Lower bounds to eigenvalues for vibrations and buckling of structures by analytical applications of a priori known qualitative information (Q1125170)

The author presents general practical methods in order to obtain quickly lower (sometimes also upper) bounds for eigenvalues by replacing the given problem by a related, easily solvable auxiliary problem. Such quick estimates can be very useful in the early technical design. The choice of the auxiliary problem uses essentially a priori information on the (unknown) exact eigenfunctions. In vibration problems, the auxiliary problem is constructed by some redistribution of masses, while the total mass remains unchanged. One-dimensional examples illustrate the approach.