應用彎曲振動法評估非均勻斷面梭柱之動彈性模數

Evaluation of Dynamic Young's Modulus of Shuttle-Shaped Column with Non-Uniform Cross Section Properties using Flexural Vibration Test

卓志隆(Chih-Lung Cho) ； 黃仰禾(Yang-He Huang)

《林產工業》 28卷2期 (2009/06) Pp. 99-111

https://doi.org/10.6561/FPI.2009.28(2).4

摘要

本研究目的以Galerkin''''s逼近法評估非均勻斷面木製梭柱之動彈性模數，梭柱以直徑3 cm；長度60 cm之相對應巒大杉（Cunninghamia konishii）圓柱車製而成，圓柱與梭柱經彎曲振動試驗法及模態分析所測得之各模態共振頻率，梭柱並根據Galerkin''''s逼近法計算其在各彎曲模態下之等效斷面慣性矩及斷面積，最後依Euler梁理論計算動彈性模數並與圓柱者進行差異性比較。研究結果顯示應用模態分析方法可準確判定彎曲各振動模態之共振頻率。根據Galerkin''''s逼近法所計算出梭柱的等效斷面慣性矩與振動模態間呈曲線狀減低趨勢，等效斷面積則呈曲線狀增加趨勢。依圓柱動彈性模數計算之相對應梭柱彎曲第1至第5振態共振頻率預測值與實測值之絕對差異百分率，依序為1.59%、2.84%、3.22%、3.42%及4.05%。不論圓柱或梭柱，其彎曲振動彈性模數在較高次的振動模態時會偏低。應用Galerkin''''s方法所計算之梭柱第1到第5彎曲振態之動彈性模數與圓柱的平均絕對差異百分率分別為3.38%、5.83%、6.59%、7.20%及8.58%。由研究結果建議以彎曲基本共振頻率推算梭柱動彈性模數之準確性較高。

關鍵字

梭柱 ； 彎曲振動 ； 非均勻斷面 ； 動彈性模數

並列摘要

The purpose of this study is to evaluate the dynamic modulus of elasticity (DMOE) of shuttle-shaped columns with non-uniform cross-section along their lengths using Galerkin's approximate method. The shuttle-shaped column was made of the corresponding Cunninghamia konishii round column with 3 cm in diameter and 60 cm in length. The natural frequencies of various vibration modes of round and shuttle-shaped column were determined by flexural vibration test and modal analysis. The equivalent moment of inertia and area of cross-section for each shuttle-shaped column was determined according to Galerkin's approximate method. The DMOE of each round or shuttle-shaped column was determined by Euler beam theory.The results showed that natural frequencies with respect to each flexural vibration mode could be identified accurately using modal analysis. The equivalent moment of inertia of shuttle-shaped columns with respect to Galerkin's approximate method decreased in a curve trend as the modes of vibration increasing and those of equivalent area of cross-section would be increased. The mean absolute percentage differences between predicted and measured natural frequencies of the first, second, third, fourth, and fifth flexural vibration mode for shuttled-shaped columns are 1.59%, 2.84%, 3.22%, 3.42%, and 4.05%, respectively. The DMOE determined from higher vibration mode frequencies are lower than those from fundamental frequency, no matter the specimens is round column or shuttle-shaped column. The mean absolute percentage differences between DMOE of round and shuttle-shaped columns with regard to the first, second, third, fourth, and fifth flexural vibration mode are 3.38%, 5.83%, 6.59%, 7.20%, and 8.58%, respectively. This study suggests that the DMOE of shuttle-shaped column determined from fundamental frequencies would be more accurate than the others.

並列關鍵字

Shuttle-shaped column ； Flexural vibration ； Non-uniform cross-section ； Dynamic modulus of elasticity