Vol. 16, No. 4, 2021

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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
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