HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Full Text Full Text (PDF) Submit a response Alert me when this article is cited Alert me when eLetters are posted Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Similar articles in ISI Web of Science Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via ISI Web of Science (10) Citing Articles via Google Scholar Google Scholar Articles by Spatz, H.-C. Articles by Speck, O. Search for Related Content PubMed Articles by Spatz, H.-C. Articles by Speck, O. Agricola Articles by Spatz, H.-C. Articles by Speck, O.

Oscillation frequencies of tapered plant stems¹

Institute for Biology III, University of Freiburg, Germany

Free oscillations of upright plant stems, or in technical terms, slender tapered rods with one end free, can be described by considering the equilibrium between bending moments in the form of a differential equation with appropriate boundary conditions. For stems with apical loads, where the mass of the stem is negligible, Mathematica 4.0 returns solutions for tapering modes = 0, 0.5, and 1. For other values of , including cases where the modulus of elasticity varies over the length of the stem, approximations leading to an upper and a lower estimate of the frequency of oscillation can be derived. For the limiting case of = 0, the differential equation is identical with Greenhill's equation for the stability against Euler buckling of a top-loaded slender pole. For stems without top loads, Mathematica 4.0 returns solutions only for two limiting cases, zero gravity (realized approximately for oscillations in a horizontal orientation of the stem) and for = 0 (Greenhill's equation). Approximations can be derived for all other cases. As an example, the oscillation of an Arundo donax plant stem is described.

Key Words: Arundo donax • differential equations • free oscillation • taper • top load

This article has been cited by other articles:

				D. Sellier, Y. Brunet, and T. Fourcaud A numerical model of tree aerodynamic response to a turbulent airflow Forestry, July 1, 2008; 81(3): 279 - 297. [Abstract] [Full Text] [PDF]

				G. Jaouen, T. Almeras, C. Coutand, and M. Fournier How to determine sapling buckling risk with only a few measurements Am. J. Botany, October 1, 2007; 94(10): 1583 - 1593. [Abstract] [Full Text] [PDF]

				H.-C. Spatz, F. Bruchert, and J. Pfisterer Multiple resonance damping or how do trees escape dangerously large oscillations? Am. J. Botany, October 1, 2007; 94(10): 1603 - 1611. [Abstract] [Full Text] [PDF]

				J. Friedman and L. D. Harder Functional associations of floret and inflorescence traits among grass species Am. J. Botany, November 1, 2005; 92(11): 1862 - 1870. [Abstract] [Full Text] [PDF]

				D. Sellier and T. Fourcaud A mechanical analysis of the relationship between free oscillations of Pinus pinaster Ait. saplings and their aerial architecture J. Exp. Bot., June 1, 2005; 56(416): 1563 - 1573. [Abstract] [Full Text] [PDF]

				O. Speck and H.-C. Spatz Damped oscillations of the giant reed Arundo donax (Poaceae) Am. J. Botany, June 1, 2004; 91(6): 789 - 796. [Abstract] [Full Text] [PDF]

				O. Speck Field measurements of wind speed and reconfiguration in Arundo donax (Poaceae) with estimates of drag forces Am. J. Botany, August 1, 2003; 90(8): 1253 - 1256. [Abstract] [Full Text] [PDF]