The teachings of the present disclosure enable the manufacture of one or more piezoelectric micromachined ultrasonic transducers (PMUTs) having a resonant frequency of a specific target value and/or substantially matched resonant frequencies. In accordance with the present disclosure, a flexible membrane of a PMUT is modified to impart a desired parameter profile for stiffness and/or mass to tune its resonant frequency to a target value. The desired parameter profile is achieved by locally removing or adding material to regions of one or more layers of the flexible membrane to alter its geometric dimensions and/or density. In some embodiments, material is added or removed non-uniformly across the structural layer to realize a material distribution that more strongly affects membrane stiffness than mass. In some embodiments, material having a specific residual stress is added to, and/or removed from, the membrane to define a desired modal stiffness for the membrane.