A HIERARCHICAL FUNCTIONS SET FOR PREDICTING VERY HIGH ORDER PLATE BENDING MODES WITH ANY BOUNDARY CONDITIONS

In this paper a new hierarchical functions set is proposed to predict flexural motion of plate-like structures in the medium frequency range. This functions set is built from trigonometric functions instead of polynomials as classically encountered in the literature. It is shown that such a trigonometric set presents all the advantages of a classical hierarchical polynomials set and additional ones which are of interest if very high order functions are intended to be used. It is stated that this new trigonometric set can be used at very high orders, up to 2048 without taking care of computer round-off errors, while the polynomials set fail, at order 46 because of the limited numerical dynamics of computers. This trigonometric set can be easily implemented on a computer. It does not require quadruple precision pre-computed arrays. Only a very low number (which does not depend on the function order) of basic operations is needed when calling such functions. Moreover, it is shown that this trigonometric set presents a better convergence rate than polynomials when predicting high order natural flexural modes of rectangular plates with any boundary conditions.