Reconstructing cross-sectional physical parameters for two-span beams with overhang using fundamental mode

Abstract

We use the semi-inverse method to find the solutions to the dynamic equation of an inhomogeneous, functionally graded two-span beam with overhang. Here, the cross-sectional area of this beam is assumed to be constant, and the corresponding natural frequency is given. With both the fundamental mode and density given as polynomial functions in terms of a non-dimensional axial coordinate, we then determine Young’s modulus for the beam expanded as a polynomial function of this axial coordinate. In addition, existence criteria for solutions are obtained. The conditions for positivity of the given density functions and the obtained Young’s modulus are investigated.