<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/64e52dd0-eb6f-4bbb-afc3-219f8b37ad24/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls4 ws3"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls4 ws3">1 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls4 ws3"> </div></div><div class="t m0 x1 h4 y5 ff2 fs1 fc1 sc0 ls4 ws3">Vibrações Mecânicas \u2013 <span class="_0 blank"> </span>Resumo </div><div class="t m0 x1 h4 y6 ff2 fs1 fc1 sc0 ls4 ws3"> </div><div class="t m0 x1 h5 y7 ff3 fs2 fc0 sc0 ls4 ws3">VIBRAÇÕES FORÇADAS EM SISTEMAS </div><div class="t m0 x1 h5 y8 ff3 fs2 fc0 sc0 ls4 ws3">COM 1 GDL \u2013 FUNÇÃO DE RESPOSTA </div><div class="t m0 x1 h5 y9 ff3 fs2 fc0 sc0 ls4 ws3">AO IMPULSO (IRF) E RESPOSTA DE </div><div class="t m0 x1 h5 ya ff3 fs2 fc0 sc0 ls4 ws3">FORÇA DO TIPO DEGRAU UNITÁRIO<span class="fs3 fc2"> </span></div><div class="t m0 x1 h6 yb ff3 fs3 fc1 sc0 ls4 ws3"> Introdução: </div><div class="t m0 x1 h7 yc ff2 fs4 fc0 sc0 ls4 ws3">Vimos na nossa <span class="_0 blank"> </span>2ª aula <span class="_0 blank"> </span>a força de excitação <span class="_0 blank"> </span>transitória, que é a <span class="_0 blank"> </span>força caracterizada por </div><div class="t m0 x1 h7 yd ff2 fs4 fc0 sc0 ls4 ws3">uma <span class="_1 blank"> </span>liberação <span class="_1 blank"> </span>de <span class="_1 blank"> </span>energia <span class="_1 blank"> </span>grande <span class="_1 blank"> </span>num <span class="_1 blank"> </span>curto <span class="_1 blank"> </span>int<span class="_2 blank"></span>ervalo <span class="_1 blank"> </span>de <span class="_1 blank"> </span>tempo <span class="_1 blank"> </span>como <span class="_1 blank"> </span>uma <span class="_1 blank"> </span>explosão </div><div class="t m0 x1 h7 ye ff2 fs4 fc0 sc0 ls4 ws3">ou um impacto. </div><div class="t m0 x1 h7 yf ff2 fs4 fc0 sc0 ls4 ws3">Trata-se <span class="_0 blank"> </span>de <span class="_0 blank"> </span>uma <span class="_0 blank"> </span>ferramenta <span class="_0 blank"> </span>matemática <span class="_0 blank"> </span>com <span class="_0 blank"> </span>uso <span class="_0 blank"> </span>muito <span class="_0 blank"> </span>comum <span class="_0 blank"> </span>na <span class="_0 blank"> </span>análise <span class="_0 blank"> </span>transiente </div><div class="t m0 x1 h7 y10 ff2 fs4 fc0 sc0 ls4 ws3">de sistemas vibratórios. </div><div class="t m0 x1 h7 y11 ff2 fs4 fc0 sc0 ls4 ws3">Um <span class="_3 blank"> </span>dos <span class="_3 blank"> </span>tipos <span class="_3 blank"> </span>de <span class="_3 blank"> </span>força <span class="_3 blank"> </span>transitória <span class="_3 blank"> </span>mais <span class="_3 blank"> </span>utilizados <span class="_3 blank"> </span>nessas <span class="_3 blank"> </span>análi<span class="_2 blank"></span>ses <span class="_3 blank"> </span>é <span class="_3 blank"> </span>o <span class="_3 blank"> </span>impulso, <span class="_3 blank"> </span>cuja </div><div class="t m0 x1 h7 y12 ff2 fs4 fc0 sc0 ls4 ws3">utilização <span class="_4 blank"> </span>tem <span class="_4 blank"> </span>destaques <span class="_4 blank"> </span>na <span class="_4 blank"> </span>obtenção <span class="_4 blank"> </span>dos <span class="_4 blank"> </span>parâmetros <span class="_4 blank"> </span>modais <span class="_4 blank"> </span>de <span class="_4 blank"> </span>um <span class="_4 blank"> </span>sistema, </div><div class="t m0 x1 h7 y13 ff2 fs4 fc0 sc0 ls4 ws3">também <span class="_5 blank"> </span>já <span class="_5 blank"> </span>citados <span class="_5 blank"> </span>anteriormente, <span class="_5 blank"> </span>como <span class="_5 blank"> </span>as <span class="_5 blank"> </span>frequências <span class="_5 blank"> </span>naturais, <span class="_5 blank"> </span>coeficientes <span class="_6 blank"> </span>de </div><div class="t m0 x1 h7 y14 ff2 fs4 fc0 sc0 ls4 ws3">rigidez <span class="_1 blank"> </span>e <span class="_7 blank"> </span>os <span class="_1 blank"> </span>mo<span class="_0 blank"> </span>dos <span class="_1 blank"> </span>de <span class="_7 blank"> </span>vibrar. <span class="_1 blank"> </span>A<span class="_0 blank"> </span> <span class="_1 blank"> </span>esco<span class="_0 blank"> </span>lha <span class="_1 blank"> </span>por <span class="_7 blank"> </span>esse <span class="_1 blank"> </span>tipo <span class="_7 blank"> </span>de <span class="_7 blank"> </span>força <span class="_1 blank"> </span>se <span class="_7 blank"> </span>dá <span class="_1 blank"> </span>pelo <span class="_7 blank"> </span>fato <span class="_1 blank"> </span>de <span class="_7 blank"> </span>os </div><div class="t m0 x1 h7 y15 ff2 fs4 fc0 sc0 ls4 ws3">sistemas <span class="_6 blank"> </span>responderem <span class="_6 blank"> </span>de <span class="_6 blank"> </span>forma <span class="_8 blank"> </span>muito <span class="_8 blank"> </span>semelhante <span class="_6 blank"> </span>a <span class="_6 blank"> </span>resposta <span class="_6 blank"> </span>dos <span class="_6 blank"> </span>sistemas <span class="_8 blank"> </span>com </div><div class="t m0 x1 h7 y16 ff2 fs4 fc0 sc0 ls4 ws3">vibração livre. </div><div class="t m0 x1 h7 y17 ff2 fs4 fc0 sc0 ls4 ws3">Outro tipo <span class="_0 blank"> </span>de <span class="_0 blank"> </span>força <span class="_0 blank"> </span>de excitação <span class="_0 blank"> </span>bastante usada <span class="_0 blank"> </span>é <span class="_0 blank"> </span>a <span class="_0 blank"> </span>força <span class="_0 blank"> </span>do tipo <span class="_0 blank"> </span>Degrau <span class="_0 blank"> </span>unitário, qu<span class="_9 blank"> </span>e </div><div class="t m0 x1 h7 y18 ff2 fs4 fc0 sc0 ls4 ws3">discutiremos mais a frente. </div><div class="t m0 x1 h6 y19 ff3 fs3 fc1 sc0 ls4 ws3">Definição de Impulso \u2013 Integral de Convolução<span class="_0 blank"> </span><span class="ff2 fs5 ls0"> </span> </div><div class="t m0 x1 h7 y1a ff2 fs4 fc0 sc0 ls4 ws3">A <span class="_1 blank"> </span>forma <span class="_7 blank"> </span>como <span class="_1 blank"> </span>a <span class="_7 blank"> </span>força <span class="_7 blank"> </span>impulso <span class="_1 blank"> </span>acontece <span class="_1 blank"> </span>está <span class="_7 blank"> </span>representada <span class="_1 blank"> </span>na <span class="_1 blank"> </span>figur<span class="_0 blank"> </span>a </div><div class="t m0 x1 h7 y1b ff2 fs4 fc0 sc0 ls4 ws3">ao <span class="_1 blank"> </span>lado. <span class="_9 blank"> </span>É <span class="_1 blank"> </span>caracterizada <span class="_9 blank"> </span>por <span class="_1 blank"> </span>um <span class="_9 blank"> </span>pico <span class="_1 blank"> </span>de <span class="_1 blank"> </span>força <span class="_9 blank"> </span>num <span class="_1 blank"> </span>curto <span class="_9 blank"> </span>intervalo <span class="_1 blank"> </span>de </div><div class="t m0 x1 h7 y1c ff2 fs4 fc0 sc0 ls4 ws3">tempo. </div><div class="t m0 x1 h7 y1d ff2 fs4 fc0 sc0 ls4 ws3">Matematicamente, <span class="_3 blank"> </span>o <span class="_3 blank"> </span>impulso, <span class="_3 blank"> </span>a <span class="_3 blank"> </span>definição <span class="_3 blank"> </span>ve<span class="_2 blank"></span>m <span class="_3 blank"> </span>das <span class="_3 blank"> </span>leis <span class="_3 blank"> </span>de <span class="_3 blank"> </span>Newton, </div><div class="t m0 x1 h7 y1e ff2 fs4 fc0 sc0 ls4 ws3">mais <span class="_7 blank"> </span>precisamente <span class="_7 blank"> </span>na <span class="_7 blank"> </span>variação <span class="_7 blank"> </span>na <span class="_7 blank"> </span>quantidade <span class="_7 blank"> </span>de <span class="_7 blank"> </span>movimento, <span class="_7 blank"> </span>dado </div><div class="t m0 x1 h7 y1f ff2 fs4 fc0 sc0 ls4 ws3">por: <span class="_a blank"> </span><span class="ff4 ws0 v1">\ue72b\ue749\ue74c\ue751\ue748\ue74f\ue74b<span class="_b blank"> </span>=<span class="_5 blank"> </span>\ue728<span class="_0 blank"> </span>. \u2206\ue750<span class="_b blank"> </span>=<span class="_5 blank"> </span>\ue749<span class="_0 blank"> </span>. </span><span class="ff5 v1"> <span class="ff4 ws1">\ue754<span class="_c blank"></span>\u0307 <span class="fs6 ls1 v2">\ueb36</span><span class="ws0">\u2212<span class="_8 blank"> </span>\ue749. <span class="ff5 ws3"> </span><span class="ws2">\ue754<span class="_c blank"></span>\u0307 <span class="fs6 ls2 v2">\ueb35</span><span class="ff2 ws3"> </span></span></span></span></span></div><div class="t m0 x1 h7 y20 ff2 fs4 fc0 sc0 ls4 ws3">Onde: </div><div class="t m0 x3 h7 y21 ff6 fs4 fc0 sc0 ls4 ws3">\u2022 <span class="_d blank"> </span><span class="ff2">F <span class="ff7 ls3">\uf0e0</span> a força, no SI é dada por N (Newtons); </span></div><div class="t m0 x4 h8 y22 ff2 fs7 fc0 sc0 ls4 ws3">Figura 01 \u2013 Força Impulso </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/64e52dd0-eb6f-4bbb-afc3-219f8b37ad24/bg2.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls4 ws3"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls4 ws3">2 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls4 ws3"> </div></div><div class="t m0 x3 h7 y23 ff6 fs4 fc0 sc0 ls4 ws3">\u2022 <span class="_d blank"> </span><span class="ff2">m <span class="ff7 ls3">\uf0e0</span> a massa, no SI é dada por kg (quilograma); </span></div><div class="t m0 x3 h7 y24 ff6 fs4 fc0 sc0 ls4 ws3">\u2022 <span class="_d blank"> </span><span class="ff2">\u2206t <span class="ff7 ls3">\uf0e0</span> um intervalo de tempo, no SI é dada por s (segundos) </span></div><div class="t m0 x3 h9 y25 ff6 fs4 fc0 sc0 ls4 ws3">\u2022 <span class="_d blank"> </span><span class="ff4 ws4">\ue754<span class="_c blank"></span>\u0307 <span class="fs6 ls5 v2">\ueb36</span><span class="ls6">,</span><span class="ff5 ws3"> </span><span class="ws2">\ue754<span class="_e blank"></span>\u0307 <span class="fs6 ls5 v2">\ueb35</span><span class="ff2 ws3"> <span class="ff7 ls3">\uf0e0</span> as velocidades no SI é dada por m/s (metros por segundo); </span></span></span></div><div class="t m0 x1 h9 y26 ff2 fs4 fc0 sc0 ls4 ws3">Sendo <span class="ff4">\ue728</span></div><div class="t m0 x5 h9 y27 ff4 fs4 fc0 sc0 ls7">\uede8<span class="ff2 ls4 ws3 v2"> a amplitude da força de impulso, vem: </span></div><div class="t m0 x6 h9 y28 ff4 fs4 fc0 sc0 ls4">\ue728</div><div class="t m0 x7 h9 y29 ff4 fs4 fc0 sc0 ls8">\uede8<span class="ls4 ws5 v2">= \uedb1<span class="_f blank"> </span>\ue728\ue740\ue750</span></div><div class="t m0 x8 ha y2a ff4 fs6 fc0 sc0 ls4 ws6">\uebe7 \ueb3e\u2206\uebe7</div><div class="t m0 x9 hb y2b ff4 fs6 fc0 sc0 ls9">\uebe7<span class="ff2 fs4 ls4 ws3 v3"> </span></div><div class="t m0 x1 h7 y2c ff2 fs4 fc0 sc0 ls4 ws3">Definimos impulso unitário com: </div><div class="t m0 xa h9 y2d ff4 fs4 fc0 sc0 ls4">\ue742</div><div class="t m0 xb h9 y2e ff4 fs4 fc0 sc0 lsa">\uf21a<span class="ls4 ws7 v2">= lim</span></div><div class="t m0 xc hc y2f ff4 fs6 fc0 sc0 ls4 ws8">\u2206\uebe7\u2192\ueb34 <span class="fs4 lsb v4">\u222b</span><span class="fs4 ws9 v5">\ue728\ue740\ue750</span></div><div class="t m0 xd ha y30 ff4 fs6 fc0 sc0 ls4 wsa">\uebe7\ueb3e\u2206\uebe7</div><div class="t m0 xe hd y31 ff4 fs6 fc0 sc0 lsc">\uebe7<span class="fs4 ls4 ws3 v6"> <span class="ff5">= F.dt = 1 </span></span></div><div class="t m0 x1 h7 y32 ff2 fs4 fc0 sc0 ls4 ws3">Essa integral também chamada de Função delta de Dirac, <span class="ff8 wsb">\uf064</span>(t): </div><div class="t m0 xf he y33 ff4 fs4 fc0 sc0 lsd">\ue7dc<span class="ff5 ls4 ws3"> </span><span class="ls4 ws9 