A theory is presented for the air flow generation caused by centrifugal forces acting in a vibrating PVF, multirnorph fan in the resonant condition. The vibration system is approximated by a mass acting at the center of inertial force against an elastic plate (the cantilever wing arm). The effect of air was represented by a non-linear dissipative load in the oscillating system. The relevant parameters of this system are then determinable, particularly the vibration amplitude and the wing tip velocity. These parameters determine the generated air flow velocity and volume flow rate. Air flow velocity is predicted to vary inversely as wing length, and the air volume flow rate to remain constant. These predictions agree well with experiment, particularly for larger wing lengths of the fan. Useful design information was obtained.

The great white shark (Carcharodon carcharias) exhibits viviparous and oophagous reproduction. A 4950 mm total length (TL) gravid female accidentally caught by fishermen in the Okinawa Prefecture, Southern Japan carried six embryos (543-624 mm TL, three in each uterus). Both uteri contained copious amounts of yellowish viscous uterine fluid (over 79.2 litres in the left uterus), nutrient eggs and broken egg cases. The embryos had yolk stomachs that had ruptured, the mean volume of which was approximately 197.9 ml. Embryos had about 20 rows of potentially functional teeth in the upper and lower jaws. Periodic acid Schiff (PAS)-positive substances were observed on the surface and in the cytoplasm of the epithelial cells, and large, secretory, OsO4-oxidized lipid droplets of various sizes were distributed on the surface of the villous string epithelium on the uterine wall. Histological examination of the uterine wall showed it to consist of villi, similar to the trophonemata of Dasyatidae rays, suggesting that the large amount of fluid found in the uterus of the white shark was likely required for embryo nutrition. We conclude that: (1) the lipid-rich fluid is secreted from the uterine epithelium only in early gestation before the onset of oophagy, (2) the embryos probably use the abundant uterine fluid and encased nutrient eggs for nutrition at this stage of their development, and (3) the uterine fluid is the major source of embryonic nutrition before oophagy onset. This is the first record of the lipid histotrophy of reproduction among all shark species.

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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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