Using Galerkin method and employing spherical eigen-functions as a complete set of solution, modal acoustic pressure and acoustic radiation efficiency of the cylinder are calculated.
But Prodan's model is highly useful as it provides a complete set of eigenmode solutions in complex nanostructures.
A complete set of series form solutions of stress and displacement functions, including all higher order terms, around the crack tip for anisotropic crack problems have been newly derived by eigenfunction expansion approach.
None of these ratchets has yet been proven to yield an optimal and complete set of solutions (and many clearly do not), but in practice they usually yield a substantial increase in computational efficiency and a solution set that is identical to a ratchet-free run.
In contrast to commonly used single objective models, which must be executed numerous times in order to provide the decision-maker with feasible solutions, multi-objective models exhibit a complete set of feasible and optimal solutions with a single execution.
As a single trace can represent a big number of solutions, by enumerating traces we can generate a set much smaller than the complete set of solutions.
In the paper, the complete set of solutions is provided for 6- and 7-ply laminates, and the methodology to find solutions for a higher number of layers is presented.
The method results in a complete set of adiabatic invariants specifying the approximate solutions for motion.
Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation.
