<p>Flow-induced vibration (FIV) of a flexible cantilever plate has many areas of application such as flutter, plant biomechanics, biolocomotion, enhancement of heat transfer and mixing, ambient flow energy harvesting, etc. Here, we conduct FIV experiments for a thin plate attached behind a cylinder subjected to a uniform flow in a wind tunnel. The Reynolds number with respect to the diameter of the cylinder ranges (4 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5540_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\times\)</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation>10<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5540_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(^3\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>, 5<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5540_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\times\)</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation>10<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5540_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(^4\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>4</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>). The reduced velocity (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5540_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(U_R\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>U</mi> <mi>R</mi> </msub> </math></EquationSource> </InlineEquation>) based on the plate’s length and second natural frequency is varied in the range of (0.5, 10.5). We illustrate the oscillation dynamics of the plate describing displacement signal, frequency response, phase plane, amplitude spectral density, and plate’s oscillation envelope. Three FIV regimes—initial excitation, transition, and lock-in—are seen based on the plate’s dynamics. The plate achieves periodic limit cycle oscillation in the lock-in regime. Further, we study the effect of mass ratio on the dynamics of the plate by varying the plate length. The variation of the plate frequency normalized with the second natural frequency with <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5540_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(U_R\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>U</mi> <mi>R</mi> </msub> </math></EquationSource> </InlineEquation> is linear in the lock-in regime and its slope increases with the decrease in the mass ratio. At low velocities within the lock-in regime, intermittency in the plate’s oscillation is observed in the experiments. A good data collapse of dimensionless amplitude and frequency response with respect to the reduced velocity, at which the maxima of dimensionless amplitude and onset of flutter occur, is reported for different geometrical and material properties of the plate. Furthermore, we compare the measurement with the wake oscillator model (WOM) where the plate is modeled as an Euler–Bernoulli beam, and the flow is modeled using the van der Pol oscillator. In addition, structural and fluid damping parameters in the WOM are varied, and the FIV response of the plate is analyzed. The WOM qualitatively predicts the measured displacement while it quantitatively captures the frequency response in the lock-in regime.</p>

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Dynamics of a flexible plate mounted behind a cylinder in airflow

  • Shubham Giri,
  • V. Kartik,
  • Amit Agrawal,
  • Rajneesh Bhardwaj

摘要

Flow-induced vibration (FIV) of a flexible cantilever plate has many areas of application such as flutter, plant biomechanics, biolocomotion, enhancement of heat transfer and mixing, ambient flow energy harvesting, etc. Here, we conduct FIV experiments for a thin plate attached behind a cylinder subjected to a uniform flow in a wind tunnel. The Reynolds number with respect to the diameter of the cylinder ranges (4 \(\times\) × 10 \(^3\) 3 , 5 \(\times\) × 10 \(^4\) 4 ). The reduced velocity ( \(U_R\) U R ) based on the plate’s length and second natural frequency is varied in the range of (0.5, 10.5). We illustrate the oscillation dynamics of the plate describing displacement signal, frequency response, phase plane, amplitude spectral density, and plate’s oscillation envelope. Three FIV regimes—initial excitation, transition, and lock-in—are seen based on the plate’s dynamics. The plate achieves periodic limit cycle oscillation in the lock-in regime. Further, we study the effect of mass ratio on the dynamics of the plate by varying the plate length. The variation of the plate frequency normalized with the second natural frequency with \(U_R\) U R is linear in the lock-in regime and its slope increases with the decrease in the mass ratio. At low velocities within the lock-in regime, intermittency in the plate’s oscillation is observed in the experiments. A good data collapse of dimensionless amplitude and frequency response with respect to the reduced velocity, at which the maxima of dimensionless amplitude and onset of flutter occur, is reported for different geometrical and material properties of the plate. Furthermore, we compare the measurement with the wake oscillator model (WOM) where the plate is modeled as an Euler–Bernoulli beam, and the flow is modeled using the van der Pol oscillator. In addition, structural and fluid damping parameters in the WOM are varied, and the FIV response of the plate is analyzed. The WOM qualitatively predicts the measured displacement while it quantitatively captures the frequency response in the lock-in regime.