Reconstructing the Mass Distribution Function of a Two-Span Beam With an Overhang via the Fundamental Mode

Abstract

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.