Dynamic Analysis of Eccentrically Prestressed Damped Beam under Moving Harmonic Force Using Higher Order Shear Deformation Theory

Abstract

The dynamic behavior of an eccentrically prestressed simply supported beam under a moving harmonic force is studied by using the higher order shear deformation theory in this paper. The prestressed tendon is assumed straight and unbonded with the concrete. The Lagrange’s equations are used to examine the dynamic response of the beam. Trial functions denoting the deflection of the beam and the rotation of the cross sections are expressed in polynomial forms. The Kelvin-Voigt model for the material of the beam is used. By using Lagrange’s equations, the problem is reduced to a system of differential equations and they are solved by using the direct time integration. Convergence study is performed. The effects of an eccentric and an axial prestress force, velocity of a moving harmonic force, excitation frequency, shear deformation, and the viscous damping of the material on the deflection of the beam are examined.