Damping-induced interplay between vibrations and waves in a forced non-dispersive elastic continuum with asymmetrically placed local attachments

We study the dynamics of a linear, uniform, undamped string under harmonic base excitation, with an attachment consisting of either a spring-dashpot system or a vibration absorber. Mode complexity caused by the local damping of the attachment can lead to coexistence of vibrations and waves in the string. We consider either identical harmonic base motions at both ends or harmonic base excitation at one end. In the case of double harmonic base excitation, it is possible to choose the parameters of the attachment, so that the mode complexity is maximal in one part of the string (leading to travelling waves and elimination of vibrations) and almost zero in the other part (with standing waves or vibration modes). Similarly, for single base excitation, we analytically predict the parameters of the attachment that maximize mode complexity and enhance the interplay of vibrations and travelling waves in the string. Under such conditions, the system acts as a passive vibration confinement device, with induced energy being transmitted through travelling waves to a region where it is confined in the form of standing waves. Our results can be used for predictive design and reveal an unexpected new application of the classical linear vibration absorber.