Differential quadrature and Adomian decomposition methods for solving thermal vibration of Euler nanobeam resting on Winkler–Pasternak foundation

Karmakar, Somnath; Chakraverty, Snehashish

doi:10.2140/jomms.2021.16.555

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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

Vol. 16 (2021), No. 4, 555–572

DOI: 10.2140/jomms.2021.16.555

Abstract

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.

Keywords

Euler beam theory, differential quadrature method, Adomian decomposition method, nonlocal elasticity

Milestones

Received: 23 May 2021

Revised: 5 July 2021

Accepted: 9 July 2021

Published: 9 November 2021

Authors

Somnath Karmakar
Department of Mathematics National Institute of Technology Rourkela Rourkela 769008 India

Snehashish Chakraverty
Department of Mathematics National Institute of Technology Rourkela Rourkela 769008 India

Vol. 16, No. 4, 2021

Somnath Karmakar and Snehashish Chakraverty

Abstract

Keywords

Milestones

Authors