Coin vibration analysis in classical and Mindlin theory
Keywords:
vibration, eigenfrequency, circular plate, elasticityAbstract
We studied 83 coins that belong to moderately thick circular plates with thickness h and radius a in the range 4.37? a/h ? 9.94. The computed values in classical thin plate and first-order shear deformation Mindlin theory overestimate and respectively underestimate the experimental values for natural frequencies of coins. The Mindlin theory approximates better the experimental frequencies having the RMS value of 0.546 lower than the RMS value of 0.630 of the classical theory. The main uncertainty related to the values of the Young modulus and Poisson ratio of the studied alloys is resolved in this article by extracting them from the first two natural frequencies. The experimental frequencies of the studied coins can be used as a benchmark to compare the first-order with higher-order shear deformation theories. The study can be relevant to discriminate the coins in the vending machines with acoustic sensor.
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Country: A -Austria (gr - groschen, sc - schilling, vi - Vienna philarmonic), CA - Canada (ma - maple), CZ - Czech Republic (kc - koruna), D- Germany (p - phening, m - mark), E - Europe (€c - eurocent, € - euro), EG -Egypt (q - quirsh), GB - Great Britain (br - britannia, p - pence, £ - lira), H - Hungary (ft - forint), HR -Croatia (k - kuna), J - Japan, MC - Monaco (ra - 50francs rainier), PL - Poland (gr - groszy, zl - zloty), RO - Romania (b - ban, L - lei), SA - South Africa (kr - krugerrand), SK - Slovakia (st - koruna), TR - Turkey (kr - kurus, L - lira), UA - Ukraine (hr - hryvnia), US - United States of America (¢ - cent, $ - dollar, ea - eagle, mp - morgan peace, wa - washington, wl - walking liberty).
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