Application of genetic algorithms (GA) for optimizing truss geometry is studied with inducing periodicity, and impulse-response based nondestructive evaluation approach is developed using the advantage of periodic system design. Using the optimized structural configuration with periodic arrangement of truss members, the impulse-response method is applied to identify the structural state of each repeating periodic unit cell. It is important to consider the damage mechanisms and their influences to structural behavior in the design process. An inverse method is proposed as a new design practice by linking the truss optimization with periodic structure design and NDE using impulse response method. The main hypothesis is that each unit cell has similar frequency response at the undamaged state. Once damage forms in a unit cell, its behavior deviates from the unit cell behavior. The approach has been numerically and experimentally demonstrated. The numerical models have been built using COMSOL Multiphysics software in the frequency domain. Numerical results include the impulse responses of the trusses with different numbers of unit cells and three different unit cell topologies for pristine and damaged conditions. In the experimental study, a steel truss bridge with eight repeating unit cells (one of the numerically modeled configurations) is built and tested using impact hammer and accelerometer.