A Novel Solution to Find the Dynamic Response of an Euler–Bernoulli Beam Fitted with Intraspan TMDs under Poisson Type Loading

摘要

This contribution considers a virtual experiment on the vibrational response of rail androad bridges equipped with smart devices in the form of damping elements to mitigate vibrations.The internal damping of the bridge is considered a discontinuity that contain a dashpot. Exactcomplex eigenvalues and eigenfunctions are derived from a characteristic equation built as thedeterminant of a 4 x 4 matrix; this is accomplished through the use of the theory of generalizedfunctions to find the response variables at the positions of the damping elements. To relate this toreal world applications, the response of a bridge under Poisson type white noise is evaluated; thisis similar to traffic loading that would be seen in a bridge’s service life. The contribution alsodiscusses the importance of smart damping and dampers to sustainability efforts through thereduction of required materials, and it discusses the role played by robust mathematical modellingin the design phase.