Transient Response of Beam Under Initial Stress

Abstract

The effect of initial stress on the transient response of a beam subjected to impulsive end loading is investigated. This loading can be prescribed in the form of stress, strain, velocity or acceleration boundary conditions. The Timoshenko equations, modified to include the presence of initial stress, are used to model the beam. The analysis is based on the concept of a wave as a carrier of discontinuities in the field variable and its derivatives. These discontinuities are determined from a set of recurrence relations that are, in turn, generated by using time‐harmonic asymptotic series solutions to the equations of motion. The numerical results obtained confirm the influence of prestress on the transient velocity, bending moment, and shear force distributions in the beam. The results for zero initial stress compare favorably with those from a closed form solution, while the other results follow a particular trend. Solutions to problems with other boundary conditions can be obtained by using the present results.