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基于线性载荷简支梁挠度方程的傅里叶级数

Keywords: 简支梁,挠度曲线方程,傅里叶级数,梁系数,伯努利数,欧拉数

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Abstract:

从受分布载荷梁的总势能泛函出发,用变分法求出梁的挠度曲线微分方程,给出受线性载荷的简支梁的挠度曲线方程的傅里叶级数,并把简支梁挠度曲线方程加以推广,展开成相应的傅里叶级数,得到一系列无穷级数的求和结果,发现它们均与伯努利数和π有关.找出梁系数、伯努利数和欧拉数之间的关系,提出相应的计算公式.

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