Mixed Variational Principles in Vibrational Mechanics

摘要

Harmonic vibrations of mechanical systems with nonholonomic constraints are analyzed using a mixed variational formulation for the spectral problem. A connection with methods of the intermediate problem type is established. Numerical bracketing of the natural frequencies of complex structures is treated by calculating an optimal stress associated with the displacement obtained by the primal method. A mixed formulation is used for a static calculation, the data for which are the results from the primal method obtained through calculation of eigenvalues. It is shown that penalization techniques with reduced integration can be applied to vibration problems. Discretization of mixed variational principles by the finite element method increases accuracy for magnitudes which do not appear directly in the displacement principle. A posteriori error estimates for natural modes and frequencies obtained by finite element methods can be deduced.