v7">(</span><span class="ls4 wsc">\ue750<span class="_8 blank"> </span>\u2212 \ue7ec<span class="_0 blank"> </span><span class="lse v7">)</span><span class="ws0">=<span class="_5 blank"> </span>0, <span class="ff5 ws3"> </span><span class="ws9">\ue74c\ue73d\ue74e\ue73d<span class="ff5 ws3"> </span>\ue750</span></span></span><span class="ff5 lsf ws3"> </span><span class="ls4 ws5">\u2260 \ue7ec<span class="_0 blank"></span><span class="ff2 ws3"> , ou </span><span class="ls10 v8">\u222b</span></span>\ue7dc<span class="ff5 ls4 ws3"> </span><span class="ls4 ws9 v7">(</span><span class="ls4 wsc">\ue750<span class="_8 blank"> </span>\u2212 \ue7ec<span class="_0 blank"> </span><span class="ws9 v7">)</span>\ue740\ue750</span></div><div class="t m0 x10 hf y34 ff5 fs6 fc0 sc0 ls4">\u221e</div><div class="t m0 x11 hd y35 ff4 fs6 fc0 sc0 ls11">\ueb34<span class="fs4 ls4 ws5 v6">= 1<span class="ff2 ws3"> </span></span></div><div class="t m0 x1 h9 y36 ff2 fs4 fc0 sc0 ls4 ws3">A convolução entre excitação <span class="ff4">\ue728</span></div><div class="t m0 x12 h9 y37 ff4 fs4 fc0 sc0 ls7">\uede8<span class="ff2 ls4 ws3 v2">(t) e o Impulso Unitário <span class="ff4">\ue742</span></span></div><div class="t m0 x13 h9 y38 ff4 fs4 fc0 sc0 ls0">\uf21a<span class="ff2 ls4 ws3 v2"> , conduz: </span></div><div class="t m0 x14 h10 y39 ff4 fs4 fc0 sc0 ls10">\u222b<span class="lsd v7">\ue7dc<span class="ff5 ls4 ws3"> </span></span><span class="ls4 ws9 v9">(</span><span class="ls4 wsc v7">\ue750<span class="_8 blank"> </span>\u2212 \ue7ec<span class="_0 blank"> </span></span><span class="ls4 ws9 v9">)</span><span class="ls4 ws0 v7">. \ue728</span></div><div class="t m0 x15 h9 y3a ff4 fs4 fc0 sc0 ls7">\uede8<span class="ls4 wsd v2">. \ue740\ue750</span></div><div class="t m0 x16 hf y3b ff5 fs6 fc0 sc0 ls4">\u221e</div><div class="t m0 x17 h11 y3c ff4 fs6 fc0 sc0 ls12">\ueb34<span class="fs4 ls13 v6">=<span class="ff5 ls4 ws3"> <span class="ff4 ls14">\ue728<span class="ls4 ws9 v7">(</span><span class="ls15">\ue7ec<span class="ls4 ws9 v7">)</span></span></span><span class="ff2"> <span class="ff7 sc1 ls16">\uf0e0</span><span class="ff3"> <span class="ff4 ls3">\ue872<span class="ls4 ws9 v7">(</span>\ue89a<span class="lse v7">)</span></span></span></span></span>=<span class="ff9 ls17 ws3"> </span><span class="ls4">\ue872</span></span></div><div class="t m0 x18 h9 y3a ff4 fs4 fc0 sc0 ls18">\uede9<span class="ls4 ws0 v2">. \ue8be<span class="ff9 ws3"> </span></span><span class="ls4 ws9 va">(</span><span class="ls4 wse v2">\ue89a \u2212 \ue8ce</span><span class="ls4 ws9 va">)</span><span class="ff3 ls19 v2">.<span class="ff2 ls4 ws3"> </span></span></div><div class="t m0 x1 h6 y3d ff3 fs3 fc1 sc0 ls4 ws3">Função de Resposta ao Impulso (IRF): Modelagem Matemática<span class="_0 blank"> </span> </div><div class="t m0 x1 h7 y3e ff2 fs4 fc0 sc0 ls4 ws3">Considerando que o sistema da figura: </div><div class="t m0 x1 h9 y3f ff2 fs4 fc0 sc0 ls4 ws3">F(t) é do tipo impulso unitário, <span class="ff4">\ue742</span></div><div class="t m0 x15 h9 y40 ff4 fs4 fc0 sc0 ls0">\uf21a<span class="ff2 ls3 v2">.<span class="fs5 lsd ws3"> <span class="fs4 ls4"> </span></span></span></div><div class="t m0 x1 h7 y41 ff2 fs4 fc0 sc0 ls4 ws3">Assim a equação de movimento, fica: </div><div class="t m0 x19 h9 y42 ff4 fs4 fc0 sc0 ls4 ws9">\ue893<span class="ff9 ls17 ws3"> </span>\ue89e</div><div class="t m0 x1a h9 y43 ff4 fs4 fc0 sc0 ls1a">\u0308<span class="ls4 wsc v0">+ \ue889\ue89e</span></div><div class="t m0 x1b h12 y43 ff4 fs4 fc0 sc0 ls1b">\u0307<span class="ls4 wsc v0">+ \ue891\ue89e<span class="_6 blank"> </span>=<span class="_0 blank"></span><span class="ff3 ws3"> </span><span class="ws9">\ue8be<span class="ff9 ws3"> </span><span class="v7">(</span><span class="wse">\ue89a \u2212 \ue8ce</span><span class="v7">)</span><span class="ff2 ws3"> </span></span></span></div><div class="t m0 x1 h7 y44 ff2 fs4 fc0 sc0 ls4 ws3">Se o sistema for subamortecido, fica: </div><div class="t m0 xa h13 y45 ff4 fs4 fc0 sc0 ls18">\ue754<span class="ls4 ws9 v7">(</span><span class="ls1c">\ue750<span class="lse v7">)</span><span class="ls13">=<span class="ff5 ls4 ws3"> <span class="ff2"> </span></span><span class="fs6 ls1d vb">\uebd8</span><span class="fs8 ls4 wsf vc">\uec37\ued0d.\ued18<span class="ws10 vd">\uecd9. </span><span class="ff5 ws3"> <span class="ff4 ls1e">\uecdf</span></span></span><span class="fs6 ls4 wsa vb">.\uebe6\uebd8\uebe1(\uec20</span><span class="fs8 ls1f ve">\ueccf</span><span class="fs6 ls4 wsa vb">.\uebe7)</span></span></span></div><div class="t m0 x1c h14 y46 ff4 fs6 fc0 sc0 ls4 wsa">\uebe0.\uec20<span class="fs8 ls20 va">\ueccf</span><span class="fs4 ls6 vf">,<span class="ff5 ls4 ws3"> <span class="ff4 ws11">\ue750<span class="_b blank"> </span>\u2265 \ue7ec</span></span></span></div><div class="t m0 x1d h15 y47 ff4 fs4 fc0 sc0 ls3">0<span class="ff5 ls4 ws3"> </span><span class="ls6">,<span class="ff5 ls4 ws3"> </span><span class="ls4 ws12">\ue750<span class="_b blank"> </span><<span class="_5 blank"> </span>\ue7ec <span class="ff2 ws3 vb"> (a) </span></span></span></div><div class="t m0 x1 h16 y48 ff2 fs4 fc0 sc0 ls4 ws3">Lembrando que:<span class="fs5"> <span class="ff4 ls21">\ue7f1<span class="fs9 ls22 v2">\uebd7</span><span class="ls4 ws13">= \ue7f1</span></span></span></div><div class="t m0 x1e h17 y49 ff4 fs9 fc0 sc0 ls23">\uebe1<span class="fs5 ls4 ws14 v10">\ueda51<span class="_10 blank"> </span>\u2212<span class="_10 blank"> </span>\ue7e6 </span><span class="ls24 v11">\ueb36</span><span class="ff2 fs5 ls4 ws3 v10"> </span></div><div class="t m0 x1 h7 y4a ff2 fs4 fc0 sc0 ls4 ws3">A equação (a) é uma resposta semelhante ao sistema com vib<span class="_2 blank"></span>ração livre que nós já </div><div class="t m0 x1 h7 y4b ff2 fs4 fc0 sc0 ls4 ws3">estudamos. </div><div class="t m0 x1 h6 y4c ff3 fs3 fc1 sc0 ls4 ws3">Função de Resposta ao Impulso (IRF): </div><div class="t m0 x1 h7 y4d ff2 fs4 fc0 sc0 ls4 ws3">A resposta <span class="_9 blank"> </span>x(t) <span class="_9 blank"> </span>do <span class="_9 blank"> </span>sistema <span class="_9 blank"> </span>é <span class="_9 blank"> </span>u<span class="_0 blank"> </span>ma <span class="_9 blank"> </span>função <span class="_9 blank"> </span>impulso <span class="_9 blank"> </span>unitário. <span class="_9 blank"> </span>Ela <span class="_9 blank"> </span>é <span class="_9 blank"> </span>tão <span class="_9 blank"> </span>importante <span class="_9 blank"> </span>que <span class="_9 blank"> </span>é<span class="_0 blank"> </span> </div><div class="t m0 x1 h7 y4e ff2 fs4 fc0 sc0 ls4 ws3">chamada <span class="_3 blank"> </span>de <span class="_3 blank"> </span><span class="fc1">Função <span class="_11 blank"> </span>de <span class="_11 blank"> </span>Resposta <span class="_3 blank"> </span>ao <span class="_11 blank"> </span>Impulso <span class="_3 blank"> </span>ou <span class="_11 blank"> </span>IRF<span class="_0 blank"> </span></span><span class="ff3">, <span class="_3 blank"> </span></span>do <span class="_11 blank"> </span>inglês, <span class="_3 blank"> </span><span class="fc1">\u201cImpulse <span class="_3 blank"> </span>Response </span></div><div class="t m0 x1 h7 y4f ff2 fs4 fc1 sc0 ls4 ws15">Function\u201d.<span class="fc0 ws3"> </span></div><div class="t m0 x1 h18 y50 ff2 fs4 fc0 sc0 ls4 ws3">Escrita como: <span class="ff4 ls19">\ue88d<span class="ls4 ws9 v7">(</span><span class="ls3">\ue89a<span class="lse v7">)</span><span class="ls4 ws9">=</span></span></span><span class="ff9"> <span class="ff4 fs6 ls25 v5">\ue88b</span><span class="ff4 fs8 wsf v12">\uec37\ue8c8.\ue8d3<span class="ws16 vd">\ue894. </span></span><span class="fs8 v12"> <span class="ff4 ls26">\ue89a<span class="fs6 ls4 wsa v13">.\ue899\ue88b\ue894(\ue8d3</span><span class="ls27 v14">\ue88a</span><span class="fs6 ls4 wsa v13">.\ue89a)</span></span></span></span></div><div class="t m0 xb h19 y51 ff4 fs6 fc0 sc0 ls4 wsa">\ue893.\ue8d3<span class="fs8 ls28 va">\ue88a</span><span class="ff2 fs4 ws3 vf"> </span></div><div class="t m0 x1 h7 y52 ff2 fs4 fc0 sc0 ls4 ws3">IRF é importante: </div><div class="t m0 x1f h8 y53 ff2 fs7 fc0 sc0 ls4 ws3">Figura 02 \u2013 Modelo </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/64e52dd0-eb6f-4bbb-afc3-219f8b37ad24/bg3.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls4 ws3"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls4 ws3">3 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls4 ws3"> </div></div><div class="t m0 x3 h7 y54 ff8 fs4 fc0 sc0 ls4 wsb">\uf0b7<span class="ff6 ls29 ws3"> <span class="ff2 ls4">Em análise transiente de sistemas estruturais e mecânicos complexos; </span></span></div><div class="t m0 x3 h7 y55 ff8 fs4 fc0 sc0 ls4 wsb">\uf0b7<span class="ff6 ls29 ws3"> <span class="ff2 ls4">Para descrever a resposta de sistemas para diversos tipos de excitação. </span></span></div><div class="t m0 x1 h9 y56 ff2 fs4 fc0 sc0 ls4 ws3">Quando a amplitude da força impulso for diferen<span class="_2 blank"></span>te de 1 (<span class="ff4">\ue728</span></div><div class="t m0 x20 h9 y57 ff4 fs4 fc0 sc0 ls8">\uede8<span class="ls4 ws5 v2">\u2260 1<span class="ff2 ws3">) utilizamos o método </span></span></div><div class="t m0 x1 h7 y58 ff2 fs4 fc0 sc0 ls4 ws3">da entegral de convolução, vem: </div><div class="t m0 x21 he y59 ff4 fs4 fc0 sc0 ls4 ws9">\ue88d<span class="v7">(</span><span class="ls3">\ue89a<span class="lse v7">)</span></span><span class="ws5">= \ue728</span></div><div class="t m0 x7 h1a y5a ff4 fs4 fc0 sc0 ls7">\uede8<span class="ff5 ls2a ws3 v2"> </span><span class="ls3 v4">\ue88b</span><span class="fs6 ls4 wsa v3">\ueb3f\ue8c8.\ue8d3</span><span class="fs8 ls4 ws10 v15">\ue894. </span><span class="ff9 fs6 ls4 ws3 v3"> <span class="ff4 ls2b">\ue89a</span></span><span class="ls4 ws0 v4">. \ue899\ue88b\ue894(\ue8d3</span><span class="fs6 ls2c v16">\ue88a</span><span class="ls4 ws0 v4">. \ue89a)</span></div><div class="t m0 x22 h9 y5b ff4 fs4 fc0 sc0 ls4 ws0">\ue893. \ue8d3<span class="fs6 ls2d v2">\ue88a</span><span class="ff2 ws3 v17"> </span></div><div class="t m0 x1 h7 y5c ff2 fs4 fc0 sc0 ls4 ws3">Se fizermos uma simulação para g(t), obtemos um gráfico semelhant<span class="_2 blank"></span>e a: </div><div class="t m0 x23 h7 y5d ff2 fs4 fc0 sc0 ls4 ws3"> </div><div class="t m0 x24 h8 y5e ff2 fs7 fc0 sc0 ls4 ws3">Figura 03: Gráfico de u<span class="_2 blank"></span>ma IRF </div><div class="t m0 x1 h6 y5f ff3 fs3 fc1 sc0 ls4 ws3">Resposta para Uma Força do Tipo Degrau Unitário <span class="_0 blank"> </span>u (t \u2013 t<span class="fs0 ws17 vd">o</span>) </div><div class="t m0 x1 h7 y60 ff2 fs4 fc0 sc0 ls4 ws3">É <span class="_1 blank"> </span>útil <span class="_9 blank"> </span>para <span class="_1 blank"> </span>análise <span class="_1 blank"> </span>de <span class="_1 blank"> </span>projeto <span class="_9 blank"> </span>de <span class="_1 blank"> </span>sistemas <span class="_1 blank"> </span>dinâmicos. <span class="_1 blank"> </span>Muito <span class="_9 blank"> </span>usado </div><div class="t m0 x1 h7 y61 ff2 fs4 fc0 sc0 ls4 ws3">para especificação de controladores. </div><div class="t m0 x1 h7 y62 ff2 fs4 fc0 sc0 ls4 ws3">A <span class="_0 blank"> </span>partir <span class="_0 blank"> </span>da <span class="_0 blank"> </span>resposta <span class="_9 blank"> </span>x(t) <span class="_0 blank"> </span>de <span class="_0 blank"> </span>um <span class="_0 blank"> </span>sistema <span class="_0 blank"> </span>a <span class="_9 blank"> </span>excitação