A Lanczos component mode synthesis algorithm for locally nonlinear systems with applications to seismic structural pounding
Lavelle, Francis M., III
Spanos, Pol D.
Doctor of Philosophy
A Component Mode Synthesis (CMS) algorithm employing load dependent Lanczos vectors is presented. The proposed algorithm yields a sparse set of reduced system equations and is an efficient method for computing the forced vibration response of multi-component and/or locally nonlinear dynamic systems. The beneficial aspects of traditional CMS methods employing fixed interface component normal modes and the computational advantages of load dependent Ritz/Lanczos vectors are combined in the new algorithm. By exploiting the tridiagonal property of Lanczos vectors, the system equations are nearly as sparse as traditional CMS equations. The Lanczos CMS transformation projects the solution onto the same subspace spanned by a previously proposed Ritz CMS transformation. For loads which have fixed spatial distributions, the complete static response of each component is completely represented by its first retained Lanczos vector. Several numerical integration techniques which take advantage of the special structure of the synthesized equations of motion are studied. Operations counts demonstrate that the integration costs for the proposed algorithm are substantially lower than the costs associated with fully coupled Ritz CMS equations and nearly identical to traditional CMS integration costs. In general, the accuracy of the proposed algorithm is comparable to traditional CMS algorithms. For specific applications, the rates of convergence of the two methods depend on the applied loading conditions and the degree of interaction between the structural components. The analysis of several multi-component earthquake engineering problems has lead to an investigation of seismic structural pounding. Structural pounding occurs when the separation between adjacent buildings is not sufficient to prevent collisions during seismic excitations. An inelastic linking mechanism which reduces pounding hazards for a particularly vulnerable class of structures is presented. Inelastic links are a viable retrofitting strategy for many existing buildings which have inadequate separation and dissimilar dynamic characteristics. The analytical model for the linked structures is a two-component locally nonlinear system. The proposed Lanczos CMS reduction algorithm is a efficient method for predicting the seismic response of inelastically linked buildings.
Civil engineering; Mechanical engineering