Modal method for dynamics analysis of cantilever type structures at large rotational deformations

• A detailed description of the calculation of rotational deformation.
• A straightforward implementation of a modal warping method in floating frame of reference formulation.
• Linear theory of elastodynamics and the modal warping method are employed for modeling leaf spring landing gear system.
• Experimental platform constructed and model accuracy validation by the comparison between experimental data and numerical results.
• Leaf spring design and UAV real time simulation e.g. hardware-in-loop simulation in the near future.

The modal warping method is extended to a floating frame of reference formulation to combine modal warping formula with rigid body simulation. The highly nonlinear mass matrix because of the inertia coupling between the reference and the elastic displacements is approximated using the linear theory of elastodynamics. By kinematics analysis of infinitesimal deformation, the calculation of rotation deformations is derived. Then modal warping method is used to model deformations for numerical accuracy and computation efficiency. The rigid-flex multibody model for a leaf spring landing gear system is developed. The accuracy of the proposed method is examined by experimental/simulation comparison.