Anharmonic vibrations of a nano-sized oscillator with fractional damping |
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| Institution: | 1. Department of Mechanics and Vibrations, Polytechnic University of Timisoara, Bd. M. Viteazu, No. 1, 300222 Timisoara, Romania;2. Department of Physics, West University of Timisoara, Bd. V. Pârvan, No. 4, 300223 Timişoara, Romania;1. Department of Obstetrics and Gynecology, Vanderbilt University Medical Center, Nashville, TN;2. Department of Obstetrics and Gynecology, University of Washington School of Medicine, Seattle, WA;3. Department of Obstetrics and Gynecology, Virginia Commonwealth University School of Medicine, Richmond, VA;4. Department of Obstetrics and Gynecology, Stony Brook Medicine, Stony Brook, NY;5. Department of Obstetrics and Gynecology, Tufts Medical Center, Boston, MA;6. Department of Obstetrics and Gynecology, University of Michigan Medical School, Ann Arbor, MI;1. Department of Applied Physics and Nanomaterials Science, Lviv Polytechnic National University, 5 Ustiyanovych St., 79013 Lviv, Ukraine;2. Department for Theoretical Physics, Ivan Franko National University of Lviv, 12, Drahomanov St., Lviv, 79005, Ukraine |
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| Abstract: | We investigate the nonlinear vibrations of nano-sized cantilever. The elastic force is considered anharmonic, deriving from a Morse potential and the nonlinearity is attributed to the Casimir force. We consider two cases, the first of viscous damping and the second of fractional damping.The solution is also established by using the Adomian decomposition method. |
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