“…The above equations are applicable to each component phase of the composite structure in Figure 1 as special cases. They have been used to study thickness vibration of plates [ 25 , 26 ], wave propagation [ 27 , 28 , 29 , 30 , 31 , 32 ], fields near cracks [ 33 , 34 , 35 ], extension of rods [ 36 , 37 , 38 , 39 ], bending of beams [ 40 , 41 , 42 , 43 , 44 , 45 ], and fields near PN junctions [ 46 , 47 , 48 , 49 ] in piezoelectric semiconductors.…”