degrau <span class="_0 blank"> </span>unitário </div><div class="t m0 x1 h7 y63 ff2 fs4 fc0 sc0 ls4 ws3">é <span class="_12 blank"> </span>possível <span class="_12 blank"> </span>definir <span class="_12 blank"> </span>vários <span class="_12 blank"> </span>parâmetros <span class="_12 blank"> </span>que <span class="_12 blank"> </span>descrevem <span class="_12 blank"> </span>o </div><div class="t m0 x1 h7 y64 ff2 fs4 fc0 sc0 ls4 ws3">comportamento dinâmico de um sistema qualquer. </div><div class="t m0 x1 h7 y65 ff2 fs4 fc0 sc0 ls4 ws3">A função degrau unitário é, matematicamente, descrita como: </div><div class="t m0 xa he y66 ff4 fs4 fc0 sc0 ls2e">\ue751<span class="ls4 ws9 v7">(</span><span class="ls4 wsc">\ue750<span class="_8 blank"> </span>\u2212 \ue750<span class="fs6 ls2f v2">\uebe2</span><span class="lse v7">)</span><span class="ls13">=</span></span><span class="ff5 ls2a ws3"> </span><span class="ls4 ws18">\uedb1<span class="_13 blank"> </span>\ue7dc .<span class="_3 blank"> </span><span class="ws9 v7">(</span><span class="wsc">\ue7ec \u2212 \ue750<span class="fs6 ls2f v2">\uebe2</span><span class="ws9 v7">)</span>\ue740\ue7ec</span></span></div><div class="t m0 x25 ha y67 ff4 fs6 fc0 sc0 ls4">\uebe7</div><div class="t m0 x26 hb y68 ff4 fs6 fc0 sc0 ls30">\ueb34<span class="ff2 fs4 ls4 ws3 v3"> </span></div><div class="t m0 x1 h7 y69 ff2 fs4 fc0 sc0 ls4 ws3">Que leva a: </div><div class="t m0 x12 h1b y6a ff4 fs4 fc0 sc0 ls2e">\ue751<span class="ls4 ws9 v7">(</span><span class="ls4 wsc">\ue750<span class="_8 blank"> </span>\u2212 \ue750<span class="fs6 ls2f v2">\uebe2</span><span class="lsf v7">)</span><span class="ls31">=</span><span class="ff5 ws3"> </span><span class="ws0 v17">0, <span class="ff5 ws3"> <span class="ff4 ws19">\ue750 \u2264 \ue750<span class="fs6 v2">\uebe2</span></span></span></span></span></div><div class="t m0 x27 h9 y6b ff4 fs4 fc0 sc0 ls4 ws0">1, <span class="ff5 ws3"> </span><span class="ws19">\ue750 > \ue750<span class="fs6 ls32 v2">\uebe2</span><span class="ff2 ws3 v4"> </span></span></div><div class="t m0 x28 h8 y6c ff2 fs7 fc0 sc0 ls4 ws3">Figura 04 \u2013 Força Degrau Unitário </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/64e52dd0-eb6f-4bbb-afc3-219f8b37ad24/bg4.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls4 ws3"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls4 ws3">4 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls4 ws3"> </div></div><div class="t m0 x1 he y23 ff2 fs4 fc0 sc0 ls4 ws3">Quando to = 0 a força de excitação degrau unitário é dada por: <span class="ff4 ls2e">\ue751<span class="ls4 ws9 v7">(</span><span class="ls4 ws1a">\ue750<span class="_8 blank"> </span>\u2212 \ue750<span class="fs6 ls2f v2">\uebe2</span><span class="lsf v7">)</span><span class="ws5">= \ue751<span class="_0 blank"></span>(\ue750<span class="_0 blank"></span>)</span></span></span> </div><div class="t m0 x1 h7 y24 ff2 fs4 fc0 sc0 ls4 ws3">Aplicando a 2ª lei de Newton no modelo da figura 2, obtem<span class="_2 blank"></span>os a seguinte Equação do </div><div class="t m0 x1 h7 y6d ff2 fs4 fc0 sc0 ls4 ws3">Movimento: <span class="_14 blank"> </span><span class="ff4 ws9 v1">\ue893</span><span class="ff9 ls17 v1"> </span><span class="ff4 v1">\ue89e</span></div><div class="t m0 x29 h9 y6e ff4 fs4 fc0 sc0 ls1a">\u0308<span class="ls4 wsc v0">+ \ue889\ue89e</span></div><div class="t m0 x2a h12 y6e ff4 fs4 fc0 sc0 ls1b">\u0307<span class="ls4 wsc v0">+ \ue891\ue89e<span class="_6 blank"> </span>=<span class="_0 blank"></span><span class="ff3 ws3"> </span><span class="ws9">\ue71d<span class="v7">(</span><span class="ls3">\ue89a</span><span class="v7">)</span><span class="ff2 ws3"> </span></span></span></div><div class="t m0 x1 h7 y6f ff2 fs4 fc0 sc0 ls4 ws3">Resolvendo a equação diferencial, chegamos: </div><div class="t m0 x2b h1c y70 ff4 fs4 fc0 sc0 ls4 ws9">\ue89e<span class="v7">(</span><span class="ls3">\ue89a<span class="lsf v7">)</span></span><span class="ws1b">=<span class="_6 blank"> </span>\ueada \u2212<span class="_8 blank"> </span><span class="ls3 v18">\ue88b</span><span class="fs6 wsa vb">\ueb3f\ue8c8.\ue8d3</span><span class="fs8 ws1c ve">\ue894. </span><span class="ff9 fs6 ws3 vb"> <span class="ff4 ls2b">\ue89a</span></span><span class="ws0 v18">. \ue899\ue88b\ue894(\ue8d3</span><span class="fs6 ls2c v4">\ue88a</span><span class="ws0 v18">. \ue89a<span class="_10 blank"> </span>+<span class="_8 blank"> </span>\ue8bd)</span></span></div><div class="t m0 x2c h9 y71 ff4 fs4 fc0 sc0 lsd">\ueda5<span class="ls4 ws1d v0">\ueada \u2212 \ue8c8<span class="fs6 ls33 v19">\ueadb</span><span class="ff2 ws3 v1a"> </span></span></div><div class="t m0 x1 h7 y72 ff2 fs4 fc0 sc0 ls4 ws3">Onde: </div><div class="t m0 x3 h7 y73 ff8 fs4 fc0 sc0 ls4 wsb">\uf0b7<span class="ff6 ls29 ws3"> <span class="ff2 ls4">x(t) <span class="ff7 ls3">\uf0e0</span> resposta do sistema, no SI é dada em m (metros) </span></span></div><div class="t m0 x3 h7 y74 ff8 fs4 fc0 sc0 ls4 wsb">\uf0b7<span class="ff6 ls29 ws3"> <span class="ff2 ls4">\u03be <span class="ff7 ls3">\uf0e0</span> fator de amortecimento, que é adimension<span class="_2 blank"></span>al </span></span></div><div class="t m0 x3 h9 y75 ff8 fs4 fc0 sc0 ls4 wsb">\uf0b7<span class="ff6 ls29 ws3"> </span><span class="ff4 ws9">\ue8d3<span class="fs6 ls34 v2">\ue894</span><span class="ff7 ls3">\uf0e0</span><span class="ff2 ws3"> frequência angular natural, no SI é dado em rad/s (radianos por segundo) </span></span></div><div class="t m0 x3 h9 y76 ff8 fs4 fc0 sc0 ls4 wsb">\uf0b7<span class="ff6 ls29 ws3"> </span><span class="ff4 ws9">\ue8d3<span class="fs6 ls35 v2">\ue88a</span><span class="ff7 ls3">\uf0e0</span><span class="ff2 ws3"> frequência angular natural amortecida, no