Theory of curved, clamped, piezoelectric film, air-borne transducers

Differential equations in the cylindrical coordinate system have been solved to calculate vibration mode of a curved, clamped, piezoelectric multilayer film. Type I has two clamps at straight ends with uniform film curvature, and Type II has the same two clamps with nonuniform curvature in which the radii are different for the central region and for side regions. The solutions include a uniform displacement term, flexural waves with sinusoidal terms, and a hyperbolic cosine term. By numerical computations, the vibration modes and frequency response of displacement are shown, as are various transducer performances. Mechanical losses of the layer materials were taken as complex Young´s moduli with Q values assumed to be constant with frequency. Numerical calculations for 28-/spl mu/m PVDF with 25-/spl mu/m polyester enforcement have shown that (1) the resonance frequency is not necessarily proportional to the inverse of curvature radius as classical theory describes, and, furthermore, resonance diminishes for a certain range of radii, forming a stop band; (2) a back air cavity thinner than 150 /spl mu/m significantly increases the resonance frequency; (3) Type II generates much higher output pressure than Type I; (4) receiver sensitivities for Type I and Type II are not much different; and (5) the effect of radiation impedance is small leading to /spl sim/7% output reduction.