The basic boundary-contact oscillation problems are considered for a three-dimensional piecewise-homogeneous isotropic elastic medium bounded by several closed surfaces. Using Carleman’s method, the asymptotic formulas for the distribution of eigenfunctions and eigenvalues are obtained. 1. After the remarkable papers of T. Carleman [1–2] the method based on the asymptotic investigation of the r...

In this paper a novel time integration numerical method based on artificial perturbation of damping is proposed. Viscous dissipative terms in the structural dynamics equations motion are perturbed by an parameter. The subsequent asymptotic expansion transient response results infinite series which can be summed, leading to well-defined new step-by-step explicit iterative scheme. Precise algorit...