Aeroelastic oscillations of a cantilever with structural nonlinearities: theory and numerical simulation.
- Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering
- Royal Military College of Canada, Kingston (Canada). Dept. of Mechanical and Aerospace Engineering
- US Naval Academy, Annapolis, MD (United States). Dept. of Mechanical and Aerospace Engineering
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Our study details the derivation of the nonlinear equations of motion for the axial, biaxial bending and torsional vibrations of an aeroelastic cantilever undergoing rigid body (pitch) rotation at the base. The primary attenstion is focussed on the geometric nonlinearities of the system, whereby the aeroelastic load is modeled by the theory of linear quasisteady aerodynamics. This modelling effort is intended to mimic the wind-tunnel experimental setup at the Royal Military College of Canada. While the derivation closely follows the work of Hodges and Dowell [1] for rotor blades, this aeroelastic system contains new inertial terms which stem from the fundamentally different kinematics than those exhibited by helicopter or wind turbine blades. Using the Hamilton’s principle, a set of coupled nonlinear partial differential equations (PDEs) and an ordinary differential equation (ODE) are derived which describes the coupled axial-bending-bending-torsion-pitch motion of the aeroelastic cantilever with the pitch rotation. The finite dimensional approximation of the coupled system of PDEs are obtained using the Galerkin projection, leading to a coupled system of ODEs. Subsequently, these nonlinear ODEs are solved numerically using the built-in MATLAB implicit ODE solver and the associated numerical results are compared with those obtained using Houbolt’s method. It is demonstrated that the system undergoes coalescence flutter, leading to a limit cycle oscillation (LCO) due to coupling between the rigid body pitching mode and teh flexible mode arising from the flapwise bending motion.
- Research Organization:
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA); Natural Sciences and Engineering Research Council of Canada (NSERC); Mitacs, Vancouver (Canada); Department of National Defence (DND) (Canada)
- DOE Contract Number:
- AC04-94AL85000; NA-0003525
- OSTI ID:
- 1429633
- Report Number(s):
- SAND-2017-10370J; 657282
- Country of Publication:
- United States
- Language:
- English
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