Experimental and numerical assessment of the equivalent-orthotropic-thin-plate model for bending of corrugated panels

Numerous papers deal with the Equivalent Plate Model (EPM) for corrugated panels. Comparison of published formulas for the four relevant equivalent bending stiffnesses D11eq, D22eq, D66eq, andD12eq revealed ambiguities: Three different formulas were found for D22eq, which describes the bending of the ridges and troughs; for D66eq two 'competing' formulas emerged. Expressions not converging to the flat-plate values in the limit of vanishing corrugation height were discarded. All discussed formulas are written in a uniform notation for general one-dimensionally periodic shapes. Formulas derived for isotropic panel materials were generalized to the orthotropic case. In order to resolve the ambiguities and assess the EPM with regard to its range of applicability, vibration modes of six rectangular corrugated panels were measured. While agreement with numerical results obtained with COMSOL was fair, the EPM predictions of natural frequencies were satisfactory only for low-order modes. Finally, equivalent bending stiffnesses were determined numerically from COMSOL results for a few low-order modes by inverse methods. Thus the ambiguities with regard to D22eq and D66eq could be resolved. However, the D12eq values determined numerically came out significantly larger than the EPM prediction, in particular for stronger corrugations. Even though this discrepancy had little effect on the natural frequencies tested in the present paper, it remains a theoretical challenge.