Transfer Function Formulation of Constrained Distributed Parameter Systems, Part I: Theory

Analysis of constrained distributed parameter systems by the transfer function formulation is presented. The methodology is suitable for symbolic computation coding. The distributed system is an assembly of distributed elements. A generalized displacement method (GDM) is developed to evaluate the free and forced responses of the system. It is shown that, while classical methods require the satisfaction of both the displacement and force boundary conditions at the subsystem interfaces, GDM only needs to impose generalized force constraints. The continuity of generalized displacements at the interfaces is embedded in the present formulation. Thus, computation efforts are greatly reduced, in particular, for systems with a large number of distributed subsystems. Eigenfunctions of constrained systems are obtained by solving a finite-dimensional eigenvalue problem governing the generalized coordinate vector. The formulation can be applied to damped and non-selfadjoint systems.