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A new simple closed-form equation that accurately predicts the effect of an arbitrarily large constant axial load, residual stress or temperature shift on the natural frequencies of an uniform single-span beam, with various end conditions, is presented. Its accuracy and applicability range are studied by comparing its predictions with numerical simulations and with the approximate Galef's and Bokaian's formulas. The new equation may be understood as a refinement or extension of these twodoi:10.1016/j.ijmecsci.2019.02.014 fatcat:7ei7wgghsrcxrfjtlaluh75gty