A thermoelastic model with two relaxations for the vibration of a microbeam resting on elastic foundations

• Published in: Applied mathematics and mechanics Vol. 46; no. 4; pp. 711 - 722
• Main Authors: Hafed, Z. S., Zenkour, A. M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2025; Springer Nature B.V
• Edition: English ed.
• Subjects: Applications of Mathematics; Beam theory (structures); Classical Mechanics; Damage prevention; Elastic foundations; Fluid- and Aerodynamics; Frequency control; High temperature; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Microbeams; Parameters; Partial Differential Equations; Relaxation time; Resonant frequencies; Thermoelasticity; Thickness ratio; Vibration analysis; Green-Lindsay’s (G-L) model; 74F05; elastic foundation; 74H45; thermoelastic vibration; O343; Euler-Bernoulli (E-B) theory; 74-XX
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-025-3241-8

The Euler-Bernoulli (E-B) beam theory is combined with Green-Lindsay’s (G-L) generalized thermoelasticity theory to analyze the vibration of microbeams. The frequency control equation, based on the two-parameter Winkler-Pasternak elastic foundation for simply-supported microbeams, is presented. This study investigates the effects of the side-to-thickness ratio and relaxation time parameters on the vibrational natural frequency of thermoelastic microbeam resonators. The frequencies derived from the present model are compared with those from Lord and Shulman’s (L-S) theory. The fourth-order solutions for natural vibration frequencies are graphically displayed for comparison. Therefore, attention should be paid to the use of effective foundations to prevent microbeam damage caused by contraction and expansion problems caused by high temperatures.