Transient response of an elastic beam with discrete impedances from decelerating boundaries

Analyzed is transient response of an elastic beam from decelerating boundaries. It is shown that passive attenuation of peak transient deceleration is possible by coupling the beam to a tuned one-degree-of-freedom (1-dof) oscillator. For a fixed oscillator mass, optimum spring stiffness yields the lowest deceleration response. Furthermore, over a finite range of spring stiffness, the second coupled system mode disappears yielding an additional sharp reduction in transient deceleration response. The disappearance of the second mode is independent of boundary conditions from the weakest simple supports to the strongest clamped ends.