靜不定樑的拉普拉斯變換解法

A Solution to Indeterminate Beams Using the Laplace Transform

鍾文貴(Wen-Guey Chung) ； 王弘祐(Hung-Yu Wang) ； 胡竣傑(Jiunn-Jye Hwu)

《科學與工程技術期刊》 5卷4期 (2009/12) Pp. 69-76

https://doi.org/10.7117/JSET.200912.0069

摘要

靜不定樑是常見的工程結構，連續樑即是典型的例子，其特徵爲樑的約束反力多於靜力平衡方程式，用一般方法求解較繁雜且易出錯。本文用拉普拉斯變換將均質等截面樑的撓曲曲線方程式Ely(上標 (4))=−q(x)化爲代數方程式，推導得包含作用在樑上的載重函數Q(x)與樑的端點邊界條件y(0),y'(0),y”(0)及y””(0)等輸入參數之解析公式，並以四個範例說明應用此公式求解靜不定樑的具體方法與步驟。計算過程簡潔且方便應用，具有實用價值。

關鍵字

靜不定樑 ； 拉普拉斯變換 ； 撓曲

並列摘要

Statistically indeterminate beams such as continuous ones are commonly applied to practical engineering structures. A solution to such indeterminate beams, based on the Laplace transform, is presented in this report. A facilitating formula with loading functions and boundary conditions upon the beam was derived; moreover, four examples were used for testing the formula. The computational results from these examples show that this formula can easily and efficiently solve the problem of indeterminate beams, thereby evidently demonstrating the practicability of the presented method.

並列關鍵字

indeterminate beams ； Laplace transform