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標題: 受集中載重且含有混合邊界的矩形複材層疊板之自由振動分析
Free Vibration Analysis of Mass-loaded of Rectangular Composite Laminates with Mixed Boundaries
作者: 吳孟鴻
Wu, M.H
關鍵字: Free Vibration;集中載重;Mass-loaded;Composite Laminates;Mixed Boundaries;混合邊界;複材層疊板;自由振動分析
出版社: 應用數學研究所
合邊界的矩形複材層疊板之振動頻率與振動模態.首先, 我們發展小區域
的方法推求主導特徵方程式, 在求解的過程, 我們使用 Subdomain
Weighted Residual 來解決倆相鄰不同邊界條件的小區域之連續性並求得
關聯的連續矩陣, 其中, 符合小區域的正交多項式乃採用 Gran-
Schmidt 之正交過程求得. 最後, 由關聯的連續矩陣推導全區域的能量方
程,再應用 Rayleigh-Ritz 的方法獲得主導的特徵方程式, 藉著求解主導
板之振動頻率與振動模態, 而且, 也可觀察混合比率,層疊板角度以及集

In this paper, the free vibration analysis of mass-loaded
rectangular composite laminates plate with mixed boundaries is
performed by using the orthogonal polynomial functions and Ritz
method. We develop the subdomain method to derive the governing
eigenvalue equation. In the solution process, we use the
Subdomain Weighted Residual to satisfy the compatibility at the
interconnect boundaries for two adjacent subdomain and carry
out continuity matrices, then we adopt the Gram-
Schmidtorthogonalization process to find the orthogonal
functions fythe simply subdomain boundary condition.Finally, we
use continuous matrices to develop the global energy functional
andapply the Ritz method to obtain the governing eigenvalue
equation.By solving the governing eigenvalue equation, we can
obtain the natural frequenciesand mode shapes of the composite
laminates.Furthermore, we also investigate the effects of mixed
edge ratio, ply orientation andconcentrated masses on the free
vibration of the rectangular symmetric composite laminates.
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