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This research deals with the dynamical evolutions exhibited by a simple mechanical model of building, comprising a parallelepiped standing on a horizontal plane. The main goal is the introduction of a pendulum in order to control the vibrations; dry friction has also been considered. The theoretical part of the work consists of a Lagrange formulation and Galerkin approximation method. From this theoretical standpoint, we derive many important analytical or numerical results, providing us the tools suitable for the design of absorbers in practical cases. <\/jats:p>","DOI":"10.1177\/0959651815616715","type":"journal-article","created":{"date-parts":[[2015,12,10]],"date-time":"2015-12-10T03:08:40Z","timestamp":1449716920000},"page":"104-114","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Oscillations of a rocking block with an added pendulum"],"prefix":"10.1177","volume":"230","author":[{"given":"Luca","family":"Collini","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering, University of Parma, Parma, Italy"}]},{"given":"Rinaldo","family":"Garziera","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Parma, Parma, Italy"}]},{"given":"Aleksander V","family":"Karapetyan","sequence":"additional","affiliation":[{"name":"Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia"}]},{"given":"Maria A","family":"Munitsyna","sequence":"additional","affiliation":[{"name":"Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia"}]},{"given":"Alessandro","family":"Tasora","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering, University of Parma, Parma, Italy"}]}],"member":"179","published-online":{"date-parts":[[2015,12,9]]},"reference":[{"volume-title":"Dynamics of structures","year":"1993","author":"Clough RW","key":"bibr1-0959651815616715"},{"issue":"2","key":"bibr2-0959651815616715","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1785\/BSSA0530020403","volume":"53","author":"Housner GW","year":"1963","journal-title":"B Seismol Soc Am"},{"key":"bibr3-0959651815616715","doi-asserted-by":"publisher","DOI":"10.5459\/bnzsee.11.3.141-150"},{"issue":"2","key":"bibr4-0959651815616715","first-page":"377","volume":"106","author":"Aslam M","year":"1980","journal-title":"Proc Am Soc Civ Eng"},{"key":"bibr5-0959651815616715","doi-asserted-by":"publisher","DOI":"10.1002\/eqe.4290080606"},{"volume-title":"Review and discussion on overturning of bodies by earthquake motion","year":"1980","author":"Ishiyama Y","key":"bibr6-0959651815616715"},{"key":"bibr7-0959651815616715","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9399(1984)110:11(1627)"},{"key":"bibr8-0959651815616715","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9399(1993)119:7(1387)"},{"key":"bibr9-0959651815616715","doi-asserted-by":"publisher","DOI":"10.1002\/eqe.4290100502"},{"key":"bibr10-0959651815616715","unstructured":"Kaneko M, Hayashi Y. 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