An approach to reduce vibration and avoid shimmy on landing gears based on an adapted eigenstructure assignment theory

Landing gear shimmy is a self excited vibration phenomenon which must be avoided during aircraft design due to its potentially catastrophic behaviour. In a preliminary specification of structural properties of a landing gear, if shimmy is verified through the engineering process of analysis, typically is a difficult task to identify how its mechanical property must be modified to get a shimmy free system. In this sense, this article introduces an adaptation of the eigenstructure assignment theory (EAT) to design a nose landing gear free of the dynamic behaviour of shimmy. EAT is a classical theory employed to compute a feedback control gain which represents a linear transformation of the system states to control forces. The common application of this theory involves active and semi-active controllers, which require electro-mechanical actuators and additional source of energy. However, in this article EAT is adapted to write the matrix of gain in terms increments of structural stiffness and damping of the landing gear to update a previous design to get a shimmy free system. The proposed process allows to specify a desired new structural mode (though an eigenvector) and both frequency and damping ratio (through an eigenvalue). The strategy allows to compute new values of stiffness and damping to redesign a stable system with better vibration response of landing gear. The proposed approach can be applied in the eigenstructure assignment of any linear system, by means a practical process of changing the system properties (stiffness and damping), in the case of this article, to avoid landing gear shimmy. The results shows the effectiveness of the method.