Purpose In this research, a numerical investigation was performed on the unconventional nonlinear dynamic feedbacks of plate-type multilayer energy microharvesters under sinusoidal impulsive time-dependent loadings. Methods To do so, without needing integration process and background meshes, meshless collocation models based on conventional and nonlocal couple-based exponential shear flexible plate formulations were established and edge conditions were imposed directly to boundary nodes. Gaussian random field pattern was applied to determine the characteristics of porous-material-made passive cores with two graded and uniform porosity dispersions along the thickness. Results For the extracted voltage, five extremum points were identified within clamped multilayer energy microharvester forced dynamical response, while three extremum points were observed for the simply supported one. Conclusion It was found that nonlocality effect enhanced the average extracted voltages of extremum points for simply supported and clamped exponential shear flexible microharvesters from <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1653_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">$214.5277$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>214.5277</mn> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1653_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="86" /> </InlineMediaObject> <EquationSource Format="TEX">$234.0496 mv$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>234.0496</mn> <mi>m</mi> <mi>v</mi> </mrow> </math></EquationSource> </InlineEquation> (9.10% increase) and from <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1653_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">$108.6055$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>108.6055</mn> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1653_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="86" /> </InlineMediaObject> <EquationSource Format="TEX">$117.9522 mv$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>117.9522</mn> <mi>m</mi> <mi>v</mi> </mrow> </math></EquationSource> </InlineEquation> (8.61% increase), respectively. However, rotation gradient tensor effect reduced the average extracted voltages of extremum points for simply supported and clamped exponential shear flexible microharvesters from <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1653_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">$214.5277$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>214.5277</mn> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1653_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="86" /> </InlineMediaObject> <EquationSource Format="TEX">$194.7843 mv$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>194.7843</mn> <mi>m</mi> <mi>v</mi> </mrow> </math></EquationSource> </InlineEquation> (9.21% decrease) and from <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1653_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">$108.6055$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>108.6055</mn> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42417_2024_1653_Article_IEq8.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="79" /> </InlineMediaObject> <EquationSource Format="TEX">$99.0225 mv$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>99.0225</mn> <mi>m</mi> <mi>v</mi> </mrow> </math></EquationSource> </InlineEquation> (8.82% decrease), respectively. That is, for both edge conditions, rotation gradient tensor played more significant roles in exponential shear flexible multilayer energy microharvester nonlinear dynamics than the nonlocal stress tensor.

Nonlocal Couple Stress-Based Exponential Shear Flexible Plate Model to Study Nonlinear Feedback of Impulsive Excited Multilayer Energy Microharvesters

期刊论文
发表日期：

2025年2月1日

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Muhammad Atif Shahzad,
Saeid Sahmani,
Babak Safaei

摘要

Purpose

In this research, a numerical investigation was performed on the unconventional nonlinear dynamic feedbacks of plate-type multilayer energy microharvesters under sinusoidal impulsive time-dependent loadings.

Methods

To do so, without needing integration process and background meshes, meshless collocation models based on conventional and nonlocal couple-based exponential shear flexible plate formulations were established and edge conditions were imposed directly to boundary nodes. Gaussian random field pattern was applied to determine the characteristics of porous-material-made passive cores with two graded and uniform porosity dispersions along the thickness.

Results

For the extracted voltage, five extremum points were identified within clamped multilayer energy microharvester forced dynamical response, while three extremum points were observed for the simply supported one.

Conclusion

It was found that nonlocality effect enhanced the average extracted voltages of extremum points for simply supported and clamped exponential shear flexible microharvesters from $214.5277$ $214.5277$ to $234.0496 mv$ $234.0496 m v$ (9.10% increase) and from $108.6055$ $108.6055$ to $117.9522 mv$ $117.9522 m v$ (8.61% increase), respectively. However, rotation gradient tensor effect reduced the average extracted voltages of extremum points for simply supported and clamped exponential shear flexible microharvesters from $214.5277$ $214.5277$ to $194.7843 mv$ $194.7843 m v$ (9.21% decrease) and from $108.6055$ $108.6055$ to $99.0225 mv$ $99.0225 m v$ (8.82% decrease), respectively. That is, for both edge conditions, rotation gradient tensor played more significant roles in exponential shear flexible multilayer energy microharvester nonlinear dynamics than the nonlocal stress tensor.