Curtin University Homepage
  • Library
  • Help
    • Admin

    espace - Curtin’s institutional repository

    JavaScript is disabled for your browser. Some features of this site may not work without it.
    View Item 
    • espace Home
    • espace
    • Curtin Theses
    • View Item
    • espace Home
    • espace
    • Curtin Theses
    • View Item

    Vibration frequencies of whirling rods and rotating annuli

    16363_Shum W 2005 Full.pdf (1.011Mb)
    Access Status
    Open access
    Authors
    Shum, Wai Sun
    Date
    2005
    Supervisor
    Dr. Rodney Entwistle
    Type
    Thesis
    Award
    PhD
    
    Metadata
    Show full item record
    Faculty
    Faculty of Engineering and Computing
    URI
    http://hdl.handle.net/20.500.11937/1404
    Collection
    • Curtin Theses
    Abstract

    Static Whirling Rods: Past researchers suggested that “static instabilities” exist at certain rotational speeds of whirling rods. This thesis shows these instabilities are an artefact of the material constitutive laws that are being used well outside their range of applicability. An alternative approach is developed where strains due to rotation are separated from the superimposed vibration. This enables the generally predicted lowering of longitudinal natural frequencies with rotational speed shown to be simply a result of the bulk changes in the geometry of whirling rods. Steady state equations of whirling rods are formulated in Lagrangian coordinates. Due to the non-linear nature of the governing equations, an original numerical method is applied to solve the problem. Numerical results are compared with analytical results obtained from the linearized uniaxial model. There is a close agreement between these two models at low angular velocities. However, at high angular velocities, discrepancies between them arise, confirming that the nonlinear strain-displacement relationship has significant effect on the results and the inferred “static instabilities”. This approach first solves the “static” problem of the deformed geometry of a highly strained whirling rod before longitudinal natural modes are determined by classical methods. Furthermore, conditions for existence and uniqueness of solutions are derived. Dynamic Rotating Annuli: In-plane modes of vibration of annular plates are investigated. Two different models of equations one from Bhuta and Jones and the other from Biezeno and Grammel that govern the rotational motions of annuli will be studied. Since Biezeno and Grammel’s model was originally derived in Eulrian coordinates, their model will be transformed to the Lagrangian coordinates for the purpose of comparison with Bhuta and Jones’ model.The solutions of the equations assume small oscillations of vibration being superimposed on the steady state of the annulus while it is in rotation. Exact and approximate solutions are obtained for the Bhuta and Jones’ model, where the approximate solutions on in-plane displacements and natural frequencies are acquired by ignoring the Coriolis effect. A proposed numerical scheme is implemented to solve the governing equations coupled with radial and circumferential displacements. Uniqueness of solutions will be mentioned although it will not be rigorously derived because it is out of the scope of this thesis. Approximate analytical results show that both radial and circumferential natural frequencies are decreasing when the rotational speed of an annulus is increasing. The exact and numerical results on both models that take the Coriolis effect into account show that radial natural frequencies are increasing and circumferential natural frequencies are decreasing when the rotational speed of an annulus is increasing.

    Related items

    Showing items related by title, author, creator and subject.

    • Controlling aero-elastic instability of curtain wall systems in high-rise buildings
      Tan, Ben Hoea; Lucey, Anthony; Pitman, Mark (2011)
      Nowadays modern high-rise buildings have unique facades which partly rely on the incorporation of curtain walls. A curtain-wall system encloses the building to separate the internal and external environments. It can reduce ...
    • Analytical Modeling of Self-Powered Electromechanical Piezoelectric Bimorph Beams with Multidirectional Excitation
      Lumentut, Mikail; Howard, Ian (2011)
      Unused mechanical energies can be found in numerous ambient vibration sources in industry including rotating equipment, vehicles, aircraft, piping systems, fluid flow, and even external movement of the human body. A portion ...
    • Mathematical dynamics of electromechanical piezoelectric energy harvesters
      Lumentut, Mikail F. (2011)
      This research investigates vibration energy harvesting by modelling several piezoelectric-based structures. The usage of piezoelectric transduction under input vibration environments can be profitable for obtaining ...
    Advanced search

    Browse

    Communities & CollectionsIssue DateAuthorTitleSubjectDocument TypeThis CollectionIssue DateAuthorTitleSubjectDocument Type

    My Account

    Admin

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Follow Curtin

    • 
    • 
    • 
    • 
    • 

    CRICOS Provider Code: 00301JABN: 99 143 842 569TEQSA: PRV12158

    Copyright | Disclaimer | Privacy statement | Accessibility

    Curtin would like to pay respect to the Aboriginal and Torres Strait Islander members of our community by acknowledging the traditional owners of the land on which the Perth campus is located, the Whadjuk people of the Nyungar Nation; and on our Kalgoorlie campus, the Wongutha people of the North-Eastern Goldfields.