Dmitry Tihomirov

Dmitry Tihomirov


Daniella Raveh
Non-linear Aerodynamic Effects on Static Aeroelasticity of Flexible Missiles

A general direction now days in the missiles industry is towards longer, higher speed and maneuverability missiles. This trend makes the missiles more and more flexible, thus the missiles become more exposed to aeroelastic effects, such as static and dynamic aeroelastic instability and stability problems due to thrust misalignment.

Today, the solution of aeroelastic problems is mostly done with linear aeroelastic models, supported with nonlinear aerodynamics from wind tunnel tests or computational fluid dynamics.

Previous studies were making effort to deal with this matter. Hodges [1] investigated the interaction of the missile thrust as a follower force with aeroelastic loads of missiles. According to the results, the aerodynamics serve to decrease the effective stiffness of the missile. Hodges suggested a numerical method for the dynamic stability, structural dynamics and aeroelastic response analyses of a missile, based on a geometrically-exact, mixed finite element method. The aerodynamic model in this study was based on slender body theory, and nonlinear aerodynamics were not taken into consideration.

In a study by Karpel et al. [2] dynamic response parameters (pitch angle, induced angle due to vertical velocity, angle of attack, and frequencies) were calculated during the accelerated phase of the flight, with rapid changing velocities and mass properties, with follower forces and thrust misalignment, and with structural joint nonlinearities. A nonlinear computational scheme, based on Increasing-Order Modeling approach was offered and successfully simulated. In this study, the unsteady aerodynamic forces during the rocket acceleration were calculated with the assumption that they are mostly affected by changes in dynamic pressure. Hence, velocity and Mach effects on the aerodynamic coefficients were neglected.

Another study by Karpel et al. [3] showed the dynamic aeroelastic stability analysis of free flight rockets. Effects of follower force, imperfection factors, and the coupling between thrust, roll rate and rocket flexibility were investigated. In this study, the Mach dependent aerodynamic forces were assumed to be linear.

The proposed study focuses on the issue of nonlinear aerodynamic effects on the trimmed flight of elastic missiles, and proposes to examine these effects for a large range of angle of attack and Mach number values. The investigation will be based on static aeroelastic trim analyses of flexible missile configurations using three models: a linear aerodynamics model, a linear aerodynamic model augmented with nonlinear rigid aerodynamics corrections (the later are from Computational Fluid Dynamics, CFD, simulations), and a full nonlinear aerodynamic, Navier-Stokes, model.

The study will be based on a generic Air-to-Air missile configuration. The missile model includes four canards and four tails, all of which can be used as control surfaces. The structural model is a modal model, based on a finite element method. The two aerodynamic models are a linear panel method, and a nonlinear CFD model, based on the Navier-Stokes flow equations.


  1. Hodges, D., “A New Approach to Aeroelastic Response, Stability and Loads of Missiles and Projectiles”, US Army Research Office Report, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA.
  2. Karpel, M.,  Shousterman, A., Livshits, D.,  and Yujelevski, Y.,  “Dynamic Response of an Accelerated Rocket with Nonlinear Effects,” 54th Israeli Conference on Aerospace Sciences, Tel-Aviv and Haifa, Israel, Feb. 2014.
  3. Livshits, D., Yaniv S., Karpel M., “Dynamic stability of free flight rockets”, 37th AIAA/ASME/ASCE/AHS/ASC Structural Dynamics, and Materials Conference and Exhibit, Salt Lake City, UT, Apr. 15-17, 1996.