The generation of waves in infinite structures by moving harmonic loads

Abstract The theory of convolution is extended to account for time-varying loads moving over infinite systems. Fourier transforms are used to simplify the convolution, reducing it to a multiplication of transforms of system impulse response and load. If a harmonic load is moving over the system it is found that the possible existence of travelling waves can be identified, for a given system, load frequency and velocity, without the need to perform the inverse Fourier transform, a task which is often difficult. The possible presence of travelling waves can be identified by a simple method involving straight line constructions on a plot of the system’s frequency spectrum. The phase velocities, group velocities and frequencies of waves ahead of and behind the load can be identified along with any critical speeds and velocities that may exist.