SI é dado em rad/s (radianos </span></span></div><div class="t m0 x5 h7 y77 ff2 fs4 fc0 sc0 ls4 ws3">por segundo) </div><div class="t m0 x3 h7 y78 ff8 fs4 fc0 sc0 ls4 wsb">\uf0b7<span class="ff6 ls29 ws3"> <span class="ff2 ls4">\u03b3 <span class="ff7 ls3">\uf0e0</span> ângulo de fase, no SI é dado em rad (radianos) </span></span></div><div class="t m0 x1 h7 y79 ff2 fs4 fc0 sc0 ls4 ws3">O ângulo \u03b3 pode ser descrito como: </div><div class="t m0 x2d h1c y7a ff4 fs4 fc0 sc0 ls4 ws1e">\ue7db<span class="_b blank"> </span>=<span class="_5 blank"> </span>\ue73d\ue74e\ue73f\ue750\ue743 <span class="ls3 v0">\ued6d<span class="lsd v18">\ueda5</span></span><span class="ws1f v18">1<span class="_10 blank"> </span>\u2212<span class="_8 blank"> </span>\ue7e6 </span><span class="fs6 v1b">\ueb36</span></div><div class="t m0 x2e h1d y7b ff4 fs4 fc0 sc0 ls36">\ue7e6<span class="ls3 v17">\ued71</span><span class="ff2 ls4 ws3 v17"> </span></div><div class="t m0 x1 h7 y7c ff2 fs4 fc0 sc0 ls4 ws3">Se fizermos uma simulação, obteremos um gráfico semelhan<span class="_2 blank"></span>te a: </div><div class="t m0 x2f h7 y7d ff2 fs4 fc0 sc0 ls4 ws3"> </div><div class="t m0 x30 h8 y7e ff2 fs7 fc0 sc0 ls4 ws3">Figura 05 \u2013 Resposta para u<span class="_2 blank"></span>ma </div><div class="t m0 x31 h8 y7f ff2 fs7 fc0 sc0 ls4 ws3">Força do tipo Degrau Unitári<span class="_2 blank"></span>o </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/64e52dd0-eb6f-4bbb-afc3-219f8b37ad24/bg5.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls4 ws3"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls4 ws3">5 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls4 ws3"> </div></div><div class="t m0 x1 h7 y23 ff2 fs4 fc0 sc0 ls4 ws3">Note que no gráfico podemos destascar alguns parâmetros, como, o <span class="fc1 ws15">sobresinal</span>, OS, o </div><div class="t m0 x1 h7 y80 ff2 fs4 fc1 sc0 ls4 ws3">tempo de pico<span class="fc0">, t<span class="fs9 ls37 v1c">p</span>, o </span>período de oscilações<span class="ff3 fc2 ws20">,</span><span class="fc0"> T<span class="fs9 ws21 v1c">d</span> e o </span>tempo de ajuste<span class="fc0">, t<span class="fs9 ls38 v1c">s</span>. </span></div><div class="t m0 x1 h7 y6d ff2 fs4 fc0 sc0 ls4 ws3">Esses parâmetros podem ser calculados, através: </div><div class="t m0 x1 h7 y81 ff2 fs4 fc0 sc0 ls4 ws3">Sobresinal <span class="_9 blank"> </span>o<span class="_0 blank"> </span>u <span class="_1 blank"> </span>overshoot <span class="_9 blank"> </span>(OS): <span class="_1 blank"> </span> <span class="_1 blank"> </span>Valor <span class="_9 blank"> </span>de <span class="_1 blank"> </span>resposta <span class="_1 blank"> </span>máximo <span class="_9 blank"> </span>menos <span class="_1 blank"> </span>o <span class="_1 blank"> </span>valor <span class="_1 blank"> </span>de <span class="_9 blank"> </span>resposta<span class="_0 blank"> </span> </div><div class="t m0 x1 h7 y82 ff2 fs4 fc0 sc0 ls4 ws3">quando os istema entra em regime permanente, ou: </div><div class="t m0 x32 h1c y83 ff4 fs4 fc0 sc0 ls4 ws5">\ue731\ue735<span class="_b blank"> </span>= \ue754<span class="fs6 ws22 v2">\uebe0\uebd4\uebeb </span><span class="ws9 v7">(</span><span class="ls1c">\ue750<span class="ls39 v7">)</span></span><span class="ws23">\u2212<span class="_10 blank"> </span>1<span class="_5 blank"> </span>=<span class="_5 blank"> </span>\ue741\ue754\ue74c \uf246<span class="_15 blank"> </span><span class="ws24 v18">\u2212\ue7e6 .<span class="_3 blank"> </span>\ue7e8</span></span></div><div class="t m0 x10 h1e y84 ff4 fs4 fc0 sc0 lsd">\ueda5<span class="ls4 ws1f v0">1<span class="_10 blank"> </span>\u2212<span class="_8 blank"> </span>\ue7e6 <span class="fs6 ls2 v19">\ueb36</span><span class="ls3 v1a">\uf247</span><span class="ff2 ws3 v1a"> </span></span></div><div class="t m0 x1 h7 y85 ff2 fs4 fc0 sc0 ls4 ws3">Tempo de Pico, t<span class="fs9 ls37 v1c">p</span>: Tempo necessário para o sistema atingir a resposta máxima, ou <span class="_16 blank"> </span> </div><div class="t m0 x33 h1c y86 ff4 fs4 fc0 sc0 ls4 ws9">\ue750<span class="fs6 ls3a v2">\uebe3</span><span class="ls3b">=</span><span class="v18">\ue7e8</span></div><div class="t m0 x34 h9 y87 ff4 fs4 fc0 sc0 ls4">\ue7f1</div><div class="t m0 x35 h1f y88 ff4 fs6 fc0 sc0 ls3c">\uebe1<span class="fs4 ls6 v10">.<span class="lsd v0">\ueda5<span class="ls4 ws1f v0">1<span class="_10 blank"> </span>\u2212<span class="_8 blank"> </span>\ue7e6 </span></span></span><span class="ls5 vf">\ueb36</span><span class="ff2 fs4 ls4 ws3 vb"> </span></div><div class="t m0 x1 h7 y89 ff2 fs4 fc0 sc0 ls4 ws3">Período de Oscilações, T<span class="fs9 ws21 v1c">d</span>: <span class="_17 blank"> </span> </div><div class="t m0 x12 h9 y8a ff4 fs4 fc0 sc0 ls4">\ue736</div><div class="t m0 x15 h20 y8b ff4 fs6 fc0 sc0 ls3d">\uebd7<span class="fs4 ls3e v10">=<span class="ls4 wsd v18">2. \ue7e8</span></span></div><div class="t m0 x6 h9 y8c ff4 fs4 fc0 sc0 ls4">\ue7f1</div><div class="t m0 x36 h21 y8d ff4 fs6 fc0 sc0 ls3c">\uebe1<span class="fs4 ls2a v10">.<span class="lsd v0">\ueda5<span class="ls4 ws1f v0">1<span class="_10 blank"> </span>\u2212<span class="_8 blank"> </span>\ue7e6 </span></span></span><span class="ls3f vf">\ueb36</span><span class="fs4 ls4 ws0 vb">=<span class="_5 blank"> </span>2. \ue750</span><span class="ls40 v1a">\uebe3</span><span class="ff2 fs4 ls4 ws3 vb"> </span></div><div class="t m0 x1 h7 y8e ff2 fs4 fc0 sc0 ls4 ws3">Tempo de Ajustes, t<span class="fs9 ls38 v1c">s</span>: <span class="_18 blank"></span>Que <span class="_5 blank"> </span>é <span class="_b blank"> </span>o <span class="_b blank"> </span>tempo <span class="_b blank"> </span>necessário <span class="_5 blank"> </span>para <span class="_b blank"> </span>o <span class="_b blank"> </span>sistema <span class="_5 blank"> </span>atingir <span class="_b blank"> </span>o <span class="_b blank"> </span>regime </div><div class="t m0 x1 h7 y8f ff2 fs4 fc0 sc0 ls4 ws3">permanente dentro de um intervalo de ±3%, ou ±5%, depen<span class="_2 blank"></span>dendo do autor. </div><div class="t m0 x37 h1c y90 ff4 fs4 fc0 sc0 ls4 ws9">\ue750<span class="fs6 ls41 v2">\uebe6</span><span class="ls42">=</span><span class="v18">3</span></div><div class="t m0 x26 h9 y91 ff4 fs4 fc0 sc0 ls4">\ue7f1</div><div class="t m0 x2c h1f y92 ff4 fs6 fc0 sc0 ls3c">\uebe1<span class="fs4 ls4 ws24 v10">.