Definition of a high-frequency threshold for plates and acoustical spaces

An extension of the modal overlap factor is introduced that includes ensemble variations and frequency averaging of plates and acoustic spaces. Uniformly and normally distributed variations of geometric and material parameters are considered. Using this modal overlap factor, approximate formulas are derived to identify the limit of predictability for the combined case of damping, ensemble variation, and frequency averaging. The extended modal overlap factor is used to define a high-frequency threshold for plates and acoustical spaces that depends on system parameters and their variations as well as on damping, and the bandwidth of frequency averaging. Monte-Carlo simulations are shown to illustrate and validate the results.