The strain energy in loosening the clamped end of a beam (part II)

Abstract

In the second part of the paper, the dynamic behavior of a doubly clamped beam is presented, where the right clamped end of the beam is weakened by introducing a weakening coefficient. The analytical calculation is based on the determination of the bending moment from the weakened clamped end expressed as a function of slope, after which the modal function, strain energy and the characteristic equation are determined to obtain the eigenvalues of the first six vibration modes depending on the weakened coefficient of the clamped end. The obtained mode shapes and strain energies are determined for seven values of the weakened coefficient.