In situ ambient vibration modal analysis of saguaro cacti (Carnegiea gigantea)

The 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.

I 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.

Saguaro 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.

This non-destructive approach for structural assessment provides valuable data for biomechanical characterization and stability and ecological analyses.