Abstract:

This communication proposes a new hierarchical functions set to predict flexural motion of platelike 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 desired 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 roundoff errors, while the polynomials set fails at order 46 because of the limited numerical dynamic of computers. This trigonometric set can be easily implemented on a computer. It does not require quadruple precision precomputed arrays. Only a very low number (which do 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.