Introduction of time-varying properties in a background medium can enable unconventional wave behavior. Furthermore, it is well-known that subjecting nonlinear materials to time-varying stress can be used for material characterization [Appl. Phys. Lett. 94, 011905 (2009)]. We propose a technique called Dynamic Asymmetric Transmission Measurement (DATM) that combines structural dynamic (SD) and ultrasonic (US) testing modalities in an elastic waveguide to detect and characterize changes in the global stress state of a structure that result in local time-varying stress conditions due to local nonlinearity. Asymmetric geometric features in beams and plates, paired with time-varying stress conditions, result in asymmetric mode conversion of guided US waves that depend on large-scale structural dynamics. The DATM technique is explored through finite element modeling, semi-analytical methods, and experiments and discussed in a structural health monitoring context. We also discuss the use of dynamic structures with engineered defects to introduce time-varying stress conditions for the purpose of manipulating elastic waves. [Sandia National Laboratories is a multimission laboratory managed and operated by the National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.]