教師資料查詢 | 類別: 期刊論文 | 教師: 馮朝剛 FENG CHAO-KANG (瀏覽個人網頁)

標題:The similarity analysis of vibrating membrane with its applications
學年93
學期2
出版(發表)日期2005/06/01
作品名稱The similarity analysis of vibrating membrane with its applications
作品名稱(其他語言)
著者Feng, Chao-Kang; Lee, Chi-Yuan
單位淡江大學航空太空工程學系
出版者Kidlington: Pergamon
著錄名稱、卷期、頁數International Journal of Mechanical Sciences 47(6), pp.961-981
摘要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.
關鍵字Boundary conditions; Differential equations; Eigenvalues and eigenfunctions; Laplace transforms; Problem solving; Wave equations; Helmholtz equation; Rayleigh-Ritz method; Scaling law; Similarity analysis; Vibrations (mechanical)
語言英文
ISSN0020-7403
期刊性質國外
收錄於
產學合作
通訊作者Feng, Chao-Kang
審稿制度
國別英國
公開徵稿
出版型式紙本
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