Time Varying Methods for Identification of Constrained Flexible Structures

This paper reports the research carried out by the authors in the confluence of dynamics and system identification of constrained flexible structures. It is shown that under certain considerations the elastic coordinates of a general flexible multibody system can be transformed into a linear time varying second order mechanical system where the forces enter dynamical equations at momentum level. To delineate the conditions under which high order quadratic gyroscopic terms can be neglected, the equations of motion of constrained flexible structures are derived using variational principles. An assumed modes solution to the classical “slider-crank” mechanism with a flexible joint demonstrates a correct application of the constraints to influence the dynamics of participating modes. Preliminary numerical results demonstrate the fact that high frequency oscillations of the flexible member are not transmitted to the slider in the traditional implementations of the constraint boundary conditions for the elastic components. Time varying linear system theory is used to derive minimum norm solution to the special coordinate transformations required to map the identified states into physical coordinates. It is shown that the control influence matrix plays an important role in the existence and uniqueness of the time varying transformations to the physical coordinates.