<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/10beeb3d-54c0-4574-8724-997922c5239a/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls9 ws6"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls9 ws6">1 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls9 ws6"> </div></div><div class="t m0 x1 h4 y5 ff2 fs1 fc1 sc0 ls9 ws6">Vibrações Mecânicas \u2013 <span class="_0 blank"> </span>Resumo </div><div class="t m0 x1 h4 y6 ff2 fs1 fc1 sc0 ls9 ws6"> </div><div class="t m0 x1 h5 y7 ff3 fs2 fc0 sc0 ls9 ws6">VIBRAÇÕES FORÇADAS EM SISTEMAS </div><div class="t m0 x1 h5 y8 ff3 fs2 fc0 sc0 ls9 ws6">COM 1 GDL \u2013 VIBRAÇÃO CAUSADA POR </div><div class="t m0 x1 h5 y9 ff3 fs2 fc0 sc0 ls9 ws6">FORÇA DE DESBALANCEAMENTO EM </div><div class="t m0 x1 h5 ya ff3 fs2 fc0 sc0 ls9 ws6">MÁQUINAS ROTATIVAS </div><div class="t m0 x1 h6 yb ff4 fs3 fc1 sc0 ls9 ws6"> <span class="ff3 ws0">Introdução</span>: </div><div class="t m0 x1 h7 yc ff2 fs4 fc0 sc0 ls9 ws6">No <span class="_1 blank"> </span>início <span class="_1 blank"> </span>de <span class="_1 blank"> </span>nosso <span class="_1 blank"> </span>curso, <span class="_1 blank"> </span>lá <span class="_1 blank"> </span>na <span class="_1 blank"> </span>aula <span class="_1 blank"> </span>2 <span class="_1 blank"> </span>nós <span class="_1 blank"> </span>citamos, <span class="_1 blank"> </span>como <span class="_1 blank"> </span>exemplo <span class="_1 blank"> </span>de <span class="_1 blank"> </span>vibração </div><div class="t m0 x1 h7 yd ff2 fs4 fc0 sc0 ls9 ws6">forçada, <span class="_2 blank"> </span>o <span class="_2 blank"> </span>caso <span class="_2 blank"> </span>da <span class="_2 blank"> </span>roda <span class="_2 blank"> </span>desbalanceada <span class="_2 blank"> </span>de <span class="_2 blank"> </span>um <span class="_2 blank"> </span>carro. <span class="_2 blank"> </span>Comentávamos <span class="_2 blank"> </span>que <span class="_2 blank"> </span>o </div><div class="t m0 x1 h7 ye ff2 fs4 fc0 sc0 ls9 ws6">desbalanceamento provoca instabilidade no veículo. </div><div class="t m0 x1 h8 yf ff2 fs4 fc0 sc0 ls9 ws6">Na <span class="_0 blank"> </span>realidade, <span class="_0 blank"> </span>qualquer <span class="_0 blank"> </span>equipamento <span class="_0 blank"> </span>rotativo<span class="fs5 ls0 v1">1</span> <span class="_0 blank"> </span>está <span class="_0 blank"> </span>sujeito <span class="_0 blank"> </span>a <span class="_0 blank"> </span>desbalanceamento </div><div class="t m0 x1 h7 y10 ff2 fs4 fc0 sc0 ls9 ws6">e <span class="_3 blank"> </span>poderá <span class="_3 blank"> </span>ter <span class="_3 blank"> </span>problemas <span class="_3 blank"> </span>sérios, <span class="_3 blank"> </span>podendo <span class="_3 blank"> </span>t<span class="_4 blank"></span>er <span class="_3 blank"> </span>sua <span class="_3 blank"> </span>vida <span class="_3 blank"> </span>útil <span class="_3 blank"> </span>reduzida </div><div class="t m0 x1 h7 y11 ff2 fs4 fc0 sc0 ls9 ws6">drasticamente. </div><div class="t m0 x1 h7 y12 ff2 fs4 fc0 sc0 ls9 ws6"> Podemos citar com exemplo: </div><div class="t m0 x3 h7 y13 ff5 fs4 fc0 sc0 ls9 ws1">\uf0b7<span