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Nonlinear thermo-vibration of sensitive double adsorber under coupling spring-driven resonance via nonlocal multiple scales-Galerkin approach.

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Title: Nonlinear thermo-vibration of sensitive double adsorber under coupling spring-driven resonance via nonlocal multiple scales-Galerkin approach.
Authors: Djellali, Brahim Said1,2 (AUTHOR) djellali.brahimsaid@ens-bousaada.dz, Bourouina, Hicham1,2 (AUTHOR) bourouina.hicham@ens-bousaada.dz, Khouni, Soumia1,2 (AUTHOR) khouni.soumia@ens-bousaada.dz, Lamari, Abir1,2 (AUTHOR) lamari.abir@ens-bousaada.dz, Maiza, Yahia1,2 (AUTHOR) maiza.yahia@ens-bousaada.dz, Mektout, Mohamed1,2 (AUTHOR) mektout.mohamed@ens-bousaada.dz, Elaihar, Lamine1 (AUTHOR) elaihar.lamine@ens-bousaada.dz
Source: Acta Mechanica. Jun2026, Vol. 237 Issue 6, p2901-2933. 33p.
Subjects: Physisorption, Functionally gradient materials, Asymptotic expansions, Galerkin methods, Resonance, Resonant vibration, Mechanical vibration research
Abstract: This study aims to provide an in-depth understanding of the nonlinear frequency shifts induced by adsorption in a system comprising two coupled microbeams fabricated from functionally graded porous (FGP) materials. The proposed configuration adopts a sandwich-like architecture, where surface layers encapsulate a longitudinally perforated core embedded with a regular array of periodic square holes (PSH) along the beam axis. Geometric nonlinearity is treated using the von Kármán hypothesis, while the scale-dependent mechanical behavior fabricated from functionally graded porous (FGP) materials is characterized within the framework of nonlocal elasticity theory. The study focuses on analyzing the influence of a set of key physical parameters on the dynamic response, including nonlocal effects, the spatial distribution of adsorbed atoms (adatoms), the thermal loading applied across the beam thickness, as well as porosity distribution, hole geometry, and adsorption density. To account for adsorption energy originating from van der Waals (vdW) interactions, the Lennard–Jones (6–12) potential is employed. A formulation of these interactions is developed within the framework of the Rayleigh beam theory. Furthermore, the conventional Euler–Bernoulli model is extended to incorporate the influence of adsorption by revising its governing equations. The system is reduced to a single nonlinear differential equation using the Galerkin method, which is then analytically treated via the multiple scale method. The results indicate a reduction in the nonlinear response of the microbeam as the temperature increases. The analyses further show that atomic adsorption on the beam surface leads to a clear attenuation of nonlinearity. In addition, the findings reveal that increasing the gradation index, porosity level, and volume fraction contributes to a decrease in the nonlocality loaded with atoms. The developed model demonstrates a strong capability to accurately capture the dynamic behavior and surface adsorption, thereby confirming its effectiveness for the development of advanced sensing platforms based on functional structures. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:This study aims to provide an in-depth understanding of the nonlinear frequency shifts induced by adsorption in a system comprising two coupled microbeams fabricated from functionally graded porous (FGP) materials. The proposed configuration adopts a sandwich-like architecture, where surface layers encapsulate a longitudinally perforated core embedded with a regular array of periodic square holes (PSH) along the beam axis. Geometric nonlinearity is treated using the von Kármán hypothesis, while the scale-dependent mechanical behavior fabricated from functionally graded porous (FGP) materials is characterized within the framework of nonlocal elasticity theory. The study focuses on analyzing the influence of a set of key physical parameters on the dynamic response, including nonlocal effects, the spatial distribution of adsorbed atoms (adatoms), the thermal loading applied across the beam thickness, as well as porosity distribution, hole geometry, and adsorption density. To account for adsorption energy originating from van der Waals (vdW) interactions, the Lennard–Jones (6–12) potential is employed. A formulation of these interactions is developed within the framework of the Rayleigh beam theory. Furthermore, the conventional Euler–Bernoulli model is extended to incorporate the influence of adsorption by revising its governing equations. The system is reduced to a single nonlinear differential equation using the Galerkin method, which is then analytically treated via the multiple scale method. The results indicate a reduction in the nonlinear response of the microbeam as the temperature increases. The analyses further show that atomic adsorption on the beam surface leads to a clear attenuation of nonlinearity. In addition, the findings reveal that increasing the gradation index, porosity level, and volume fraction contributes to a decrease in the nonlocality loaded with atoms. The developed model demonstrates a strong capability to accurately capture the dynamic behavior and surface adsorption, thereby confirming its effectiveness for the development of advanced sensing platforms based on functional structures. [ABSTRACT FROM AUTHOR]
ISSN:00015970
DOI:10.1007/s00707-026-04635-3