Iran;4. Department of Mechanical Engineering, Islamshahr Branch, Islamic Azad University, Tehran, Iran;5. Environmental Sciences Research Center, Islamshahr Branch, Islamic Azad University, Tehran, Iran |
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| Abstract: | This study explores heat-induced nonlinear vibration of a functionally graded (FG) capacitive nanobeam within the framework of nonlocal strain gradient theory (NLSGT). The elastic FG beam, which is firstly deflected by a DC voltage, is driven to vibrate about its deflected position by a periodic heat load. The nano-structure, which consists of a clamped-clamped nanobeam, is modeled assuming Euler–Bernoulli beam assumption which accounts for the nonlinear von-Karman strain and the electrostatic and intermolecular forcing. To simulate the static and dynamic responses, a model reduction procedure is carried out by employing the Galerkin method. The method of Averaging as a regular semi-analytic perturbation method is applied to obtain governing equations of the steady-state responses. With the purpose of establishing the validity of the solution, a Shooting technique in conjunction with the Floquet theory is used to capture the periodic motions and then examine their stability. The nonlinear resonance frequency of the FG nanobeam near its fundamental natural frequency (primary resonance) and near principal parametric resonance is investigated while the emphasis is placed on studying the effect of various parameters including DC voltage, amplitude of the periodic heat source, material index, damping ratio, and small scale parameters. The main objective of this study is to model a miniature structure which can be used as either a sensitive remote temperature sensor or a high-efficiency thermal energy harvester. |
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