On the boundedness of damped strings and beams with boundary and distributed inputs

This paper proves the boundedness of boundary and distributed damped strings and Euler-Bernoulli beams under combined distributed and boundary inputs. Distributed viscous or Kelvin-Yoigt damping or a translational boundary damper stabilize strings and beams. Pointwise bounded response is proven using the energy multiplier method. Without disturbances, the method proves strong exponential stability. With disturbances, the response is shown to be strongly bounded.