TY - JOUR
T1 - A dynamic spar numerical model for passive shape change
AU - Calogero, J. P.
AU - Frecker, M. I.
AU - Hasnain, Z.
AU - Hubbard, J. E.
N1 - Funding Information:
The authors gratefully acknowledge the support of the Air Force Office of Scientific Research (AFOSR), grant number FA9550-13-0126 under the direction of Dr David Stargel. We would like to thank James Lankford and Kaleb Bordner from the Alfred Gessow Rotorcraft Center at The University of Maryland for allowing us to use their facility and aiding us in the experiment. The resources of the NASA Langley Research Center, The Pennsylvania State University, University of Maryland and Morpheus Lab are also appreciated.
Publisher Copyright:
© 2016 IOP Publishing Ltd.
PY - 2016/9/7
Y1 - 2016/9/7
N2 - A three-dimensional constraint-driven dynamic rigid-link numerical model of a flapping wing structure with compliant joints (CJs) called the dynamic spar numerical model is introduced and implemented. CJs are modeled as spherical joints with distributed mass and spring-dampers with coupled nonlinear spring and damping coefficients, which models compliant mechanisms spatially distributed in the structure while greatly reducing computation time compared to a finite element model. The constraints are established, followed by the formulation of a state model used in conjunction with a forward time integrator, an experiment to verify a rigid-link assumption and determine a flapping angle function, and finally several example runs. Modeling the CJs as coupled bi-linear springs shows the wing is able to flex more during upstroke than downstroke. Coupling the spring stiffnesses allows an angular deformation about one axis to induce an angular deformation about another axis, where the magnitude is proportional to the coupling term. Modeling both the leading edge and diagonal spars shows that the diagonal spar changes the kinematics of the leading edge spar verses only considering the leading edge spar, causing much larger axial rotations in the leading edge spar. The kinematics are very sensitive to CJ location, where moving the CJ toward the wing root causes a stronger response, and adding multiple CJs on the leading edge spar with a CJ on the diagonal spar allows the wing to deform with larger magnitude in all directions. This model lays a framework for a tool which can be used to understand flapping wing flight.
AB - A three-dimensional constraint-driven dynamic rigid-link numerical model of a flapping wing structure with compliant joints (CJs) called the dynamic spar numerical model is introduced and implemented. CJs are modeled as spherical joints with distributed mass and spring-dampers with coupled nonlinear spring and damping coefficients, which models compliant mechanisms spatially distributed in the structure while greatly reducing computation time compared to a finite element model. The constraints are established, followed by the formulation of a state model used in conjunction with a forward time integrator, an experiment to verify a rigid-link assumption and determine a flapping angle function, and finally several example runs. Modeling the CJs as coupled bi-linear springs shows the wing is able to flex more during upstroke than downstroke. Coupling the spring stiffnesses allows an angular deformation about one axis to induce an angular deformation about another axis, where the magnitude is proportional to the coupling term. Modeling both the leading edge and diagonal spars shows that the diagonal spar changes the kinematics of the leading edge spar verses only considering the leading edge spar, causing much larger axial rotations in the leading edge spar. The kinematics are very sensitive to CJ location, where moving the CJ toward the wing root causes a stronger response, and adding multiple CJs on the leading edge spar with a CJ on the diagonal spar allows the wing to deform with larger magnitude in all directions. This model lays a framework for a tool which can be used to understand flapping wing flight.
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U2 - 10.1088/0964-1726/25/10/104006
DO - 10.1088/0964-1726/25/10/104006
M3 - Article
AN - SCOPUS:84989945195
SN - 0964-1726
VL - 25
JO - Smart Materials and Structures
JF - Smart Materials and Structures
IS - 10
M1 - 104006
ER -