Hello!,
If you are looking for Dynamic Unstability you need to perform a
Flutter Analysis.
Flutter is the dynamic aeroelastic stability problem. It can be solved in any speed regime simply by selecting the appropriate aerodynamic theory. In the linear case, the solution involves a series of complex eigenvalue solutions; the eigenvalue problem to be solved depends on the way in which the aerodynamic loads are included in the equations of motion or whether certain damping terms are included.
The manner in which the aerodynamic loads are included depends on how the dimensionless oscillatory aerodynamic coefficients are defined. When Theodorsen (1935) first developed the American method (K-method) of flutter analysis, he introduced the aerodynamics into a vibration analysis as complex inertial terms and the flutter analysis became a vibration analysis requiring complex arithmetic. At the same time, he introduced an artificial complex structural damping, proportional to the stiffness, to sustain the assumed harmonic motion. Flutter analysis is then a double eigenvalue problem in frequency and velocity, and an iterative solution, using the reduced frequency of the assumed harmonic motion as the iteration parameter, leads to the neutrally stable conditions (flutter frequencies and velocities) at which no artificial damping is required. The artificial damping is therefore seen not to be physically meaningful, other than, perhaps, at speeds near flutter speeds.
At about the same time, Frazer and Duncan (1928) in England were attempting to solve the flutter problem using aerodynamic stability derivatives in the tradition of Bryan (1911) who had studied the flight mechanics of rigid aircraft. This approach introduced the aerodynamic loads into the equations of motion as frequency dependent stiffness and damping terms. In this representation it should be noted that the aerodynamic terms are slowly varying functions of the reduced frequency, in contrast to the representation of the aerodynamics in the K-method as mass terms that are highly dependent on the reduced frequency. In what has become known as the “British” method of flutter analysis some iteration is still necessary to “line-up” the eigenvalue solution for frequency with the reduced frequency in each mode.
A description of the British method and a comparison with the American method has been given by Lawrence and Jackson (1970). A variation of the British method in which the aerodynamic loads are treated as complex springs has been developed by Hassig (1971). Hassig called his method the p-k method, and NX Nastran has adopted his terminology, although it is now applied to the British method. The NX Nastran terminology is K-method for the American method, and PK-method for the British method. NX Nastran also has a very efficient K-method, called the KE-method, but it does not provide eigenvectors and has no provisions for viscous damping type terms, such as arise in an automatic control system in the equations of motion.
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Best regards,
Blas.
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Blas Molero Hidalgo
Ingeniero Industrial
Director
IBERISA
48011 BILBAO (SPAIN)
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