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<p>In this article, an analytical approach to characterize the breathing mode vibration for thermoelastic nanosphere using the coupled thermoelastic theory is developed. In other words, the inclusion of the temperature field takes into account the concept of heat wave and the energy equation of heat conduction is combined with the elastic theory. The frequency equation is derived from the solution of bi-harmonic function. Two different boundary conditions in the temperature field are considered, insulated and isothermal. The validation of the frequency equation is confirmed by the simulation of COMSOL. Two dimensionless parameters, thermoelastic coupling constant <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="707_2025_4258_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(\epsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation> and Peclet number <i>Pe</i>, are introduced to study their influences on the frequencies and quality factors of the nanosphere vibration. Furthermore, the effects of thermodynamic parameters, such as the reference temperature, the coefficient of linear expansion, the thermal conductivity, and the heat capacity, are also studied in this article. Some parameters have monotonic effect on the frequency and quality factors, while others are more complex. The Peclet number plays a role as thermal damping factor in the model. The concise frequency equations obtained during the analysis could be a useful guide for interpreting the experimental observation and measurement of thermoelastic nanosphere vibrations.</p>

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An analytical approach to characterize the breathing mode vibration for thermoelastic nanosphere

  • 期刊论文

  • 发表日期：

    2025年2月25日

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  • Xin Huang,
  • Adil El Baroudi,
  • Amine Ammar

摘要

In this article, an analytical approach to characterize the breathing mode vibration for thermoelastic nanosphere using the coupled thermoelastic theory is developed. In other words, the inclusion of the temperature field takes into account the concept of heat wave and the energy equation of heat conduction is combined with the elastic theory. The frequency equation is derived from the solution of bi-harmonic function. Two different boundary conditions in the temperature field are considered, insulated and isothermal. The validation of the frequency equation is confirmed by the simulation of COMSOL. Two dimensionless parameters, thermoelastic coupling constant \(\epsilon \) ϵ and Peclet number Pe, are introduced to study their influences on the frequencies and quality factors of the nanosphere vibration. Furthermore, the effects of thermodynamic parameters, such as the reference temperature, the coefficient of linear expansion, the thermal conductivity, and the heat capacity, are also studied in this article. Some parameters have monotonic effect on the frequency and quality factors, while others are more complex. The Peclet number plays a role as thermal damping factor in the model. The concise frequency equations obtained during the analysis could be a useful guide for interpreting the experimental observation and measurement of thermoelastic nanosphere vibrations.