Abstract
Analytical equations that describe the dynamic behavior of beams with a soft clamped end are very little treated in the literature. The paper aims to solve this problem by introducing a stiffness in the hinged end of the beam, respectively by comparing the bending moment in the clamped end with the slope in the hinge of the same end of the beam. The other end of the beam is permanently hinged. The characteristic equation for determining the eigenvalues and the modal function is deduced. The results show the first four vibration modes for seven stiffness values and the eigenvalues for eleven cases of soft clamped end.
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