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Title: Aeroelastic oscillations of a cantilever with structural nonlinearities: theory and numerical simulation.

Abstract

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 demonstratedmore » 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.« less

Authors:
 [1];  [1];  [2];  [3];  [4];  [1]
  1. Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering
  2. Royal Military College of Canada, Kingston (Canada). Dept. of Mechanical and Aerospace Engineering
  3. US Naval Academy, Annapolis, MD (United States). Dept. of Mechanical and Aerospace Engineering
  4. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); Natural Sciences and Engineering Research Council of Canada (NSERC); Mitacs, Vancouver (Canada); Department of National Defence (DND) (Canada)
OSTI Identifier:
1429633
Report Number(s):
SAND-2017-10370J
657282
DOE Contract Number:  
AC04-94AL85000; NA-0003525
Resource Type:
Program Document
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Nonlinear aeroelasticity; Limit cycle oscillation; Geometric nonlinearity; Flutter

Citation Formats

Robinson, Brandon, Rocha da Costa, Leandro Jose, Poirel, Dominique, Pettit, Chris, Khalil, Mohammad, and Sarkar, Abhijit. Aeroelastic oscillations of a cantilever with structural nonlinearities: theory and numerical simulation.. United States: N. p., 2017. Web.
Robinson, Brandon, Rocha da Costa, Leandro Jose, Poirel, Dominique, Pettit, Chris, Khalil, Mohammad, & Sarkar, Abhijit. Aeroelastic oscillations of a cantilever with structural nonlinearities: theory and numerical simulation.. United States.
Robinson, Brandon, Rocha da Costa, Leandro Jose, Poirel, Dominique, Pettit, Chris, Khalil, Mohammad, and Sarkar, Abhijit. 2017. "Aeroelastic oscillations of a cantilever with structural nonlinearities: theory and numerical simulation.". United States.
@article{osti_1429633,
title = {Aeroelastic oscillations of a cantilever with structural nonlinearities: theory and numerical simulation.},
author = {Robinson, Brandon and Rocha da Costa, Leandro Jose and Poirel, Dominique and Pettit, Chris and Khalil, Mohammad and Sarkar, Abhijit},
abstractNote = {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.},
doi = {},
url = {https://www.osti.gov/biblio/1429633}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Sep 01 00:00:00 EDT 2017},
month = {Fri Sep 01 00:00:00 EDT 2017}
}

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