Abstract
A formulation using the new concept of “Ectoplasm” that allows prediction of high order eigenfrequencies and mode shapes of a simply supported plate with cut-outs of any shape is presented. Hamilton's principle is used with a functional basis that does not depend on the shape of the cut-outs (boundary conditions for stresses around the holes do not matter). Such a basis allows easy computation but leads to a non-unique problem with ill-conditioned mass and stiffness matrices. The use of “Ectoplasm” overcomes these problems without increasing numerical calculation. Extreme examples of holes can be treated and high order modes can be calculated. The convergence of the method is studied and criteria are given to enable its use with a good accuracy. The method is validated by comparison with a finite element approach and previously published results.
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