https://doi.org/10.1140/epjp/s13360-025-06120-7
Regular Article
Forward and inverse solutions for hygro-magneto vibration of Euler nanobeam in thermal environment
1
Department of Mathematics, National Institute of Technology, Rourkela, India
2
Department of Mathematics, Koneru Lakshmaiah Education Foundation, Vaddeswaram, A.P., India
Received:
14
May
2024
Accepted:
11
February
2025
Published online:
7
March
2025
The objectives of this article are two fold—first analyze the vibration behavior of Euler nanobeam under hygro-magnetic-thermal environment resting on a Winkler–Pasternak foundation as a forward process, based on two semi analytical techniques: Differential Quadrature Method (DQM) and Differential Transform Method (DTM), second introduced DTM-based inverse problem to obtain the system parameters by using the obtained frequency parameters by forward problem. The governing differential equation is obtained by Hamilton’s principle and the nonlocal strain gradient theory is implemented to capture the nanoscale effects. A complete mathematical process for DQM and DTM has been discussed and vibration frequencies are obtained by using both methods under three different classical boundary conditions: Simply Supported–Simply Supported (SS), Clamped–Simply Supported (CS), and Clamped–Clamped (CC) in the forward problem. In the inverse case, those obtained frequencies are used to find the unknown parameters by inverse DTM. A convergence study for both forward and inverse methods is discussed in terms of frequency and other characteristic parameters under these three boundary conditions. Also the effects of nonlocal parameters, length scale parameters, Winkler–Pasternak foundation, Hygro-Magnetic and Thermal parameters on the vibration have been discussed by tables and graphical results. The main novelty of this work is that DTM-based inverse problem is introduced, which can be extended in experimental works in future research.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
