淡江大學機構典藏:Item 987654321/46035
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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/46035


    Title: The similarity analysis of vibrating membrane with its applications
    Authors: Feng, Chao-Kang;Lee, Chi-Yuan
    Contributors: 淡江大學航空太空工程學系
    Keywords: Boundary conditions;Differential equations;Eigenvalues and eigenfunctions;Laplace transforms;Problem solving;Wave equations;Helmholtz equation;Rayleigh-Ritz method;Scaling law;Similarity analysis;Vibrations (mechanical)
    Date: 2005-06
    Issue Date: 2013-03-20 16:31:31 (UTC+8)
    Publisher: Kidlington: Pergamon
    Abstract: The similarity analysis is applied to the study of vibrating membrane with variable density. In this paper, the design of the eigenvalue problems of the vibrating mode (Helmholtz equation) by the infinitesimal transformation groups is exhibited.

    The exact similarity solutions of the eigenvalue problems of Helmholtz equation with variable weighting function under the spiral and inversion groups are constructed in the regions of spiral, concentric circles, eccentric circles, and upper-half plane with circle removed.

    The similitude and scaling law are also built under the study and manipulation of the differential equations that are known to govern the behavior of the eigenvalue problems of Helmholtz equation. Without the requirement of geometrically similitude or mapping, the eigenvalues of a complicated domain can be obtained directly from a given simple region through the scaling law and they are verified and checked by numerical calculation and the Rayleigh–Ritz method.
    Relation: International Journal of Mechanical Sciences 47(6), pp.961-981
    DOI: 10.1016/j.ijmecsci.2004.12.001
    Appears in Collections:[Graduate Institute & Department of Aerospace Engineering] Journal Article

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