Structural health monitoring systems and methods are described that incorporate one or more acoustic black holes in a sensing capacity. The acoustic black hole provides low- or no-reflection capabilities combined with high displacement of an edge upon excitation. The sensor can be utilized to differentiate in-plane acousto-ultrasonic wave excitations from out-of-plane excitations as well as to separate the in-plane and out-of-plane components of an excitation acousto-ultrasonic wave. Sensors can incorporate features such as mode selectivity, omnidirectional sensing, frequency tunability, quasi-static strain insensitivity, and mechanical amplification.