Vibrations of a weakly nondegenerate 1D-3D multi-structure

Abstract

We study the effect of the transition between degenerate and nondegenerate configurations for a 1D-3D multi-structure, by considering a particular nondegenerate configuration. Analytical asymptotic formulae are derived for the first six eigenfrequencies which include information about the location of the 1D parts (legs) of the multi-structure. This enables us to analyse the transition region by moving the legs closer to each other. Accuracy of the asymptotic formulae is compared with numerical solution for the pile structure (skeleton) and with finite element computations. Some inaccuracies associated with numerical and finite element computations are discussed. In addition, a discussion on two-sided estimates for the eigenfrequencies is also included.