According to Wikipedia :
"Like many claims in the cymatics community, the hypothesis that the carvings represent Chladni patterns is not supported by scientific or historical evidence.[citation needed] One of the problems is that many of the 'box' carvings are not original, having been replaced in the 19th century following damage by erosion."
Citation needed indeed, but there's no academic research about this extravagant theory anyways, and with my foray into the subject, I just found the patterns to be decorative geometric shapes with a coincidental resemblance to Chladni patterns.