<p>Power law correlation between the rising time, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:R\)</EquationSource> </InlineEquation>, and amplitude,<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:\:A\)</EquationSource> </InlineEquation>, of the detected acoustic emission, AE, signals is investigated in the framework of a driven damped harmonic oscillator model. It is shown, in contrast to the previous model calculation, that <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="89" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:R\sim{A}^{1-{\varphi}_{AE}}\)</EquationSource> </InlineEquation> holds, similarly to the well-known enigma for acoustic emission; <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="90" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:E\sim{A}^{3-{\varphi}_{AE}}\:\)</EquationSource> </InlineEquation>as well as <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:S\sim{A}^{2-{\varphi}_{AE}}\)</EquationSource> </InlineEquation>, where <i>E</i> and <i>A</i> are the energy and area, and 3 and 2 are the expected exponents from the mean field theory, MFT. The same value <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{\varphi}_{AE}=1\)</EquationSource> </InlineEquation> was obtained for all the above exponents and transfer distortions cause mechanism independent changes. For the experimental value <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq7.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="122" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{\varphi}_{exp}={\varphi}_{AE}+{\varphi}_{o}\)</EquationSource> </InlineEquation> is fulfilled, where <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq8.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{\varphi}_{o}\)</EquationSource> </InlineEquation> is the exponent in the power relation between the amplitude and the rising time of the source function (<InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq9.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="83" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{\varphi}_{o}=-0.32\)</EquationSource> </InlineEquation> beyond the MFT and <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq10.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{\varphi}_{o}=0\:\)</EquationSource> </InlineEquation>in MFT). The calculated value of <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{\varphi}_{AE}=1\)</EquationSource> </InlineEquation> is in good agreement with experimental data obtained for different structural changes: <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq12.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="102" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:{\varphi}_{exp}\:0.8\pm\:0.2\)</EquationSource> </InlineEquation>. Universal functions, well scaled together, can be obtained for the temporal avalanche shapes at fixed area normalizing the voltage by <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq13.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:A\)</EquationSource> </InlineEquation> and the time by <InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_26238_Article_IEq14.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="89" /> </InlineMediaObject> <EquationSource Format="TEX">\(\:R\sim{A}^{1-{\varphi}_{exp}}\)</EquationSource> </InlineEquation>. The first part (around the peak) of it is not sensitive to transfer distortions, while the tail region can be heavily distorted.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Transfer distortions of acoustic emission signals - power relations between the signal parameters and normalized temporal shapes of avalanches

  • Asmaa A. Azim,
  • Dezső L. Beke,
  • László Z. Tóth,
  • Lajos Daróczi

摘要

Power law correlation between the rising time, \(\:R\) , and amplitude, \(\:\:A\) , of the detected acoustic emission, AE, signals is investigated in the framework of a driven damped harmonic oscillator model. It is shown, in contrast to the previous model calculation, that \(\:R\sim{A}^{1-{\varphi}_{AE}}\) holds, similarly to the well-known enigma for acoustic emission; \(\:E\sim{A}^{3-{\varphi}_{AE}}\:\) as well as \(\:S\sim{A}^{2-{\varphi}_{AE}}\) , where E and A are the energy and area, and 3 and 2 are the expected exponents from the mean field theory, MFT. The same value \(\:{\varphi}_{AE}=1\) was obtained for all the above exponents and transfer distortions cause mechanism independent changes. For the experimental value \(\:{\varphi}_{exp}={\varphi}_{AE}+{\varphi}_{o}\) is fulfilled, where \(\:{\varphi}_{o}\) is the exponent in the power relation between the amplitude and the rising time of the source function ( \(\:{\varphi}_{o}=-0.32\) beyond the MFT and \(\:{\varphi}_{o}=0\:\) in MFT). The calculated value of \(\:{\varphi}_{AE}=1\) is in good agreement with experimental data obtained for different structural changes: \(\:{\varphi}_{exp}\:0.8\pm\:0.2\) . Universal functions, well scaled together, can be obtained for the temporal avalanche shapes at fixed area normalizing the voltage by \(\:A\) and the time by \(\:R\sim{A}^{1-{\varphi}_{exp}}\) . The first part (around the peak) of it is not sensitive to transfer distortions, while the tail region can be heavily distorted.