Transient response of a string on an elastic base

Abstract

The transient response of a stretched string resting on an elastic base and subjected to impulsive end loading is treated herein. 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 recurrence relation which is in turn generated by using a time-harmonic asymptotic series solution to the equation of motion. Numerical examples are treated where the responses of the string to delta and step function boundary loads are obtained. The results confirm the influence of the base modulus on the transient displacement, velocity and slope distributions in the string. The distortion of the transients and the discontinuities in the velocity and slope are evident from the results presented. The transient response of the string due to other boundary conditions can be obtained by using the present results. © 1986.