In this paper, we discuss the following inverse problem: how to reconstruct the mass distribution function of a two-span beam with an overhang via its polynomial fundamental mode and polynomial stiffness function. This leads to a basic equations group constituted by the coefficients of the mass distribution and the stiffness distribution function. To make the basic equations group match, one way is to divide it into two sub- equations, and solve them. We specify the method for solving this inverse problem, and research the existence and rationality of the positive solutions.

中文翻译：

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用基本模态重构两跨悬挑梁的质量分布函数

在本文中，我们讨论了以下逆问题：如何通过其多项式基模和多项式刚度函数重建具有悬垂的两跨梁的质量分布函数。这导致了一个由质量分布系数和刚度分布函数构成的基本方程组。为了使基本方程组匹配，一种方法是将其分成两个子方程，并求解它们。我们指定了求解这个反问题的方法，并研究了正解的存在性和合理性。