Competing Effects of Buckling and Anchorage Strength on Optimal Wheat Stalk Geometry

[+] Author and Article Information
Tony Farquhar, Jiang Zhou, William H. Wood

Department of Mechanical Engineering, University of Maryland, Baltimore, MD 21250

J Biomech Eng 124(4), 441-449 (Jul 30, 2002) (9 pages) doi:10.1115/1.1488934 History: Received August 01, 2000; Revised April 01, 2002; Online July 30, 2002
Copyright © 2002 by ASME
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Grahic Jump Location
Wheat stem geometry can be idealized as a series of cojoined cylinders (or internodes) of varying diameter separated by solid bulkheads (or nodes). A typical wheat stem has 5 to 8 such internodes of length Li, outer diameter Di, and wall thickness Ti. The mid-internode dimensions were obtained using standard measuring instruments. The presence of the nodes has a negligibly small influence on stem flexural stiffness.
Grahic Jump Location
Predicted optimal stalk resonant frequency as a function of lateral forcing frequency, for a) two peak force intensities or b) two stem lengths. All simulations assumed fixed anchorage strength Mc and a) fixed stem length Lt, or b) fixed peak force intensity fo.
Grahic Jump Location
Predicted optimal resonant frequency as a function of anchorage strength, for two peak force intensities, with fixed forcing frequency ωf and stem length Lt.
Grahic Jump Location
Predicted optimal resonant frequency as a function of peak force intensity, for two stem lengths, with fixed anchorage strength and forcing frequency.
Grahic Jump Location
Predicted optimal stem cross section for a) three resonant frequencies, or b) three stem lengths. The right side shows the outer mid-point of each segment comprising the stem wall and the left side shows the stepped cross section for one a) resonant frequency, or b) stem length, only. Refer to text for further explanation.
Grahic Jump Location
Predicted optimal (right side) or observed (left side) stem geometry of two varieties of wheat. In a) the actual stem geometry of an elite semidwarf variety called Kauz (Rht1) (n=6) is contrasted to the predicted optimum for three material property Cases. In b) the actual geometry of a nearly isogenic tall research cross designated Kauz (rht) is contrasted to the predicted optimum. The three Cases are described in the text.
Grahic Jump Location
Predicted optimal stem mass as a function of anchorage strength. In a) the lower (L) and upper (U) solution branches are shown for two stem lengths with fixed peak force intensity and forcing frequency ωf=1.0 Hz. In b) the optimal stem mass is shown in the lower branch only for two peak force intensities with fixed stem length and forcing frequency ωf=0.4 Hz.
Grahic Jump Location
Predicted optimal stem mass as a function of forcing frequency for a) two stem lengths, or b) two peak force intensities, with fixed anchorage strength. The points labeled a) A-A or b) B-B are equal mass lower and upper solutions, and represent stalks with resonant frequencies either below or above the forcing frequency, respectively.
Grahic Jump Location
Predicted optimal stem mass as a function of resonant frequency for two stem lengths, either a) Lt=0.5 m, or b) Lt=0.7 m, for all three material property Cases.
Grahic Jump Location
Predicted optimal stem geometry based on m=25 starting vectors for Case 1, with fixed stem length and resonant frequency. Analytical solutions for a uniform rod and a smoothly tapered tube are shown for comparison. The bandwidth δ is a measure of model uncertainty, which was addressed using a multi-tiered scheme to identify the most suitable starting vector.




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