Spatial Response Concentrations in Extended Structures

Abstract

When an extended structure is excited at frequencies above the resonance of its lowest modes, spatial variations in the mean square response occur since the mode shapes are functions of the spatial coordinates. For excitation consisting of band-limited noise or a pure sinusoid, one may calculate the mean square response relatively easily. The spatial variance of the mean square temporal response can also be found and can be interpreted by application of the “central limit theorem.” Vibration modes generally are coherent to some degree. Rather large variations of response may occur at positions where coherent modes have in-phase antinodes. The probability of the occurrence of such response concentrations is studied in this paper. The probability of the occurrence of a concentration at some position on the plate is found to approach unity for some assumed statistical distribution of the resonating modes. (It is felt that the conclusions are not strongly dependent on these assumptions.)