Simulation with minimum equipment of random vibration induced by complex excitation

Complete simulation of random response induced in service by complex, ergodic, Gaussian excitation requires the exact reproduction of the response spectral densities at all points of the system and the cross-spectral densities between each pair of points. This in turn requires exact reproduction of the service loading. If a less-than-complete exact simulation of the response spectra at and between n system locations is acceptable, this can be accomplished using n discrete random forces. For certain types of systems previous theorization has shown that one discrete random force can be used to produce simulation which is accurate in the neighborhood of the resonance frequencies and approximate in the vicinity between resonance peaks. These systems must have light damping and widely spaced resonances so that modal coupling does not exist. The discrete random simulation force must have the appropriately shaped spectrum and must be properly located so that all modes will be excited. For systems of this type the theory shows that reproduction of the response spectral density at any one point assures reproduction of the spectral and cross-spectral densities at and between all other points. In order to assess the practicability of using one electromechanical shaker to simulate random structural vibration which had been induced by complex excitation environments, an experimental study was conducted on two, lightly damped, far-coupled structures having widely separated resonances in their lower frequency range, i.e., a cantilever beam and a simply-supported rectangular plate. The complex, random excitation environment was provided for the beam by two mechanical shakers and for the plate by acoustic noise. One properly located shaker, providing an appropriately shaped input force spectrum, was used to reproduce practicably the narrow-band response spectra and cross-spectra for two measurement locations on each structure. Comparisons made between experimentally and theoretically determined frequency response functions show exceptional agreement. The effects of attaching shakers directly to the structures are discussed. From the results it is concluded that reproduction of the response spectral density at any one point on structures of this type assures reproduction with the same degree of accuracy of the spectra at all other points and the cross-spectra between points.