Wpływ Naprężeni Własnych na Drgania Sprężyste Prętów o Stałym Przekroju - Bogusz, W. (Engineering Transactions, 1958)
Discussion of a method for the determination of initial stress in bars of constant cross-section by means of vibration measurement. In the equation of longitudinal vibration of a beam with one end fixed, the elastic force appears, depending on the elongation. If the dependency is parabolic, the elastic force is determined by two coefficients, f and g. An analysis of the vibration by means that the coefficients f and of successive approximations shows 9 may be determined by measuring the amplitude and the displacement of the vibration centre and the fundamental frequency. Thus, the dynamic relation between the elastic force and the elongation is obtained. With small amplitudes, the relation obtained may be compared with the statical relation between the elastic force and the elongation, and the range of stress of the vibration may be determined. If the coefficient g is small, the dynamic dependency approaches the linear form, and vibration occurs in the range of stress below the limit of proportionality. The equation of flexural vibration of a bar with one end clamped is analyzed. In both cases, that is for longitudinal and flexural vibrations the internal drag of the material is disregarded, which is justified by the assumption of small amplitudes.