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Background <p>Based on a simple structure, the fish bone active camber morphing airfoil achieved an effective deformation mechanism, however, there were few theoretical studies on the structural dynamics of the fishbone scheme.</p> Purpose <p>A mesh-independent dynamic analytical model was presented to describing the structural dynamics of the fish bone active camber morphing airfoil.</p> Methods <p>The airfoil was divided into several parts according to geometric features, these parts were simplified into uniform thickness plates, variable thickness plates and Euler beams based on the Kirchhoff–Love plate theory and Euler beam theory. The deflection shape functions of these parts were constructed by the first kind of Chebyshev polynomials, and the associations between these shape functions were established by the classical laminated plate theory (CLPT) and penalty function method. Governing equations were finally solved by Rayleigh–Ritz method to capture the structural dynamic characteristics.</p> Results <p>Two solution cases were given. The difference lay in the material of elastic plate, one was conventional isotropic material, the other was Carbon fiber-reinforced polymer (CFRP). Compared with the finite element method, the solution accuracy of the airfoil with isotropic elastic plate was higher than that with the CFRP elastic plate. The first order natural frequency errors were 1.75% and 2.23%, respectively. The Modal Assurance Criterion (MAC) values of the first three order modes were dominated by diagonal elements, which were all above 0.96. The proposed mesh-independent dynamic analytical method reduced the highest order of the frequency equation by <i>k</i> times, while <i>k</i> is the piece number of the elastic plate elements, and provided fast and accurate dynamics results, not only for fish bone active camber morphing airfoil, but also for other discontinuous elastic plates with ribs.</p> Conclusion <p>It was feasible to obtain the dynamic characteristics of the airfoil based on the Rayleigh–Ritz method by using the unified shape functions and ignoring the local discontinuous curvature caused by the supporting ribs.</p>

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Theoretical Analysis and Solution of Transverse Free Vibration of Fish Bone Active Camber Morphing Airfoil

  • 期刊论文

  • 发表日期：

    2025年6月17日

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  • Yueyin Ma,
  • Zhenhua Chen,
  • Wanhua Chen,
  • Daokui Li,
  • Bin Ma,
  • Xutao Nie

摘要

Background

Based on a simple structure, the fish bone active camber morphing airfoil achieved an effective deformation mechanism, however, there were few theoretical studies on the structural dynamics of the fishbone scheme.

Purpose

A mesh-independent dynamic analytical model was presented to describing the structural dynamics of the fish bone active camber morphing airfoil.

Methods

The airfoil was divided into several parts according to geometric features, these parts were simplified into uniform thickness plates, variable thickness plates and Euler beams based on the Kirchhoff–Love plate theory and Euler beam theory. The deflection shape functions of these parts were constructed by the first kind of Chebyshev polynomials, and the associations between these shape functions were established by the classical laminated plate theory (CLPT) and penalty function method. Governing equations were finally solved by Rayleigh–Ritz method to capture the structural dynamic characteristics.

Results

Two solution cases were given. The difference lay in the material of elastic plate, one was conventional isotropic material, the other was Carbon fiber-reinforced polymer (CFRP). Compared with the finite element method, the solution accuracy of the airfoil with isotropic elastic plate was higher than that with the CFRP elastic plate. The first order natural frequency errors were 1.75% and 2.23%, respectively. The Modal Assurance Criterion (MAC) values of the first three order modes were dominated by diagonal elements, which were all above 0.96. The proposed mesh-independent dynamic analytical method reduced the highest order of the frequency equation by k times, while k is the piece number of the elastic plate elements, and provided fast and accurate dynamics results, not only for fish bone active camber morphing airfoil, but also for other discontinuous elastic plates with ribs.

Conclusion

It was feasible to obtain the dynamic characteristics of the airfoil based on the Rayleigh–Ritz method by using the unified shape functions and ignoring the local discontinuous curvature caused by the supporting ribs.