Browsing by Subject "Lagrange"

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    Component Modal Analysis of a Folding Wing
    (2011) Wang, Ivan

    This thesis explores the aeroelastic stability of a folding wing with an arbitrary number of wing segments. Simplifying assumptions are made such that it is possible to derive the equations of motion analytically. First, a general structural dynamics model based on beam theory is derived from a modal analysis using Lagrange's equations, and is used to predict the natural frequencies of different folding wing configurations. Next, the structural model is extended to an aeroelastic model by incorporating the effects of unsteady aerodynamic forces. The aeroelastic model is used to predict the flutter speed and flutter frequencies of folding wings. Experiments were conducted for three folding wing configurations - a two-segment wing, a three-segment wing, and a four-segment wing - and the outboard fold angle was varied over a wide range for each configuration. Very good agreement in both magnitude and overall trend was obtained between the theoretical and experimental structural natural frequencies, as well as the flutter frequency. For the flutter speed, very good agreement was obtained for the two-segment model, but the agreement worsens as the number of wing segments increases. Possible sources of error and attempts to improve correlation are described. Overall, the aeroelastic model predicts the general trends to good accuracy, offers some additional physical insight, and can be used to efficiently compute flutter boundaries and frequency characteristics for preliminary design or sensitivity studies.

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    Global biogeography of scaly tree ferns (Cyatheaceae): evidence for Gondwanan vicariance and limited transoceanic dispersal.
    (Journal of biogeography, 2014-02) Korall, P; Pryer, KM
    AIM:Scaly tree ferns, Cyatheaceae, are a well-supported group of mostly tree-forming ferns found throughout the tropics, the subtropics and the south-temperate zone. Fossil evidence shows that the lineage originated in the Late Jurassic period. We reconstructed large-scale historical biogeographical patterns of Cyatheaceae and tested the hypothesis that some of the observed distribution patterns are in fact compatible, in time and space, with a vicariance scenario related to the break-up of Gondwana. LOCATION:Tropics, subtropics and south-temperate areas of the world. METHODS:The historical biogeography of Cyatheaceae was analysed in a maximum likelihood framework using Lagrange. The 78 ingroup taxa are representative of the geographical distribution of the entire family. The phylogenies that served as a basis for the analyses were obtained by Bayesian inference analyses of mainly previously published DNA sequence data using MrBayes. Lineage divergence dates were estimated in a Bayesian Markov chain Monte Carlo framework using beast. RESULTS:Cyatheaceae originated in the Late Jurassic in either South America or Australasia. Following a range expansion, the ancestral distribution of the marginate-scaled clade included both these areas, whereas Sphaeropteris is reconstructed as having its origin only in Australasia. Within the marginate-scaled clade, reconstructions of early divergences are hampered by the unresolved relationships among the Alsophila, Cyathea and Gymnosphaera lineages. Nevertheless, it is clear that the occurrence of the Cyathea and Sphaeropteris lineages in South America may be related to vicariance, whereas transoceanic dispersal needs to be inferred for the range shifts seen in Alsophila and Gymnosphaera. MAIN CONCLUSIONS:The evolutionary history of Cyatheaceae involves both Gondwanan vicariance scenarios as well as long-distance dispersal events. The number of transoceanic dispersals reconstructed for the family is rather few when compared with other fern lineages. We suggest that a causal relationship between reproductive mode (outcrossing) and dispersal limitations is the most plausible explanation for the pattern observed.