Use of ritz vectors in wave propagation and foundation response

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<jats:title>Abstract</jats:title><jats:p>The accuracy of a numerical method is demonstrated for the dynamic analysis of large complex finite element systems in which the spatial distribution of the loading is constant. The method is based on the use of a special class of Ritz vectors which were previously proposed and can be generated with minimum numerical effort. The purpose of this paper is to extend the use of these vectors to the solution of wave propagation and foundation response problems.</jats:p><jats:p>The method is applied to one‐, twoand three‐dimensional problems in order to illustrate the efficiency and accuracy of the technique. Unless it is necessary to evaluate the very high‐frequency behaviour of a structural system, it is shown that a small number of Ritz vectors will produce excellent results. Therefore, they can be very effective in the solution of three‐dimensional soil‐structure systems subjected to earthquake loading.</jats:p>

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