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<p>The purpose of this article is to study the free vibration of tri-directional functionally graded (3D-FGM) nanoplates employing isogeometric analysis (IGA) in conjunction with the trigonometric shear deformation theory (Tr-SDT). The small-scale effect present in nanostructures is accounted for by using non-local elasticity theory (NET). The mechanical properties of 3D-FGM vary along all the three directions, i.e., <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5555_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(x\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>x</mi> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5555_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(y\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>y</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5555_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(z\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>z</mi> </math></EquationSource> </InlineEquation> directions. The convergence and accuracy of the proposed method are confirmed by comparing it with other methods found in the existing literature. Furthermore, various examples are presented to investigate how geometric dimensions, material properties and boundary conditions (BCs) affect the free vibration of 3D-FGM nanoplates. The obtained numerical results are expected to be useful for designing and fabricating nanoplates in practice. </p>

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Isogeometric free vibration analysis of tri-directional functionally graded nanoplates based on non-local elasticity theory

  • 期刊论文

  • 发表日期：

    2025年4月28日

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  • Truong Son Le,
  • Huu Trong Dang,
  • Trung Thanh Tran,
  • Nguyen Vinh Du,
  • Huy Gia Luong,
  • Quoc Hoa Pham

摘要

The purpose of this article is to study the free vibration of tri-directional functionally graded (3D-FGM) nanoplates employing isogeometric analysis (IGA) in conjunction with the trigonometric shear deformation theory (Tr-SDT). The small-scale effect present in nanostructures is accounted for by using non-local elasticity theory (NET). The mechanical properties of 3D-FGM vary along all the three directions, i.e., \(x\) x , \(y\) y and \(z\) z directions. The convergence and accuracy of the proposed method are confirmed by comparing it with other methods found in the existing literature. Furthermore, various examples are presented to investigate how geometric dimensions, material properties and boundary conditions (BCs) affect the free vibration of 3D-FGM nanoplates. The obtained numerical results are expected to be useful for designing and fabricating nanoplates in practice.