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Differential
quadrature and Adomian decomposition methods for solving
thermal vibration of Euler nanobeam resting on
Winkler–Pasternak foundation
Somnath Karmakar and Snehashish Chakraverty |
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Vol. 16 (2021), No. 4, 555–572
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Abstract |
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We study the effectiveness of the differential quadrature method (DQM) and the Adomian decomposition method (ADM) on free vibrations of an Euler nanobeam resting on a Winkler–Pasternak foundation in a thermal environment. The mathematical formulations and procedures to handle different boundary conditions by both methods are discussed in detail. The effects of the Pasternak foundation parameter, small scale parameter, mechanical properties of material, and thermal coefficients on vibrational frequencies are investigated. The results obtained by DQM and ADM are tabulated along with the exact results, that obtained from analytical formulations and an excellent agreement is observed. A comparative study for the convergence of DQM and ADM approaches is also carried out. |
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Keywords
Euler beam theory, differential quadrature method, Adomian
decomposition method, nonlocal elasticity
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Milestones
Received: 23 May 2021
Revised: 5 July 2021
Accepted: 9 July 2021
Published: 9 November 2021
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Authors |
| Somnath Karmakar | |
| Department of Mathematics National Institute of Technology Rourkela Rourkela 769008 India |
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| Snehashish Chakraverty | |
| Department of Mathematics National Institute of Technology Rourkela Rourkela 769008 India |
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