1. An Introduction to Rotorcraft Dynamics
Dr. Wenbin Yu
School of Aerospace Engineering
Georgia Institute of Technology
URL:

2. Outline of the Course Introductions Theory of resonance
Introduction to DYMORE
Blade dynamics
The rotor as a filter, airframe dynamic response and coupled blade-fuselage response
Vibration control devices
Typical instabilities
Ground resonance
Pitch-lag instability
Pitch-flap instability
Flap-lag instability

3. Introduction
Rotorcraft are dynamic machinery. The dynamic problem are very important
Some dynamic problem are detrimental to the vehicle performance. If not dealt properly, they could cause catastrophic tragedies
Three categories of rotorcraft vibration
Vibrations due to rotor excitation. The frequencies are integral multiples of the rotor rotation speed
Vibrations due to random aerodynamic excitation. The frequencies are the natural frequencies of the structure
Self-excited vibrations, such as flutter and ground resonances. Negative damping could cause divergent oscillations

4. Theory of Resonance A single DOF dynamic system Natural frequency
Forced vibration of the system without damping
The importance of natural frequency for design
Vibration with damping
Mathematica example
Flapping blade
Lagging blade

5. Finite Element Based Formulation for Nonlinear Multibody Systems
Model configurations of arbitrary topology:
Assemble basic components chosen from an extensive library of structural and constraint elements
Avoids modal expansion
This approach is that of the finite element method which has enjoyed, for this very reason, an explosive growth
This analysis concept leads to simulation software tools that are modular and expandable
Elements of the library can be validated independently

6. Rotor as a Nonlinear Multibody System

7. Transmission as a Nonlinear Multibody System

8. Simulation of Rotor on Ship Board
The complete model involves:
17 beam elements,
5 prescribed displacements,
1 prismatic joint,
1 relative displacement,
21 rigid bodies,
12 revolute joints,
12 relative rotation,
3 spherical joints,
1 universal joints,
For a total of 950 degrees of freedom.

9. Element Library: Structural Elements
Rigid bodies
Flexible joints: linear and torsional springs and damper
Cable element
Beam elements: geometrically exact, shear deformable. Capable of modeling all the elastic coupling effects arising from the use of advanced laminated composite materials
Shell elements: geometrically exact, shear deformable, modeling of composite material effects
The finite element formulation is used for all elements, no modal reduction is performed

10. Element Library: Beam Elements
Geometrically exact beam elements. Six degrees of freedom (three displacements, three rotations) per node
Accounts for
Shearing deformation effects
Offsets of the center of mass, shear center, and centroid
All elastic couplings that can arise from the use of laminated composite materials (Fully coupled 6x6 stiffness matrix)
Material viscous dissipation

11. Element Library: Shell Elements
Geometrically exact shell elements. Five degrees of freedom (three displacements, two rotations) per node. Locking free element is achieved using the mixed interpolations of strains tensorial components
Accounts for
Shearing deformation effects
Offsets of the center of mass
All elastic couplings that can arise from the use of laminated composite materials (Fully coupled 8x8 stiffness matrix)
Material viscous dissipation

12. The Six Lower Pairs

13. Blade Dynamics Blade dynamics is important because
High blade vibratory response results in high stresses
High blade vibratory response leads to high fuselage vibration levels
Blade resonances and mode shapes are important in stability analysis of rotor systems
DYMORE example for a single blade
DYMORE example for a complete rotor (ITU LCH)
FAN plot for ITU LCH
Changing frequencies by playing with weight

14. DYMORE Rotor Model
The DYMORE model for the ITU LCH Rotor

15. Fan Plot of Frequencies for the Rotor
Fan plot in Vacuum for the ITU LCH Rotor (Verifying the Auto-Trim concept)

16. Dynamic Responses - Displacements
Time history of blade tip displacement
red: axial displacement; green: in-plane displacement; blue: out-of-plane displacement

17. Dynamic Responses - Rotations
Time history of blade tip rotations
red: pitching; green: flapwise direction; blue: chordwise direction

18. Dynamic Responses - Forces
Time history of forces at different locations
red: at flex root; green: at flex tip

19. Dynamic Responses - Moments
Time history of moments at different locations
red: at flex root; green: at flex tip

20. Pitch-lag Instability

21. Pitch-flap Instability

22. Flap-lag Instability
Ground resonance

23. Conclusions
Dynamic problem are very important for rotorcraft. A good design must come from a good understanding to dynamic behavior of the vehicle
Locating the natural frequencies of the system is the key to avoid resonance
DYMORE is a handy tool to deal with rotorcraft dynamics
Either passive (damping) or active devices (vibration absorbers) can be used to reduce the resonance or shift the natural frequencies
Dynamic instabilities should and can be avoided by design tradeoffs