<span class="_3 blank"> </span>\ue7e6 <span class="ff2 ws3 v17"> </span></span></div><div class="t m0 x1 h7 y93 ff2 fs4 fc0 sc0 ls4 ws3">Importante <span class="_b blank"> </span>ressaltar <span class="_b blank"> </span>que <span class="_13 blank"> </span>a <span class="_b blank"> </span>partir <span class="_b blank"> </span>das <span class="_b blank"> </span>equações <span class="_b blank"> </span>que <span class="_13 blank"> </span>acabamos <span class="_b blank"> </span>de <span class="_b blank"> </span>apresentar, <span class="_b blank"> </span>é </div><div class="t m0 x1 h7 y94 ff2 fs4 fc0 sc0 ls4 ws3">possível <span class="_19 blank"> </span>projetar <span class="_19 blank"> </span>um <span class="_19 blank"> </span>sistema <span class="_19 blank"> </span>com <span class="_19 blank"> </span>um <span class="_19 blank"> </span>determinado <span class="_19 blank"> </span>fator <span class="_19 blank"> </span>de <span class="_19 blank"> </span>amortecimento <span class="_19 blank"> </span>e </div><div class="t m0 x1 h7 y95 ff2 fs4 fc0 sc0 ls4 ws3">frequência natural que atenda as características desejadas. </div><div class="t m0 x1 h6 y96 ff3 fs3 fc1 sc0 ls4 ws3">Exemplo: Resposta de uma Estrutura a Impacto<span class="_0 blank"> </span> </div><div class="t m0 x1 h7 y97 ff2 fs4 fc0 sc0 ls4 ws3">No <span class="_3 blank"> </span>teste de <span class="_3 blank"> </span>vibração de <span class="_3 blank"> </span>uma estrutura, <span class="_11 blank"> </span>ilustrada na <span class="_3 blank"> </span>figura abaixo, <span class="_11 blank"> </span>u<span class="_0 blank"> </span>m <span class="_3 blank"> </span>martelo de </div><div class="t m0 x1 h7 y98 ff2 fs4 fc0 sc0 ls4 ws3">impacto <span class="_9 blank"> </span>munido <span class="_1 blank"> </span>de <span class="_1 blank"> </span>uma <span class="_9 blank"> </span>célula <span class="_1 blank"> </span>de <span class="_9 blank"> </span>carga <span class="_1 blank"> </span>para <span class="_1 blank"> </span>medir <span class="_9 blank"> </span>a <span class="_1 blank"> </span>força <span class="_9 blank"> </span>de <span class="_1 blank"> </span>impacto <span class="_1 blank"> </span>é <span class="_9 blank"> </span>usado <span class="_1 blank"> </span>para </div><div class="t m0 x1 h7 y99 ff2 fs4 fc0 sc0 ls4 ws3">causar excitação, <span class="_0 blank"> </span>como ilustrado <span class="_0 blank"> </span>na figura. <span class="_0 blank"> </span>Supondo <span class="_0 blank"> </span> <span class="_0 blank"> </span> <span class="_0 blank"> </span> <span class="_0 blank"> </span>m = <span class="_0 blank"> </span>5 <span class="_0 blank"> </span>(kg), k <span class="_0 blank"> </span>= <span class="_0 blank"> </span>2.000 (N/m), <span class="_0 blank"> </span>c <span class="_0 blank"> </span>= </div><div class="t m0 x1 h9 y9a ff2 fs4 fc0 sc0 ls4 ws3">10 (N.s/m) e <span class="ff4">\ue728</span></div><div class="t m0 x38 h9 y9b ff4 fs4 fc0 sc0 ls7">\uede8<span class="ff2 ls4 ws3 v2"> = 20 (N.s), determine a resposta do sistema: </span></div><div class="t m0 x39 h7 y9c ff2 fs4 fc0 sc0 ls4 ws3"> </div><div class="t m0 x3a h8 y9d ff2 fs7 fc0 sc0 ls4 ws3">Figura 05 \u2013 Exercício </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/64e52dd0-eb6f-4bbb-afc3-219f8b37ad24/bg6.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls4 ws3"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls4 ws3">6 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls4 ws3"> </div></div><div class="t m0 x1 h7 y23 ff2 fs4 fc1 sc0 ls4 ws15">Solução:<span class="fs7 ws3"> </span></div><div class="t m0 x1 h7 y9e ff2 fs4 fc0 sc0 ls4 ws3">Calculando a frequência angular natural, <span class="ff8">\uf077</span></div><div class="t m0 x8 h22 y9f ff2 fs9 fc0 sc0 ls4 ws21">n<span class="fs4 ws3 v9">: </span></div><div class="t m0 xf h9 ya0 ff4 fs4 fc0 sc0 ls4">\ue7f1</div><div class="t m0 x17 h23 ya1 ff4 fs6 fc0 sc0 ls43">\uebe1<span class="fs4 ls13 v10">=<span class="ff5 ls4 ws3"> <span class="ff4 ws9 v19">\ueda7<span class="v16">\ue747</span></span></span></span><span class="ls4 ws25 v17">\uebd8\uebe4 <span class="fs4 v1d">\ue749</span></span></div><div class="t m0 x24 h24 ya2 ff4 fs4 fc0 sc0 ls44">\ued57<span class="ls13 v2">=<span class="ff5 ls4 ws3"> </span></span><span class="ls4 ws9 v1e">\ueda7</span><span class="ls4 ws26 v1f">2000 <span class="v20">5</span></span></div><div class="t m0 x8 h25 ya3 ff4 fs4 fc0 sc0 ls45">\ued57<span class="ls4 ws9 v0">=<span class="ff3 fs3 ws3"> 20,0 (rad/s)<span class="ff2 fs4"> </span></span></span></div><div class="t m0 x1 h7 ya4 ff2 fs4 fc0 sc0 ls4 ws3">Calculando o fator de amortecimento, \u03be: </div><div class="t m0 x1e h26 y2b ff4 fs4 fc0 sc0 ls4 ws5">\ue7e6<span class="_b blank"> </span>= <span class="ff5 ls46 ws3"> </span><span class="fs6 v5">\uebd6</span></div><div class="t m0 x12 h27 ya5 ff4 fs6 fc0 sc0 ls4 wsa">\uebd6<span class="fs8 ls47 va">\uecce</span><span class="fs4 ls13 vf">=<span class="ff5 ls48 ws3"> </span></span><span class="v21">\uebd6</span></div><div class="t m0 x6 h27 ya5 ff4 fs6 fc0 sc0 ls4 wsa">\ueb36.<span class="v8">\u221a</span><span class="ws27">\uebde.