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Nonlinear Aeroelasticity


Analysis of Aircraft Aeroelasticity with Taking into Account Nonlinearities and Uncertainties

Tech Area / Field

  • SAT-AER/Aeronautics/Space, Aircraft and Surface Transportation

8 Project completed

Registration date

Completion date

Senior Project Manager
Ryzhova T B

Leading Institute
Central Aerodynamic Institute, Russia, Moscow reg., Zhukovsky


  • National Research Council Canada / Institute for Aerospace Research / Structures and Materials Performance Laboratory, Canada, ON, Ottawa

Project summary

During the design of an airplane generally linear approaches are used due to their relative simplicity to obtain initial data. However, it is necessary to understand, that these linear approaches for the analysis of the airplane structure are idealizations, which do not always adequately reflect the actual phenomena. Nevertheless in general, specifically linear models are used for an airplane design during the main structure selection and optimization. After manufacture of a design of an airplane, some characteristics can appear that do not correspond to predictions owing to the nonlinearities and dispersion of the design data.

As a rule, mechanical behavior of airplane structures is described by systems of non-linear equations. Practically all structures of a flight vehicle are non-linear systems. The main nonlinearities in a structure of aircraft are local nonlinearities which for example can include the free-play and dry friction in mounting units of controls, engines, nonlinearity of actuators and anti-flutter dampers etc. These non-linear dependences can be linearized in most cases; therefore research of their dynamic characteristics is carried out with the help of the relevant approximate linear mathematical models. However, only the boundaries of areas of stability of the relevant linear systems can be explored by this method.

For example, free-play may arise in modern airplanes for technological reasons or in operational regimes of a control system. The value of the free-play can exceed values, regulated by the normal requirements. Therefore the actual problem to be investigated is research of the influence of free-play on aeroelastic performances and dynamic response of an airplane to estimate a danger of flutter onset and a confirmation of satisfying of the normal requirements for expected values of free-play in the system. Self-oscillations of an airplane in flight can affect strength and resource of the structure at large values of free-play in the control surfaces. It is necessary to specify the maximal permissible values of free-play based on the results of research of stress-deformation conditions of a structure for the various forms of a flutter.

From the point of view of the physics of the phenomenon, there are several sources of nonlinearity in either the aerodynamic flow or the elastic structure of a flying vehicle and in a control system. The main types of nonlinearities are listed below.


  1. Oscillatory motion of shock waves in transonic flow;
  2. Stalled phenomena such as buffets;
  3. Consideration of large deformations in the calculation of aerodynamic flow.

  1. Free-play in connection units resulting in nonlinear stiffness;
  2. Geometrical nonlinearity arising from large displacement gradients and/or loss of skin stability;
  3. Dry friction - nonlinear damping arising from structural components in sliding contact.

Control system:
  1. Limitation of a velocity of actuator rod motion (saturation) and dead zone;
  2. Nonlinear filters in control laws.

One of the important problems in the analysis of aeroelasticity is the great many inevitably uncertainties arising in the mathematical modeling of a real aircraft structure. These include: dispersion of the characteristics of materials, irregularity of a weight report, idealization of various boundary conditions etc. In this connection it is very actually to consider a prediction of possible uncertainties influence on aeroelasticity characteristics in the flying vehicle design stage.

The main purpose of this project is the definition of the influence of a various types of nonlinearities and dispersion of parameters on the characteristics of aeroelasticity of perspective regional passenger airplanes.

In the project the creation of the methodology for researching not only flutter boundaries of an airplane, but also for calculation of parameters of both limit cycle oscillation (LCO) and flutter onset and evolution in supercritical area is proposed.

The development of a methodology includes following elements of research:

  • forming of a flutter mathematical models for study the oscillations of controls with local nonlinearity, for example, with free-play;
  • calculation of flutter boundaries of an airplane considered as a linear system;
  • determination of limit cycle oscillations dependence from parameters of a flow;
  • calculation of a response of an airplane with nonlinearities in a controls actuator on normalized effects;
  • creation of a computational model for flutter taking into account nonlinearity caused by motion of shock waves in a transonic flow;
  • research on non-linear flutter in the time domain by a method of a numerical integration.

The proposed methodology of research of LCO of an airplane with free-play in controls actuators will also allow rapid determination of accelerations levels and reliability of the LCO forms at actual possible levels of disturbances.


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