Abstract
The semi-inverse method was used to solve the inverse problem of the vibration of a symmetric rod with two elastic supports. We discuss when the linear density function of the symmetric rod with two elastic supports is a symmetric polynomial function how to construct the axial stiffness of the symmetric rod with two elastic supports for the same symmetric polynomial function, when the symmetric or anti-symmetric mode and the corresponding circular frequency are known. We discuss the axial stiffness of a symmetric rod with two free ends and two fixed ends that was constructed from the symmetric mode or anti-symmetric mode and the associated linear density function.
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