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Novel aspects of elastic flapping wing: Analytical solution for inertial forcing

  • Zare, Hadi (Center of Excellence in Aerospace Systems, Department of Aerospace Engineering, Sharif University of Technology) ;
  • Pourtakdoust, Seid H. (Center of Excellence in Aerospace Systems, Department of Aerospace Engineering, Sharif University of Technology) ;
  • Bighashdel, Ariyan (Center of Excellence in Aerospace Systems, Department of Aerospace Engineering, Sharif University of Technology)
  • Received : 2017.06.14
  • Accepted : 2017.10.09
  • Published : 2018.05.25
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Abstract

The structural dynamics (SD) behavior of Elastic Flapping Wings (EFWs) is investigated analytically as a novel approach in EFWs analysis. In this regard an analytical SD solution of EFW undergoing a prescribed rigid body motion is initially derived, where the governing equations are expressed in modal space. The inertial forces are also analytically computed utilizing the actuator induced acceleration effects on the wing structure, while due to importance of analytical solution the linearity assumption is also considered. The formulated initial-value problem is solved analytically to study the EFW structural responses, where the effect of structure-actuator frequency ratio, structure-flapping frequency ratio as well as the structure damping ratio on the EFW pick amplitude is analyzed. A case study is also simulated in which the wing is modeled as an elastic beam with shell elements undergoing a prescribed sinusoidal motion. The corresponding EFW transient and steady response in on-off servo behavior is investigated. This study provides a conceptual understanding for the overall EFW SD behavior in the presence of inertial forces plus the servo dynamics effects. In addition to the substantial analytical results, the study paves a new mathematical way to better understanding the complex role of SD in dynamic EFWs behavior. Specifically, similar mathematical formulations can be carried out to investigate the effect of aerodynamics and/or gravity.

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References

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