\uebe0 <span class="fs4 ls13 vf">=<span class="ff5 ls49 ws3"> </span></span></span><span class="v21">\ueb35\ueb34</span></div><div class="t m0 x27 h14 ya5 ff4 fs6 fc0 sc0 ls4 wsa">\ueb36.<span class="v8">\u221a</span><span class="ws28">\ueb36\ueb34\ueb34\ueb34.\ueb39 <span class="fs4 ls13 vf">=<span class="ff9 ls4 ws3"> <span class="ff3">0,05 </span></span></span></span></div><div class="t m0 x1 h7 ya6 ff2 fs4 fc0 sc0 ls4 ws3">Calculando a frequência angular natural amortecida </div><div class="t m0 x19 h9 ya7 ff4 fs4 fc0 sc0 ls4 ws9">\ue7f1<span class="fs6 ls4a v2">\uebd7</span><span class="ws5">= \ue7f1</span></div><div class="t m0 x3b h28 ya8 ff4 fs6 fc0 sc0 ls3c">\uebe1<span class="fs4 lsd v10">\ueda5<span class="ls4 ws1f v0">1<span class="_10 blank"> </span>\u2212<span class="_8 blank"> </span>\ue7e6 </span></span><span class="ls3f vf">\ueb36</span><span class="fs4 ls4 ws5 v10">= 20<span class="lsd v7">\ueda5</span><span class="ws29">1 \u2212 0,05</span></span><span class="ls4b vf">\ueb36</span><span class="ff2 fs4 ls4 ws3 v10"> <span class="ff4 ws9">=<span class="ff3 ws3"> 19,98 (rad/s)</span></span> </span></div><div class="t m0 x1 h7 ya9 ff2 fs4 fc0 sc0 ls4 ws3">Admitindo que o impacto seja dado em t = 0, a resposta do sistema é da<span class="_2 blank"></span>da por: </div><div class="t m0 x2d he yaa ff4 fs4 fc0 sc0 ls4 ws9">\ue88d<span class="v7">(</span><span class="ls3">\ue89a<span class="lse v7">)</span></span><span class="ws5">= \ue728</span></div><div class="t m0 x3c h1a yab ff4 fs4 fc0 sc0 ls7">\uede8<span class="ff5 ls2a ws3 v2"> </span><span class="ls3 v4">\ue88b</span><span class="fs6 ls4 wsa v1a">\ueb3f\ue8c8.\ue8d3</span><span class="fs8 ls4 ws10 v15">\ue894. </span><span class="ff9 fs6 ls4 ws3 v1a"> <span class="ff4 ls2b">\ue89a</span></span><span class="ls4 ws0 v4">. \ue899\ue88b\ue894(\ue8d3</span><span class="fs6 ls2c v16">\ue88a</span><span class="ls4 ws0 v4">. \ue89a)</span></div><div class="t m0 x3d h9 yac ff4 fs4 fc0 sc0 ls4 ws0">\ue893. \ue8d3<span class="fs6 ls2d v2">\ue88a</span><span class="ff3 ws3 v17"> </span></div><div class="t m0 x1 h7 yad ff2 fs4 fc0 sc0 ls4 ws3">Substituindo os valores calculados anteriormente, temos: </div><div class="t m0 x32 he yae ff4 fs4 fc0 sc0 ls19">\ue88d<span class="ls4 ws9 v7">(</span><span class="ls3">\ue89a<span class="lse v7">)</span><span class="ws2a">=<span class="_5 blank"> </span>\uead9, \ueadb\uead9\uead9\ueadb\ueade. \ue88b</span><span class="fs6 ls4 ws2b v16">\ueb3f\ue89a </span><span class="ls4 ws0">. \ue899\ue88b\ue894(\ueada\ueae2, \ueae2\ueae1. \ue89a)<span class="ff2 ws3"> </span></span></span></div><div class="t m0 x1 h7 yaf ff2 fs4 fc0 sc0 ls4 ws3">Simulando no Scilab, fica: </div><div class="t m0 x3e h7 yb0 ff2 fs4 fc0 sc0 ls4 ws3"> </div><div class="t m0 x1 h7 y65 ff2 fs4 fc0 sc0 ls4 ws3">Note <span class="_5 blank"> </span>que <span class="_5 blank"> </span>como <span class="_6 blank"> </span>é <span class="_5 blank"> </span>esperado <span class="_5 blank"> </span>num <span class="_5 blank"> </span>sistema <span class="_5 blank"> </span>com <span class="_5 blank"> </span>fator <span class="_5 blank"> </span>de <span class="_5 blank"> </span>amortecimento <span class="_5 blank"> </span>baixo, <span class="_6 blank"> </span>o </div><div class="t m0 x1 h7 yb1 ff2 fs4 fc0 sc0 ls4 ws3">sistema oscila várias vezes até voltar a posição de equilíb<span class="_2 blank"></span>rio. </div><div class="t m0 x1 h7 yb2 ff2 fs4 fc0 sc0 ls4 ws3">Chegando assim a resposta desejada. </div><div class="t m0 x1 h7 yb3 ff2 fs4 fc0 sc0 ls4 ws3">Algorítmo no Scilab: </div><div class="t m0 x1 h29 yb4 ff2 fs0 fc3 sc0 ls4 ws3"> </div><div class="t m0 x1 h7 yb5 ff2 fs4 fc3 sc0 ls3 ws2c">for<span class="fc0 ls4 ws3"> <span class="fc4 ws15">i<span class="fc5 lsd">=<span class="fc6">1</span></span><span class="fc7">:<span class="fc6">1001</span></span></span> </span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf7" class="pf w0 h0" data-page-no="7"><div class="pc pc7 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/64e52dd0-eb6f-4bbb-afc3-219f8b37ad24/bg7.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls4 ws3"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls4 ws3">7 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls4 ws3"> </div></div><div class="t m0 x1 h7 y23 ff2 fs4 fc0 sc0 ls4 ws3"> <span class="fc4 ws15">t<span class="fc8">(</span>i<span class="fc8">)<span class="fc5 lsd">=</span>(</span>i<span class="fc5 lsd">-<span class="fc6">1</span></span><span class="fc8">)<span class="fc5">*<span class="fc6">5</span>/<span class="fc6">1000</span></span></span>;</span> </div><div class="t m0 x1 h7 yb6 ff2 fs4 fc0 sc0 ls4 ws3"> <span class="fc4 ws15">x<span class="fc8">(</span>i<span class="fc8">)<span class="fc5 lsd">=</span><span class="fc6">0.20025<span class="fc5 lsd">*</span><span class="fc9">exp</span></span>(<span class="fc5 lsd">-</span></span>t<span class="fc8">(</span>i<span class="fc8">))<span class="fc5 lsd">*</span><span class="fc9">sin</span>(<span class="fc6">19.98<span class="fc5">*</span></span></span>t<span class="fc8">(</span>i<span class="fc8">))</span><span class="ls19">;</span></span> </div><div class="t m0 x1 h7 yb7 ff2 fs4 fc3 sc0 ls4 ws15">end<span class="fc0 ws3"> </span></div><div class="t m0 x1 h7 yb8 ff2 fs4 fc4 sc0 ls4 ws15">plot<span class="fc8">(</span>t,x<span class="fc8">)</span><span class="ls19">;</span><span class="fc0 ws3"> </span></div><div class="t m0 x1 h7 yb9 ff2 fs4 fc0 sc0 ls4 ws3"> </div><div class="t m0 x1 h7 yba ff2 fs4 fc0 sc0 ls4 ws3"> </div><div class="t m0 x1 h2 ybb ff1 fs0 fc0 sc0 ls4 ws3"> </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>
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