An apparatus for ultrasonic generation and sensing, comprising: (a) at least one elastic layer (42; 136); (b) at least one piezoelectric material layer (38; 140) mechanically coupled to said elastic layer (42; 136); and (c) at least one electrode (40, 44; 142, 138) of electrically conductive material disposed in electrical contact with each side of said piezoelectric material (38; 140) providing electrodes for said piezoelectric material as a backside electrode (44; 138) and frontside electrode (40; 142), wherein the backside electrode (44; 138) is placed at least partially between said elastic layer (42; 136) and said piezoelectric material layer (38; 140); (d) wherein a combination of said elastic layer (42; 136), piezoelectric material layer (38; 140), backside electrode (44; 138), and frontside electrode (40; 142) form an ultrasonic diaphragm for generating ultrasonic signals in response to applying a selected transmission voltage waveform signal between said backside electrode (44; 138) and said frontside electrode (40; 142), and/or for sensing ultrasonic signals in response to sensing a received voltage waveform signal between said backside electrode (44; 138) and said frontside electrode (40; 142); and (e) wherein said diaphragm has a surface patterned with selective thinned areas through a combination of at least said piezoelectric material layer and said electrodes to vary the diaphragm thickness at specific locations to independently select mass and stiffness toward increasing bandwidth and reducing sensitivity to residual stress; said specific locations forming ribs (39; 59) extending from a perimeter of said diaphragm to a central portion in said diaphragm around which at least said piezoelectric material (38; 140) and said backside electrode material (44; 138) have been removed. (a) at least one elastic layer (42; 136); (b) at least one piezoelectric material layer (38; 140) mechanically coupled to said elastic layer (42; 136); and (c) at least one electrode (40, 44; 142, 138) of electrically conductive material disposed in electrical contact with each side of said piezoelectric material (38; 140) providing electrodes for said piezoelectric material as a backside electrode (44; 138) and frontside electrode (40; 142), wherein the backside electrode (44; 138) is placed at least partially between said elastic layer (42; 136) and said piezoelectric material layer (38; 140); (d) wherein a combination of said elastic layer (42; 136), piezoelectric material layer (38; 140), backside electrode (44; 138), and frontside electrode (40; 142) form an ultrasonic diaphragm for generating ultrasonic signals in response to applying a selected transmission voltage waveform signal between said backside electrode (44; 138) and said frontside electrode (40; 142), and/or for sensing ultrasonic signals in response to sensing a received voltage waveform signal between said backside electrode (44; 138) and said frontside electrode (40; 142); and (e) wherein said diaphragm has a surface patterned with selective thinned areas through a combination of at least said piezoelectric material layer and said electrodes to vary the diaphragm thickness at specific locations to independently select mass and stiffness toward increasing bandwidth and reducing sensitivity to residual stress; said specific locations forming ribs (39; 59) extending from a perimeter of said diaphragm to a central portion in said diaphragm around which at least said piezoelectric material (38; 140) and said backside electrode material (44; 138) have been removed.