Maximum Tip Displacement Research Articles

Dynamics of arthropod filiform hairs. II. Mechanical properties of spider trichobothria ( Cupiennius salei Keys.)

Adults of the wandering spider Cupiennius salei (Ctenidae) have 936 ( ± 31 s.d.) trichobothria or filiform hairs on their legs and pedipalps. This is the largest number of these air movement detectors recorded for a spider. The trichobothria are 100-1400 μm long and 5-15 μm wide (diameter at base). Many of them are bent distally pointing towards the spider body. Their feathery surface increases drag forces and thus mechanical sensitivity by enlarging the effective hair diameter. Typically, trichobothria are arranged in clusters of 2-30 hairs which increase in length towards the leg tip. The trichobothria’s mechanical directionality is either isotropic or it exhibits a preference for air flow parallel or perpendicular (from lateral) to the long leg axis. These differences are neither due to the distal bend of the hair nor to the bilateral symmetry of the cuticular cup at the hair base but to the spring supporting the hair. Different directional properties may be combined in the same cluster of hairs. Trichobothria are tuned to best frequency ranges between 40 and 600 Hz depending on hair length. Because, with increasing hair length, absolute mechanical sensitivity changes as well, the arrangement of hairs in a cluster provides for a fractionation of both the intensity and frequency range of a stimulus, in addition, in some cases, to that of stimulus direction. Boundary layer thickness above the spider leg in oscillating airflow varies between about 2600 μm at 10 Hz and 600 μm at 950 Hz. It is well within the range of hair lengths. In airflow perpendicular to the long leg axis particle velocity above the leg increases considerably as compared to the free field. The curved surface of the cuticular substrate has therefore to be taken into account when calculating hair motion. The experimentally measured properties of hair and air motion were also determined numerically using the theory developed in the companion paper (Humphrey et al. Phil. Trans. R. Soc. Lond . B 340, 423-444 (1993)). There is good agreement between the two. Short hairs are as good or better velocity sensors as long hairs but more sensitive acceleration sensors. In agreement with most of our measurements optimal hair length is not larger than boundary layer thickness at a hair’s best frequency. Best frequencies of hair deflection and of ratio a (maximum hair tip displacement:air particle displacement) differ from each other. The highest measured value for ratio a was 1.6. In only 22% of the cases hair tip displacement exceeded air particle displacement. Hair motion is insensitive to changes in hair mass as shown by the numerical comparison of a solid and a hollow hair.

A Robust Testing Method for Determination of the Damping Loss Factor of Composites

This paper describes a robust testing method for the experimental determination of the vibration damping loss factor of composites. This procedure is being proposed as a result of a detailed experimental program that was undertaken to characterize the damping loss factor of glass and graphite-epoxy composite materials. During the experimental testing to determine the damping loss factor of the composites, it became evident that the amplitude of vibration of the test beam had a pronounced effect on the calculated loss factor determined using the half-power bandwidth method. Calculated loss factors were significantly reduced if the tip displacement amplitude versus time were lower than 0.001 in. (0.0025 cm) for more than 25% of the data set. To alleviate this problem, a robust testing method was developed. In this procedure, a set of 2048 displacement versus time data points are recorded. This displacement versus time data is then partitioned into 512 data point intervals. A Fourier transform is performed on each of these data sets and loss factor determined using the half-power bandwidth method. The loss factor as a function of the maximum tip displacement within each data set is plotted. A linear least squares fit is performed on the data, with an extrapolation being made to zero displacement. The extrapolation to zero displacement effectively reduces the extraneous losses, providing a more robust testing protocol for material characterization. This testing method should provide increased accuracy and precision for the determination of the damping loss factor of materials.