Lumped parameter analysis of a stringer reinforced plate excited by band limited noise
The maximum root-mean-square response of a square clamped plate, subjected to a stationary random excitation, was determined both theoretically and empirically. For the tests, a 40 x 40 x 1/4 aluminum sheet was milled out to provide a thin waffle plate with 9 panels. The plate was acoustically excited, with the frequency range limited between 25 Hz and 500 Hz. The root-mean-square power of the random excitations, 149 decibels, was nearly constant for all natural frequencies of the plate system. Strain gage readings at 14 points were plotted as power spectral densities and root-mean-square displacements. A modal damping ratio matrix was determined from the response curves. Damping ratios were found to be a function of frequency, but not of location on the plate. For comparisons with the theoretical response, the plate was subdivided into 14 modes and anlayzed as a damped, lumped parameter system by use of an approximate normal-mode method. This method gave the best predictions of the power spectral densities for the lower frequencies. That prediction errors increased for the higher frequencies is attributed to improper assumptions for mass distribution and the insufficient number of lumped mass points.