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Thermoelastic damping in bi-layered micro/nanobeam resonators using the dual-phase-lag generalized heat conduction model.

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Title: Thermoelastic damping in bi-layered micro/nanobeam resonators using the dual-phase-lag generalized heat conduction model.
Authors: Li, Shi-Rong1,2 (AUTHOR) srli@yzu.edu.cn, Wan, Ze-Qing2 (AUTHOR), Zhang, Feng1 (AUTHOR)
Source: International Journal of Heat & Mass Transfer. Apr2025, Vol. 239, pN.PAG-N.PAG. 1p.
Subjects: Euler-Bernoulli beam theory, Heat conduction, Copper, Vibration (Mechanics), Heat transfer
Abstract: • Dual-phase-lag (DPL) thermoelastic damping (TED) model for bi-layered micro/nanobeam resonators was developed. • Analytical solution of TED in the resonators was obtained using both the frequency approach and energy method. • Effect of the thermal axial force (TAF) on TED in bi-layered beam resonators is quantitively analyzed. • TAF increases (decreases) the TED in metal/ceramic (ceramic/ceramic, metal/metal) bilayer resonators. • DPL effect on the TED in a bi-layered nanobeam (ceramic/metal) is totally different from that in a homogenous beam. The existing analytical investigations on thermoelastic damping (TED) in laminated micro/nanobeam resonators have generally neglected the thermal axial force and rarely considered the time lagging in the heat transfer. However, laminated beams will very likely exhibit stretching-bending coupling deformation due to the deviation of the physical neutral surface from the beam mid-surface. Furthermore, the TED in layered beams has been predicted by using the energy rather than the complex frequency approach. In this presentation, TED in bi-layered micro/nanobeams is analyzed based on the Euler-Bernoulli beam theory and the dual-phase-lag (DPL) generalized heat conduction theory by considering the thermal axial force. Analytical solutions for the TED in bi-layered micro/nanobeams are developed by using both the complex frequency approach and the energy method. Numerical results are presented to examine the effects of the thermal axial force and DPL relaxation times on the TED in the laminated beam resonators for different physical and geometrical parameters, vibration modes and mechanical boundary conditions, which reveal that the thermal axial force will increase (decrease) the TED in metal/ceramic (ceramic/ceramic, metal/metal) bi-layered beams. The maximum underestimation for the TED due to neglecting the thermal axial force will reach about 7 % in Ag/Si beam and 15 % in Cu/Si 3 N 4 beam. The DPL effect on the TED is closely related to the material properties of the laminas and their volume fractions. For the Ag/Si beam with the thickness less than 1nm, influence of the DPL relaxation on the TED becomes significant which changes continuously from the negative contribution to the positive one with the increase in the volume fraction of the Si from 0 to 1. However, the DPL effect can be ignored in the bi-layered beams with micrometer size. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:• Dual-phase-lag (DPL) thermoelastic damping (TED) model for bi-layered micro/nanobeam resonators was developed. • Analytical solution of TED in the resonators was obtained using both the frequency approach and energy method. • Effect of the thermal axial force (TAF) on TED in bi-layered beam resonators is quantitively analyzed. • TAF increases (decreases) the TED in metal/ceramic (ceramic/ceramic, metal/metal) bilayer resonators. • DPL effect on the TED in a bi-layered nanobeam (ceramic/metal) is totally different from that in a homogenous beam. The existing analytical investigations on thermoelastic damping (TED) in laminated micro/nanobeam resonators have generally neglected the thermal axial force and rarely considered the time lagging in the heat transfer. However, laminated beams will very likely exhibit stretching-bending coupling deformation due to the deviation of the physical neutral surface from the beam mid-surface. Furthermore, the TED in layered beams has been predicted by using the energy rather than the complex frequency approach. In this presentation, TED in bi-layered micro/nanobeams is analyzed based on the Euler-Bernoulli beam theory and the dual-phase-lag (DPL) generalized heat conduction theory by considering the thermal axial force. Analytical solutions for the TED in bi-layered micro/nanobeams are developed by using both the complex frequency approach and the energy method. Numerical results are presented to examine the effects of the thermal axial force and DPL relaxation times on the TED in the laminated beam resonators for different physical and geometrical parameters, vibration modes and mechanical boundary conditions, which reveal that the thermal axial force will increase (decrease) the TED in metal/ceramic (ceramic/ceramic, metal/metal) bi-layered beams. The maximum underestimation for the TED due to neglecting the thermal axial force will reach about 7 % in Ag/Si beam and 15 % in Cu/Si 3 N 4 beam. The DPL effect on the TED is closely related to the material properties of the laminas and their volume fractions. For the Ag/Si beam with the thickness less than 1nm, influence of the DPL relaxation on the TED becomes significant which changes continuously from the negative contribution to the positive one with the increase in the volume fraction of the Si from 0 to 1. However, the DPL effect can be ignored in the bi-layered beams with micrometer size. [ABSTRACT FROM AUTHOR]
ISSN:00179310
DOI:10.1016/j.ijheatmasstransfer.2024.126478