Establishing a benchmark for comparative analysis of thin and thick plate modal frequencies: A non-dimensional paradigm

This study presents a methodological framework to establish a standardised baseline for comparing the vibrational characteristics of thin and thick rectangular orthotropic plates in acoustics. The research addresses the inherent difficulties associated with varying plate parameters by proposing the use of non-dimensional frequencies for comparative assessments. It will be shown that, under the thin-plate approximation, plates with identical aspect ratios, boundary conditions, and elastic constant ratios exhibit identical non-dimensional modal frequencies and shapes. The proposed methodology involves generating baseline non-dimensional frequencies and modal shapes via numerical simulations for a reference plate with specified parameters. Subsequent analysis entails systematically varying plate thickness while monitoring deviations of non-dimensional frequencies from the baseline. This process finally allows to determine up to which mode number the discrepancy in the dimensionless frequency between the baseline and the ensuing modelled plates can be confined within certain tolerance values. Notably, the comparison is conducted on an eigenshape basis, thereby circumventing the consideration of dimensional frequencies. This approach offers a structured framework for comparative analysis, centred on identifying modes exhibiting thin behaviour regardless of dimensional frequencies, stressing the objectivity of the presented methodology.