湖南大学学报（自然科学版）2018，Vol.45Issue(3)：136-141,6.DOI:10.16339/j.cnki.hdxbzkb.2018.03.017
对称荷载作用下弹性地基梁的傅里叶级数解
Fourier Series Solution for Elastic Foundation Beams under Symmetric Loads
摘要
Abstract
Taking into account the load due to ground displacement and the detachment between a beam and ground,a mathematical model was presented for two kinds of elastic foundation beams under symmetric loads.A kind of beams has a length larger than the width of settlement trough,and another with less length than the width of the trough.Heaviside step function and impulse function were introduced,and their Fourier series expansions were given.According to the established model and making use of the step function and impulse function,an equa-tion set for solving the coefficients of the series that represents the deflection of elastic ground beam was derived. An iteration process to find detachment interval,which is a redundant unknown in the equation set,was put for-ward.Lastly,verification was done to the proposed series solution by comprising with finite element method.The results show that Fourier series solution is of high accuracy of computation,and can be used as an analytical solu-tion of the elastic foundation beams.To achieve the same accuracy,series solution needs much less amount of cal-culation.The computed value of detachment interval in the series solution doesn't change with the number of em-ployed series items.In a whole,Fourier series solution offers high accuracy and convenience in dealing with differ-ent kinds of loads.It provides an analytical way to effectively solve the problems for an elastic foundation beam un-der complicated loads.关键词
地下结构/弹性地基梁/地基沉降/脱空/傅里叶级数Key words
underground structures/elastic foundation beam/ground settlement/detachment/Fourier series分类
交通工程引用本文复制引用
杨成永,寇鼎涛,程霖,马文辉..对称荷载作用下弹性地基梁的傅里叶级数解[J].湖南大学学报（自然科学版）,2018,45(3):136-141,6.基金项目
国家自然科学基金资助项目(51478032),National Natural Science Foundation of China(51478032) （51478032）
