{"id":4705,"date":"2019-01-14T02:44:01","date_gmt":"2019-01-14T07:44:01","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/?page_id=4705"},"modified":"2019-01-14T02:47:24","modified_gmt":"2019-01-14T07:47:24","slug":"three-dof-system-free-response","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/chapter-ii-animations\/three-dof-system-free-response\/","title":{"rendered":"Three-DOF system"},"content":{"rendered":"

Here we will look at the three natural modes of vibration for a three-DOF problem. Shown below is the response of the system for three different sets of initial conditions, each corresponding to one of the modes. Note that in all cases the response of the particles is synchronous (masses moving either in phase or completely out of phase with each other) and that the response is harmonic (of a single frequency).<\/p>\n

\u00a0<\/center><\/p>\n\n\n\n\n\n
<\/center><\/td>\n
FIRST MODE<\/span><\/i><\/b><\/center>Note that all masses are moving in phase with respect to each other. This is typical of the first natural mode of multi-DOF systems.<\/span><\/td>\n<\/tr>\n
<\/center><\/td>\n
SECOND MODE<\/span><\/i><\/b><\/center>Here the blue and green particles are moving in phase with each other and the red particle is moving out of phase with the other two.<\/span><\/td>\n<\/tr>\n
<\/center><\/td>\n
THIRD MODE<\/span><\/i><\/b><\/center>Here the red and blue particles are moving in phase with each other and the green particle is moving out of phase with the other two.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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 <\/p>\n","protected":false},"excerpt":{"rendered":"

Here we will look at the three natural modes of vibration for a three-DOF problem. Shown below is the response of the system for three different sets of initial conditions, each corresponding to one of the modes. Note that in all cases the response of the particles is synchronous (masses moving either in phase or … Continue reading Three-DOF system<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":4682,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-4705","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4705","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/comments?post=4705"}],"version-history":[{"count":3,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4705\/revisions"}],"predecessor-version":[{"id":4712,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4705\/revisions\/4712"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/pages\/4682"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/ervibrations\/wp-json\/wp\/v2\/media?parent=4705"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}