Abstract
The following problem is posed and solved in this study: Reconstruct the stiffness variation of an inhomogeneous Bernoulli–Euler beam, whose second shape expressed as a polynomial function possesses a node at any pre-selected location. It is shown that for polynomial mode shapes there are regions of allowable position of the node for three specific cases studied in detail: (1) a beam with constant mass density; (2) linear mass density and (3) parabolically varying mass density.
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