Analytical Solution of the Steady State Response of Suspension Bridge Tower-Pier Systems with Distributed Mass to Harmonic Base Excitation

Abstract

A typical suspension bridge tower-pier system is considered, the tower mass of which is not negligible and assumes an arbitary distribution along the tower. The pier rests on a viscoelastic foundation and can follow rotational and horizontal motion. The surrounding soils perform a horizontal harmonic motion. The equation of motion of the pier as well as the partial differential equation of the lateral deflections of the tower with the accompanying boundary conditions, are derived. The solution of the above p.d.e. is taken as a sum of terms, each one corresponding to an eigenshape of vibration of the tower. Applying the Galerkin method a system of ordinary differential equations results. The system of all the o.d.e.′s of motion (the pier's and the tower's) is solved for the steady state response, and based upon the resulting deflections, the stresses along the tower are determined. A parametric study is carried out.