MODELING AND-EXPERIMENTAL TESTING OF TWIST ACTUATED SINGLE CELL COMPOSITE ...

202 Pages·2009·15.03 MB·English

MODELING AND-EXPERIMENTAL TESTING OF TWIST
ACTUATED SINGLE CELL COMPOSITE BEAMS FOR
HELICOPTER BLADE CONTROL
by
ANDRIES J. DU PLESSIS
Submitted to the Department of Aeronautics and Astronautics
in Partial Fulfillment of the Requirements for the Degree of
MASTER OF SCIENCE
IN AERONAUTICS AND ASTRONAUTICS
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 1996
© 1996 Massachusetts Institute of Technology
All rights reserved
Signature of Author
Department of Aeronautics and Astronautics
February 2, 1996
Certified by '
................................................ ....... .............. ............ ............
Associate Professor Nesbitt W. Hagood
Thesis Supervisor
Accepted by
.....................................................
. / ..........
.. Professor Harold Y. Wachman
.ASSACAHUSTS TINSTET
OF TECHNOLOGY Chairman, Department Graduate Committee
Ae
FEB 211996
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MODELING AND EXPERIMENTAL TESTING OF TWIST ACTUATED
SINGLE CELL COMPOSITE BEAMS FOR HELICOPTER BLADE CONTROL
by
Andries J. du Plessis
Submitted to the Department of Aeronautics and Astronautics on January 19, 1996
in Partial Fulfillment of the Requirements for the Degree of Master of Science in
Aeronautics and Astronautics
Abstract
An adaptive beam model of anisotropically actuated, single cell, composite beams is
formulated to determine the twist actuation capabilities of anisotropic linear piezoelectric
actuators as related to the potential application for helicopter blade control. The model
allows for the inclusion of planar anisotropic actuation piezoelectric media anywhere in the
cross-section of the composite beam. Model state variables are the displacement, rotations,
twist, and twist rate of the beam cross-section. The adaptive beam model is used in a twist
actuation parameter study to determine anisotropic actuator properties which result in
maximum non-dimensionalized twist of a twist actuated composite box beam. The study
indicates that actuators should either have no stiffness anisotropy with negative actuation
anisotropy, or high stiffness anisotropy with no actuation anisotropy. The objective of the
adaptive, single cell, composite beam model is to predict the static displacement response of
an anisotropically actuated beam. To obtain the static displacement response of an actuated
beam, the model governing differential equations are solved with the finite element method.
The element used in the analysis is a high order adaptive beam finite element formulated
based on the analytical adaptive beam model. The simulation capabilities of the adaptive
beam finite element is validated with displacement comparisons for both passive and
adaptive beams. Finally, a proof of concept 1/16th scale adaptive model blade, constructed
from composite materials, is tested for twist actuation performance. Experimentally
measured twist levels proves the anisotropic actuation concept and validates the adaptive
beam model and associated adaptive beam element.
Thesis Supervisor: Dr. Nesbitt W. Hagood
Title: Associate Professor of Aeronautics and Astronautics

Acknowledgments
I wish to thank for Prof. Nesbitt Hagood for giving me the opportunity to conduct research
at MIT in the Active Materials and Structures Laboratory. To all the AMSLers: Thank you
for the friendship, support, and laughter during the past two years (it made all those late
nights bearable!). The actuators that were used for the experimental part of this study was
manufactured by Aaron A. Bent, John P. Rodgers and Alessandro Pizzochero. You saved
my life, guys! Thank you John for proof reading the thesis. To all the friends and family
back home in South Africa and in Boston: Baie dankie vir julle ondersteuning/Thanks for
your support. To her that suffered with me these two years at MIT: Thanks Berrie.
Life in Boston according to Jaco:
"Alles is COOL tot die wit kak in swart kak verander"
Everything is COOL until the white s... (stuff) turns into black s... (stuff)

Biographical Note
Andries Jacobus du Plessis is a native of Pretoria, Gauteng, Republic of South Africa. He
graduated from the University of Pretoria with a degree in Mechanical Engineering. Since
August 1993 he has been living in Boston, Massachusetts in an effort to deprive himself of
sunlight, beer, braaivleis (BBQ), and to get a master's degree from MIT.

Table of Contents
Abstract 3
Table of Contents 9
List of Figures 13
List of Tables 17
Nomenclature 19
Chapter 1: Introduction 23
1.1 Motivation .............................................................. .......23
1.2 Objectives ......................................................................... 26
1.3 Background ........................................................................... 27
1.3.1 Active Materials ............................................................ 27
1.3.2 Anisotropic Actuators .................................................... 30
1.3.3 Adaptive Structures ........................................................ 34
1.3.4 Aeroelastic Control for Aircraft .......................................... 35
1.3.5 Helicopter Blade Control....................................... ........36
1.4 Thesis Overview ..................................................................... 38
Chapter 2: Modeling of Actuated Single Cell Composite
Beams 41
2.1 Introduction ........................................................................ 41
2.2 Actuated Beam Description and Assumptions ................................... 42
2.3 Strain-Displacement Relations ..................................................... 44
2.3.1 Position Vector and Normal Projection ................................. 44
2.3.2 Beam Cross-Section Kinematics................................ 46
2.3.3 Torsional Warping Function ......................................... 48
2.3.4 Strain Relations ........................................................ 51
2.4 Constitutive Relations .............................................................. 52
2.4.1 Linear Piezoelectric Constitutive Relations .......................... 52
2.4.2 Plane Stress Problem.................................................. 54
2.4.3 Property Rotations................... 55
2.4.4 Plate Formulation ....................................................... 57
2.5 Equations of Motion .................................................................. 59
2.5.1 Internal Strain Energy ..................................................... 59
2.5.2 External Work......................................................... 61
2.5.3 Equilibrium Equations and Boundary Conditions ..................... 62
2.5.4 Force-Displacement Relations...................... ......... 63
2.5.5 Structural Coupling.................................................... 66
2.5.6 Solution of the Governing Equations ................................. 67
2.6 Summary ................................................................. 67
Chapter 3: Twist Actuator Parameter Study 69
3.1 Composite Box Beam Description ................................................. 70
3.1.1 Laminate Membrane Stiffness ..................................... 71
3.1.2 Box Beam Stiffnesses for Parameter Study ........................ 73
3.2 Actuator Description ................................................................ 73
3.2.1 Actuator Package Induced Stress Resultants ........................... 74
3.2.2 Maximized Induced Shear Stress Resultants ........................... 75
3.3 Non-Dimensional Actuated Box Beam Twist...................................... 77
3.3.1 Induced Torque and Beam Torsional Stiffness ......................77
3.3.2 Beam Tip Twist .......................................................... 80
3.3.3 Non-Dimensional Tip Twist Parameter .............................. 85