Design Using Symbolic Topological Equations

The application of a network synthesis technique to structural dynamics design is studied. Topological formulas are used to express transfer functions relating system responses to excitations in symbolic form so that numerical values do not have to be initially assigned to the system components. These relationships are valid throughout iterations on the design variables. The topological concepts are presented first in abstract form and then related to models representing idealized vibrational systems. A parameter optimization approach in which the system configuration is initially known is used in the design formulation. The optimization procedure allows the use of nonlinear merit functions and design constraints. Example problems are presented for a five-degree-of-freedom system.