A COMBINED DYNAMIC FINITE-ELEMENT RICCATI TRANSFER-MATRIX METHOD FOR SOLVING NONLINEAR EIGENPROBLEMS OF VIBRATIONS

The non-linear eigenvalue problems arising from dynamic finite element s in structural analysis are considered. A method of combining the dyn amic finite element method and the Riccati transfer matrix method is p roposed to solve non-linear eigenproblems of vibrations. This method f inds the values of the frequency using the Newton-Raphson method. By t his technique, the number of nodes required in the regular dynamic fin ite element method is reduced, and therefore a microcomputer may be us ed. Besides, no plotting of the value of the determinant versus the as sumed frequency is necessary. The Riccati transformation of state vect ors is proposed in order to avoid the propagation of round-off errors occurring in recursive multiplications of the transfer matrices. A pro gram DFERTM-W based on this method for use on an IBM PC-AT microcomput er is developed. Finally, numerical examples are presented to demonstr ate the accuracy, as well as the capability, of the proposed method fo r solving non-linear eigenproblems of vibrations.