機械學會誌

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The lateral vibration of a clamped-free bar is made the subject of the investigation in continuation of the author's article on vibrations of turbine blades, by taking the cross section and the moment of inertia to vary in a linear relation with the distance from a certain origin, and assuming the radius of gyration to be constant as in the previous note. First Rayleigh's method of an assumed type has been applied to find the frequency of the gravest mode of vibration, and then the smallest characteristic constant of an integral equation has been approximately calculated for the same end. The former method gives as is well known an upper limit to the frequency, while it is shown that a lower limit may be found by the latter method. On comparing these results with the root found by solving the boundary problem in the usual way, the lower limit is rather in good agreement with the true value, the error being 1.5% in the uniform bar, and 3.2% in the bar with a pointed tip. Lastly, the lateral vibration of a flexible bar in rotation has been considered by Rayleigh's method. The result may be combined with the frequency of the elastic bar in rest by Lamb-Southwell's method to find the approximate value of the frequency in rotation.

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Buckets of various forms are tested on a Pelton wheel, showing the efficiency of each. The efficiency of a wheel being defined by the product of the nozzle, the volumetric, the mechanical, and the hydraulic efficiency of bucket, each efficiency is measured or calculated separately. The hydraulic loss of buckets or the so-called wheel loss is the sum of bucket loss and discharge loss, both of which are separately calculated, and it is shown that the former decreases with increasing speed of rotation of the wheel, while the latter becomes minimum for a certain speed. The hydraulic efficiency of bucket is maximum for a certain ratio of the bucket and jet areas, and is the largest maximum in the neighborhood of the speed, for which the discharge loss is minimum.

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