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.
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机译：解决了圆柱坐标系中的微分方程，以计算弯曲的，夹紧的压电多层膜的振动模式。 I型在直端有两个夹具，膜的曲率均匀，而II型则有两个不均匀曲率的夹具，其中中心区域和侧面区域的半径不同。这些解决方案包括均匀位移项，具有正弦项的弯曲波以及双曲余弦项。通过数值计算，显示了位移的振动模式和频率响应，以及各种换能器性能。层材料的机械损耗被视为复杨氏模量，其中Q值假定随频率恒定。对28- / spl mu / m的聚酯纤维实施25- / spl mu / m的PVDF的数值计算表明：（1）共振频率不一定与经典理论所描述的曲率半径成反比，而且共振在一定范围的半径上减小，形成一个阻带； （2）小于150 / spl mu / m的后气腔会明显增加共振频率； （3）II型产生的输出压力要比I型高得多； （4）I型和II型接收机的灵敏度没有太大差异； （5）辐射阻抗的影响很小，导致/ spl sim / 7％的输出降低。
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