Flexural Stiffness and Modulus of Elasticity of Flower Stalks from Allium Stalks from Allium sativum as Measured by Multiple Resonance Frequency Spectra

Abstract

Multiple resonance frequency spectra (MRFS) provide a rapid and repeatable method for determining the flexural stiffness and modulus of elasticity, E, of segments of plant stems and leaves. Each resonance frequency in a spectrum can be used to compute E, and removal of the distal portion of an organ produces characteristic shifts in spectra dependent upon the geometry of an organ. Hence, MRFS can be used to quantitatively determine the extent to which a particular leaf or stem morphology can be modelled according to beam theory. MRFS of flower stalks of Allium sativum L. are presented to illustrate the technique. The fundamental, f1, and higher resonance frequencies, f2 … fn, of stems and the ratios of f2/f1 f3/f1, and f3/f2 increase as stalk length is reduced by clipping. The magnitudes of these shifts conform to those predicted from the MRFS of a linearly tapered beam. Morphometric data confirm this geometry in 21 flower stalks. Based on this model, the average modulus equals 3.71 × 108 ± 0.32 × 108 N/m2, which compares favorably with values of E determined by static loading (3.55 × 108 ± 0.22 × 108 N/m2) and is in general agreement with ultrasonic measurements (3.8 × 108 to 4.4 × 108 N/m2). Data indicate that determinations of E from a single resonance frequency are suspect, since each resonance frequency yields slightly different values for E. Statistical evaluations from all the frequencies within a MRFS are more reliable for determining E and testing the appropriateness of beam theory to evaluate the biomechanical properties of plants.