Vibrational modes of circular free plates under tension

The vibrational frequencies of a plate under tension are given by the eigenvalues $\omega$ of the equation $\Delta^2u-\tau\Delta u=\omega u$. This paper determines the eigenfunctions and eigenvalues of this bi-Laplace problem on the ball under natural (free) boundary conditions. In particular, the fundamental modes --- the eigenfunctions of the lowest nonzero eigenvalue --- are identified and found to have simple angular dependence.Comment: 17 pages. To be submitted for publication shortly

Vibration control of bridges under simultaneous effects of earthquake and moving loads using steel pipe dampers

This study aims to develop a practical methodology based on the eigenfunction expansion method to assess the effects of simultaneous action of vertical earthquake excitation and moving vehicle loads in single-span and multi-span simply-supported bridges. While the effects of vertical earthquake ground motions are generally ignored in common design practice, it is shown that the influence of simultaneous vertical earthquake excitation and vehicle loads can considerably affect the structural response of the bridge, especially in near-field earthquakes with high amplitude vertical components. To address this issue, a novel vibration suppression system is proposed using steel pipe dampers and its reliability is investigated for a wide range of bridge flexural rigidity under seven different earthquake records. The results indicate that the proposed system can significantly (up to 75%) suppress the vertical vibrations generated in the bridge, especially for the systems with lower flexural rigidity. For the same maximum deflection limits, application of pipe dampers could reduce the required flexural rigidity of the bridge (up to 50%), and therefore, lead to more economic design solutions with lower structural weight