A variational-grid method involving orthogonal finite functions for solving problems of natural vibrations of 3D elastic solids

In the present paper we consider an application of orthogonal finite functions in a combined variational-grid method of the mechanics of elastic deformable solids. The method possesses all advantages of combined methods, but is characterized by a reduced number of nodal unknowns due to the orthogonality of the basis functions. As compared with the Ritz method utilizing the Courant functions the proposed method has better computational characteristics, specifically, it provides the splitting of the global system of the grid equations into a number of subsystems and improves its conditionality. The method allows one to find approximations to the natural frequencies from below. In combination with the Ritz method, the proposed method gives two-sided estimates of the natural frequencies.