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Abstract In animal and robot swimmers of body and caudal fin (BCF) form, hydrodynamic thrust is mainly produced by their caudal fins, the stiffness of which has profound effects on both thrust and efficiency of swimming. Caudal fin stiffness also affects the motor control and resulting swimming gaits that correspond to optimal swimming performance; however, their relationship remains scarcely explored. Here using magnetic, modular, undulatory robots (μBots), we tested the effects of caudal fin stiffness on both forward swimming and turning maneuver. We developed six caudal fins with stiffness of more than three orders of difference. For aμBot equipped with each caudal fin (andμBot absent of caudal fin), we applied reinforcement learning in experiments to optimize the motor control for maximizing forward swimming speed or final heading change. The motor control ofμBot was generated by a central pattern generator for forward swimming or by a series of parameterized square waves for turning maneuver. In forward swimming, the variations in caudal fin stiffness gave rise to three modes of optimized motor frequencies and swimming gaits including no caudal fin (4.6 Hz), stiffness <10−4Pa m4(∼10.6 Hz) and stiffness >10−4Pa m4(∼8.4 Hz). Swimming speed, however, varied independently with the modes of swimming gaits, and reached maximal at stiffness of 0.23 × 10−4Pa m4, with theμBot without caudal fin achieving the lowest speed. In turning maneuver, caudal fin stiffness had considerable effects on the amplitudes of both initial head steering and subsequent recoil, as well as the final heading change. It had relatively minor effect on the turning motor program except for theμBots without caudal fin. Optimized forward swimming and turning maneuver shared an identical caudal fin stiffness and similar patterns of peduncle and caudal fin motion, suggesting simplicity in the form and function relationship inμBot swimming.
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This content will become publicly available on November 1, 2026
In situ ambient vibration modal analysis of saguaro cacti ( Carnegiea gigantea )
Abstract PremiseThe structural and dynamic properties of columnar cacti are key inputs for stability analyses; however, no previous studies have been able to resolve these properties from full‐scale tests in situ. MethodsI present an approach using non‐destructive ambient vibration data to measure the resonance properties (modal frequencies and mode shapes) of single‐stem saguaro cacti and resolve key biomechanical properties. I tested the approach on 11 spears in the Tucson, Arizona region, United States. ResultsSaguaro fundamental frequencies ranged between 0.55 and 3.7 Hz with damping ratios of 1.5–2.1%. Additional higher‐order modes were identified below 10 Hz. Fundamental frequencies scaled linearly with the ratio of stem diameter to height‐squared, but deviated from analytical theory due to an observed increase in Young's modulus for taller plants. Calculated ratios between second‐ and first‐order bending frequencies also deviated from beam theory, indicating that stiffness decreases vertically for a given stem, especially for taller spears. These deviations both likely arise from the morphology of internal wooden ribs, which provide the main flexural rigidity. Numerical modeling at one site confirmed the cantilever approximation and height‐dependent stiffness, revealing an empirically derived Young's modulus that decreased exponentially from 107 Pa at the top of the stem to 108 Pa at its base. Twelve days of monitoring at another site showed that frequencies drift with diurnal cycles, suggesting softening of the outer tissue as temperatures warm during the day. ConclusionsThis non‐destructive approach for structural assessment provides valuable data for biomechanical characterization and stability and ecological analyses.
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- Award ID(s):
- 2150896
- PAR ID:
- 10653629
- Publisher / Repository:
- American Journal of Botany
- Date Published:
- Journal Name:
- American Journal of Botany
- Volume:
- 112
- Issue:
- 11
- ISSN:
- 0002-9122
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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