Continuum Methods for Large Flexible Structures, Introduction to the Dynamic Stiffness Method, Volume 1, 11624/95/NL/JG(SC)

The subject of the project Continuum Methods for Large Flexible Structures is the improvement of the Dynamic Stiffness Method (DSM) for application to large flexible spacecraft, e.g. satellites with flexible appendages. The method is especially suitable for use in modal analysis. The DSM may also be helpful during pre-design of structures as a fast as well as highly accurate tool. With respect to numerical procedures non-linear effects as well as gyroscopic ones in case of spin-stabilised satellites have to be presented. Externally applied effects like gravity or thermal loading in space have not been considered.Within the DSM forces and moments acting on a structure are related by the dynamic stiffness matrix, often called impedance matrix, to the translational and rotational system degrees of freedom. It has been among others developed and used at ESA/ESTEC since the mid seventies. It was incorporated into a fast and easily applicable computer programmes (DISTEL, VAMP) containing an element library and algorithms of solution procedures. The state of development and application at ESA/ESTEC is illustrated by examples.The inherent capacity of extending the DSM to more complex spacecraft configurations, especially to rotating ones has been examined. Surveying the theoretical background of analytical dynamics the important methods in use are compared with the DSM to show its advantages in modal analysis. Consequently, the existing discrete and continuous elements developed for use within the DSM are presented and extended by flexible booms attached to spinning spacecraft. On the basis of the non-linearly pre-deformed, quasi-static equilibrium state the dynamic stiffness matrices to analyse small vibration about this state have been derived. The element library has also been extended by procedures to include measured relations to a stiffness matrix.Rules of assembling structures of several elements, procedures to determine the equilibrium state, to assess stability of a dynamic structural system, and the problem of transcendental eigenvalues and modes have been discussed by presenting the available solution methods