Finite element procedures for parametric resonance phenomena of arbitrary elastic shell structures
A purely numerical method for the treatment of instability problems of parametric resonance is presented. The proposed way of solution, which is applicable to all types of structures, is based on the finite element discretization of an incremental variational principle. After the derivation of the theoretical background linear and quadratic eigenvalue problems for the critical excitation-frequencies of undamped and damped systems are presented and numerical procedures for the computation of the instability charts are established. Finally the efficiency of the developed algorithms is demonstrated by means of several shell responses.
linear and quadratic eigenvalue problems
scientific article; zbMATH DE number 3995201
scientific article