During this REU, undergraduate student researchers will analyze the dynamics of vibro-impact systems used in engineering applications, such as energy harvesting and targeted energy transfer. These are mechanical systems that consist of two (or more) bodies, for example a freely moving ball inside an externally driven cylindrical capsule, that collide with each other. Students will learn and employ various techniques from nonlinear dynamics, bifurcation theory, probability, and stochastic processes. The goal is to understand how variation and noise in parameters related to the system design, as well as noise in the input signal or initial state, influence the types of solutions generated, bifurcations, and energy output. Our studies will be inspired by real data from bridge vibrations and experiments from our collaborators in Southampton, UK. Students will also develop or improve their computational skills to simulate the mathematical models describing the systems under investigation and carry out other analyses.