There are disclosed acoustic resonators and method of fabricating acoustic resonators. An acoustic resonator includes a single-crystal piezoelectric plate having front and back surfaces, the back surface attached to a surface of a substrate except for portions of the piezoelectric plate forming a diaphragm spanning a cavity in the substrate. A conductor pattern on the front surface includes an interdigital transducer (IDT) with interleaved fingers of the IDT disposed on the diaphragm. A periodic array of holes is provided in the diaphragm.