Limiting Limitants in Dynamic Problems for a Rectangular Prism

An algorithm of solving a quasi-regular infinite system of linear algebraic equations following from a boundary-value problem describing the stationary forced vibrations of an isotropic rectangular prism in the plane linear elastic case is outlined. The algorithm employs Koyalovich’s limitants, which makes it possible to estimate the upper and lower bounds for the entire infinite set of unknowns and the natural frequencies of the prism. Additionally, the sums of all the functional series in the representation of the solution of the boundary-value problem are found in the rectangular domain