| Abstract: | The dynamic analysis of structures by the standard finite element method introduces additional inaccuracies into the solution which are not present when the method is used for static analyses. These inaccuracies can arise from two sources: (i) the element formulation and (ii) the reduction of the size of the matrices by a static condensation (i.e. using the Guyan method1,2). The errors in both cases are caused by neglecting frequency-dependent terms in the functions relating the displacements at any point in the structure to the displacements at certain fixed points (i.e. nodes in the element formulation and ‘masters’ in the condensation). A new method of solution is proposed in this paper in which the frequency-dependent terms are retained implicitly by using dynamic stiffness matrices defined at a number of fixed frequencies. The dynamic stiffness matrices may be condensed efficiently to a relatively small number of master degrees-of-freedom using a front solution algorithm. The final stage in the solution uses these matrices to synthesize a high-order eigenvalue problem. A method of solving such an eigenvalue problem, of arbitrary order, is described in a separate paper.3 Numerical examples are given to show the accuracy and efficiency of the proposed method compared with conventional methods of solution. |
