No abstract

Approximate formulas are derived for upper and lower values of the three-lowest natural frequencies for transverse vibrations of cantilever bars of variable cross section. For cones, truncated cones, wedges, and truncated wedges, as well as bars of constant cross section, the effects of rotatory inertia and shear are taken into account also and compared with the results obtained by neglecting these effects according to the elementary Bernoulli-Euler's theory of bending of beams. Numerical results for the first three natural frequencies are presented in tabular form for different inertia characteristics.

Modelling of the spatial uniformity of the light output from multicolour light emitting diode (LED)-based lamps can be used to evaluate and optimize LED and reflector configurations. The percentage of the output beam that meets or exceeds a user-selected colour accuracy threshold is used as a figure of merit to compare lamp configurations. Results are presented for various distributions of red, green and blue (RGB) or red, amber, green and blue (RAGB) LEDs in a 4 )/4 square matrix. In general, the distributions with highest (4-fold rotational) symmetry have the most uniform output beams. However, those with least uniformity also have 4-fold symmetry, which indicates the importance of choosing the chip layout carefully. The colour uniformity for RAGB configurations is, in general, higher than the colour uniformity for RGB configurations. The colour uniformity at a correlated colour temperature (CCT) of 7000 K is generally higher than the colour uniformity at 3500 K for the LED spectral characteristics investigated.

A variational principle due to E. Reissner has been rewritten in a form which is applicable to small deflection problems for thin plates. The modified principle is used to obtain approximations to static deflection and vibration problems of square and skew cantilever plates of uniform thickness.