{"id":1082,"date":"2024-07-08T16:41:43","date_gmt":"2024-07-08T11:11:43","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=1082"},"modified":"2025-07-16T15:02:05","modified_gmt":"2025-07-16T09:32:05","slug":"types-of-vibration","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/me\/theory-of-machines\/types-of-vibration","title":{"rendered":"Types of Vibration"},"content":{"rendered":"<ul>\n<li style=\"text-align: justify;\"><strong>Free Vibrations:<\/strong> Elastic vibrations in which there are <strong>no friction<\/strong> and <strong>external<\/strong> forces after the initial release of the\u00a0body.<\/li>\n<li style=\"text-align: justify;\"><strong>Forced Vibrations:<\/strong> When a repeated force continuously acts on a system, the vibrations are said to be forced vibration. The frequency of the vibrations is that of the <strong>applied force<\/strong> and is <strong>independent<\/strong> of their own <strong>natural frequency<\/strong> of vibrations.<\/li>\n<li style=\"text-align: justify;\"><strong>Damped Vibrations:<\/strong> When the energy of a vibrating system is <strong>gradually dissipated<\/strong> by friction and other resistances.<\/li>\n<li style=\"text-align: justify;\"><strong>Un-damped Vibrations (Hypothetical):<\/strong> When there is <strong>no friction or resistance<\/strong> present in system to contract vibration.<\/li>\n<li style=\"text-align: justify;\"><strong>Longitudinal Vibrations:<\/strong> If the shaft is elongated and shortened so that the same <strong>moves up and down<\/strong> resulting in <strong>tensile and compressive stresses<\/strong> in the shaft. <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1083 alignright\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/shaft.jpg\" alt=\"Shaft\" width=\"101\" height=\"136\" \/><\/li>\n<li style=\"text-align: justify;\"><strong>Harmonic vibration:<\/strong> Vibration in which the motion is a sinsuoidal function of time.<\/li>\n<li style=\"text-align: justify;\"><strong>Fundamental vibration:<\/strong> Harmonic component of a vibration with the lowest frequency.<\/li>\n<li style=\"text-align: justify;\"><strong>Steady state vibration:<\/strong> When the particles of the body move in steady state condition or continuing period vibration.<\/li>\n<li style=\"text-align: justify;\"><strong>Transient vibration:<\/strong> Vibratory motion of a system other than the steady state.<\/li>\n<li style=\"text-align: justify;\"><strong>Transverse Vibrations:<\/strong> When the shaft is <strong>bent<\/strong> alternately and tensile and compressive stresses due to bending result. <img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1084 alignright\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/transverse-vibrations.jpg\" alt=\" Transverse Vibrations\" width=\"111\" height=\"144\" \/><\/li>\n<li style=\"text-align: justify;\"><strong>Torsional Vibrations :<\/strong> When the shaft is <strong>twisted and untwisted<\/strong> alternately and <strong>torsional shear stresses<\/strong> are induced.<\/li>\n<\/ul>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-1085 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/torsional-vibrations.jpg\" alt=\" Torsional Vibrations\" width=\"83\" height=\"154\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Free Longitudinal Vibrations<\/strong><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1088 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/free-longitudinal-vibrations.jpg\" alt=\"Free Longitudinal Vibrations \" width=\"721\" height=\"397\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/free-longitudinal-vibrations.jpg 721w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/free-longitudinal-vibrations-300x165.jpg 300w\" sizes=\"auto, (max-width: 721px) 100vw, 721px\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Damped Longitudinal Vibration<\/strong><\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1094 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/Damped.jpg\" alt=\"Damped\" width=\"526\" height=\"230\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/Damped.jpg 526w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/Damped-300x131.jpg 300w\" sizes=\"auto, (max-width: 526px) 100vw, 526px\" \/><\/p>\n<h5 style=\"text-align: justify;\">Dunkerley\u2019s Method<\/h5>\n<p style=\"text-align: justify;\">Let <em>W<\/em>1, <em>W<\/em>2, <em>W<\/em>3, &#8230; be the concentrated loads on the shaft due to masses <em>m<\/em><sub>1<\/sub>, <em>m<\/em><sub>2<\/sub>, <em>m<\/em><sub>3<\/sub>, &#8230; and \u03b4<sub>1<\/sub>, \u03b4<sub>2<\/sub>, \u03b4<sub>3<\/sub> &#8230; the static deflections of this shaft under each load when that load acts alone on the shaft. Let the shaft carry a uniformly distributed mass of m per unit length over its whole span and the static deflection at mid-span due to the load of this mass be \u03b4<em><sub>s<\/sub><\/em>. Also, let<\/p>\n<p style=\"text-align: justify;\"><em>f<\/em><em>n <\/em>= Frequency of transverse vibration of the whole system<\/p>\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1099 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/dunkerley-method.jpg\" alt=\"Dunkerley\u2019s Method\" width=\"656\" height=\"208\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/dunkerley-method.jpg 656w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2024\/07\/dunkerley-method-300x95.jpg 300w\" sizes=\"auto, (max-width: 656px) 100vw, 656px\" \/><\/p>\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/me\/theory-of-machines\/type-of-governors\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/me\/theory-of-machines\/gruebler-paradoxes\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a><br \/>\n<strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-the-theory-of-machines\/\" target=\"_blank\" rel=\"noopener\"><strong>What is the Theory of Machines?<\/strong><\/a><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Free Vibrations: Elastic vibrations in which there are no friction and external forces after the initial release of the\u00a0body. Forced<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[287,10],"tags":[346,347,349,348,350],"class_list":["post-1082","post","type-post","status-publish","format-standard","hentry","category-theory-of-machines","category-me","tag-damped-vibrations","tag-forced-vibrations","tag-harmonic-vibration","tag-longitudinal-vibrations","tag-torsional-vibrations"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/1082","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=1082"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/1082\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=1082"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=1082"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=1082"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}