Free vibrations of a semi-infinite cylindrical shell, localized near the edge of the shell are investigated. The dynamic equations in the Kirchhoff–Love theory of shells are subjected to asymptotic analysis. Three types of localized vibrations, associated with bending, extensional, and super-low-frequency semi-membrane motions, are determined. A link between localized vibrations and Rayleigh-type bending and extensional waves, propagating along the edge, is established. Different boundary conditions on the edge are considered. It is shown that for bending and super-low-frequency vibrations the natural frequencies are real while for extensional vibrations they have asymptotically small imaginary parts. The latter corresponds to the radiation to infinity caused by coupling between extensional and bending modes.

This article reports observations conducted in Rampur, Chitwan, Nepal, during March-April and October—December 1999. 14 continuous observations were carried out from 08:00 h to 19:00 h on 6 to 48 nests of Apis dorsata in different seasonal conditions. Detailed observations of 410 periodic mass flights (PMFs) were recorded. During the day, A. dorsata workers made 0–6 PMFs, each of which lasted about 5 min. Worker bees from 52% to 100% of colonies performed PMFs within a day. About 55% of colonies performed a second PMF and about 25% a third flight. Percentage of colonies performing PMFs and the number of PMF activities per colony were highest when the largest amount of brood was present in colonies. In cool conditions (average temp. 20.9 °C), PMF activity lasted between 4 and 7 h and peaked around noontime. In warm conditions (average 26–28 °C), the duration of this activity extended up to 9 h with no PMFs at noon. In hot conditions (average 33.6 °C), the duration of PMF activities was extended to 11 h; however, flights were made only in the morning between 8:00 h and 10:00 h and in the evening between 16:00 h and 18:00 h, with a 6-h gap of no PMF in between. The duration and distribution of PMF activities during the day were correlated with average daily temperatures. On the warmest days, more PMF activities (63–67%) were performed after the hottest midday hours were over. We suggest that both the short duration of 5 min of PMF activity as well as the distribution of PMFs during the day are strategies to avoid thermal disruption of the protective bee curtain.