Method of freeing a fixed dynamic model of an aircraft

Calculated dynamic models are developed at the design stage of an aircraft and are used to estimate operational loading, to provide strength, controllability and aeroelastic stability of the aircraft. These models accompany experimental investigations, trial and serial operation of the aircraft. Wherein the calculated dynamic models are updated by the results of ground modal tests. The calculated model of the aircraft is as a rule the model of the free dynamic system. While the aircraft vehicles are set on landing gears or are installed on the special system of elastic hanging to perform the modal tests, and the space structures are set on the offloading (zero-G) system. In the present work the method of freeing a fixed dynamic model of an aircraft after the procedure of direct updating its stiffness and/or mass matrices has been proposed. This model updating leads to the fact that it is impossible to free the model by direct returning of the degrees of freedom which were removed during the process of fixing the model. The proposed method allows to free the model from fixations in the case of the inertia characteristics of the free structure are known. As in, mass and moments of inertia regarding some point, for example, center of mass. The method is based on the fact that the fixed model is set on a virtual mobile platform which has the inertia characteristics of the input free structure. It allows to describe the movement of the structure as a rigid body in the model. Movement of the platform influences on the fixed model through inertial forces. Reverse impact is performed through the sum of all the inertial forces which is the reaction in the fixation basically. The system of equations which describes movements of the fixed model was extended by the equations of movements of the platform. The inertial forces which are conditioned by the movement as a rigid body are added to each equation of motion of the model. Moreover, transition from the local coordinate system, which is linked to the fixed model, to the global coordinate system is executed. The obtained equations do not violate the symmetry of the stiffness and mass matrices. The eigenfrequencies and eigenforms are close to the corresponding frequencies and forms of the free model. The implementation of the method has been shown on the mathematical model of linear oscillators. The example of freeing of the conditional beam model of the aircraft, which is set on the landing gears, is presented.