Purpose This research endeavors to explore the thermoelastic damping (TED) characteristics of a flexible piezothermoelastic fiber-reinforced composite (PTFRC) beam. The beam, which is modelled based on the linear Euler–Bernoulli theory, is assumed to be clamped at one end and restrained by a linear spring at the other end. An equation of motion was developed incorporating a flexible boundary condition. Methods We established a mathematical model to derive the transverse equation of motion of a thin PTFRC beam. Thereafter, incorporating a flexible boundary condition due to the attached spring, the eigenvalues of the equation of motion were computed numerically utilizing the Newton–Raphson method. Then, we examined the influences of prevalent parameters such as thermal relaxation time (<InlineEquation ID="IEq001"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2025_1770_Article_IEq001.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$t_{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>t</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>) for Green-Lindsay (GL) theory, beam dimensions, linear spring constant (<InlineEquation ID="IEq05"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2025_1770_Article_IEq05.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">$K_{L}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mi>L</mi> </msub> </math></EquationSource> </InlineEquation>), the vibrational modes, and critical thickness (<InlineEquation ID="IEq04"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2025_1770_Article_IEq04.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">$CrTh$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">CrTh</mi> </mrow> </math></EquationSource> </InlineEquation>) on the TED of the beam and provided detailed discussions. Results It is observed that peak values of damping factor <InlineEquation ID="IEq03"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2025_1770_Article_IEq03.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">$Q^{-1}_{peak}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>Q</mi> <mrow> <mi mathvariant="italic">peak</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </math></EquationSource> </InlineEquation> of the beam rise with increasing values of <InlineEquation ID="IEq09"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2025_1770_Article_IEq09.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$t_{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>t</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>. Although increasing modes diminish <InlineEquation ID="IEq07"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2025_1770_Article_IEq07.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">$CrTh$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">CrTh</mi> </mrow> </math></EquationSource> </InlineEquation> of the beam, the overall values of <InlineEquation ID="IEq08"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2025_1770_Article_IEq08.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">$CrTh$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">CrTh</mi> </mrow> </math></EquationSource> </InlineEquation> are observed to rise as the length of the beam is augmented. The findings indicate that the eigenvalues and the mode shapes can be optimized through the manipulation of the linear spring, which exerts a considerable influence on the operational spectrum of the device that fulfills appropriate applications. Conclusions In this work, we investigate and analyze the free vibration and dynamic motion of the TED of a PTFRC beam. The obtained outcomes can be utilized to improve the architectural and operational characteristics of a range of systems, including macro and micro-devices, surface/bulk acoustic wave (S/BAW) sensors, and energy harvesting devices.

The Influence of Flexible Support on the Material Properties of Piezothermoelastic Fiber-Reinforced Composite Beam

期刊论文
发表日期：

2025年2月12日

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Sayantan Guha,
Ayman Alneamy

摘要

Purpose

This research endeavors to explore the thermoelastic damping (TED) characteristics of a flexible piezothermoelastic fiber-reinforced composite (PTFRC) beam. The beam, which is modelled based on the linear Euler–Bernoulli theory, is assumed to be clamped at one end and restrained by a linear spring at the other end. An equation of motion was developed incorporating a flexible boundary condition.

Methods

We established a mathematical model to derive the transverse equation of motion of a thin PTFRC beam. Thereafter, incorporating a flexible boundary condition due to the attached spring, the eigenvalues of the equation of motion were computed numerically utilizing the Newton–Raphson method. Then, we examined the influences of prevalent parameters such as thermal relaxation time ( $t_{1}$ $t_{1}$ ) for Green-Lindsay (GL) theory, beam dimensions, linear spring constant ( $K_{L}$ $K_{L}$ ), the vibrational modes, and critical thickness ( $CrTh$ $CrTh$ ) on the TED of the beam and provided detailed discussions.

Results

It is observed that peak values of damping factor $Q^{-1}_{peak}$ $Q_{peak}^{- 1}$ of the beam rise with increasing values of $t_{1}$ $t_{1}$ . Although increasing modes diminish $CrTh$ $CrTh$ of the beam, the overall values of $CrTh$ $CrTh$ are observed to rise as the length of the beam is augmented. The findings indicate that the eigenvalues and the mode shapes can be optimized through the manipulation of the linear spring, which exerts a considerable influence on the operational spectrum of the device that fulfills appropriate applications.

Conclusions

In this work, we investigate and analyze the free vibration and dynamic motion of the TED of a PTFRC beam. The obtained outcomes can be utilized to improve the architectural and operational characteristics of a range of systems, including macro and micro-devices, surface/bulk acoustic wave (S/BAW) sensors, and energy harvesting devices.