From frequency-dependent mass and stiffness matrices to the dynamic response of elastic systems

More than three decades ago, Przemieniecki introduced a formulation for the free vibration analysis of bar and beam elements based on a power series o f frequencies. In the present paper, the authors generalize this formulatio n for the analysis of the dynamic response of elastic systems submitted to arbitrary nodal loads as well as initial displacements. Based on the mode-s uperposition method, a set of coupled, higher-order differential equations of motion is transformed into a set of uncoupled second-order differential equations, which may be integrated by means of standard procedures. Motivat ion for this theoretical achievement is the hybrid boundary element method, which has been developed by the authors for time-dependent as well as freq uency-dependent problems. This formulation, as a generalization of plan's p revious achievements for finite elements, yields a stiffness matrix for whi ch only boundary integrals are required, for arbitrary domain shapes and an y number of degrees of freedom. The use of higher-order frequency terms dra stically improves numerical accuracy. The introduced modal assessment of th e dynamic problem is applicable to any kind of finite element for which a g eneralized stiffness matrix is available. Some academic examples illustrate the theory. (C) 2001 Elsevier Science Ltd. All rights reserved.