class="ff6 ls1 ws6"> <span class="ff2 ls9"> Partes <span class="_5 blank"> </span>rotativas <span class="_5 blank"> </span>de <span class="_5 blank"> </span>motores <span class="_5 blank"> </span>a <span class="_5 blank"> </span>combustão, <span class="_5 blank"> </span>como <span class="_5 blank"> </span>o <span class="_5 blank"> </span>eixo <span class="_5 blank"> </span>cames <span class="_5 blank"> </span>de </span></span></div><div class="t m0 x4 h7 y14 ff2 fs4 fc0 sc0 ls9 ws6">acionamento de válvulas da imagem ao lado. </div><div class="t m0 x3 h7 y15 ff5 fs4 fc0 sc0 ls9 ws1">\uf0b7<span class="ff6 ls1 ws6"> <span class="ff2 ls9">Rotores de motores elétricos; </span></span></div><div class="t m0 x3 h7 y16 ff5 fs4 fc0 sc0 ls9 ws1">\uf0b7<span class="ff6 ls1 ws6"> <span class="ff2 ls9">Rotores de bombas centrífugas, </span></span></div><div class="t m0 x3 h7 y17 ff5 fs4 fc0 sc0 ls9 ws1">\uf0b7<span class="ff6 ls1 ws6"> <span class="ff2 ls9">Enfim, qualquer coisa que tem alguma parte girante. </span></span></div><div class="t m0 x1 h9 y18 ff7 fs4 fc0 sc0 ls9 ws6"> </div><div class="t m0 x1 h9 y19 ff7 fs4 fc0 sc0 ls9 ws6"> </div><div class="t m0 x1 h6 y1a ff3 fs3 fc1 sc0 ls9 ws6">Força de Desbalanceamento em Máquinas Rota<span class="_0 blank"> </span>tivas </div><div class="t m0 x1 h7 y1b ff2 fs4 fc0 sc0 ls9 ws6">Trata-se de um caso particular de <span class="fc1">Força de Excitação Harmônica</span>; </div><div class="t m0 x1 h7 y1c ff2 fs4 fc0 sc0 ls9 ws6">No caso, o sistema é excitado por uma massa desbalanceada com velo<span class="_4 blank"></span>cidade angular </div><div class="t m0 x1 h7 y1d ff5 fs4 fc0 sc0 ls9 ws1">\uf077<span class="ff2 ws6">, dado por: </span></div><div class="t m0 x5 ha y1e ff8 fs4 fc0 sc0 ls9">\ue728</div><div class="t m0 x6 hb y1f ff8 fs6 fc0 sc0 ls2">\uebd6<span class="fs4 ls9 ws2 v2">(<span class="ls3 v3">\ue750</span><span class="ls4">)<span class="ls5 v3">=<span class="ff9 ls9 ws6"> <span class="ff8 ls6">\ue749</span></span></span></span></span><span class="ls7">\uebe2<span class="fs4 ls9 ws3 v4">. \ue740<span class="_0 blank"> </span>. \ue7f1<span class="_0 blank"> </span></span><span class="ls8 v5">\ueb36</span><span class="fs4 ls9 ws3 v4">. \ue74f\ue741\ue74a<span class="_0 blank"></span><span class="ws2 v6">(</span><span class="ws4">\ue7f1 .<span class="_6 blank"> </span>\ue750 <span class="ws2 v6">)</span><span class="ff7 ws6"> </span></span></span></span></div><div class="t m0 x1 h7 y20 ff2 fs4 fc0 sc0 ls9 ws6">Onde: </div><div class="t m0 x1 h2 y21 ff1 fs0 fc0 sc0 ls9 ws6"> <span class="_0 blank"> </span> <span class="_7 blank"></span> </div><div class="t m0 x1 hc y22 ff2 fs7 fc0 sc0 ls9 ws5">1<span class="fs8 ws6 v7"> Equipamento rotativo é aqu<span class="_4 blank"></span>ele que possui parte<span class="_4 blank"></span>s girantes. </span></div><div class="t m0 x7 hd y23 ff2 fs8 fc0 sc0 ls9 ws6">Figura 01 \u2013 Roda </div><div class="t m0 x8 hd y24 ff2 fs8 fc0 sc0 ls9 ws6">Figura 02 \u2013 Eixo Cames<span class="_4 blank"></span> </div><div class="t m0 x9 hd y25 ff2 fs8 fc0 sc0 ls9 ws6">Figura 03 \u2013 Rotor Motor Elétrico </div><div class="t m0 xa hd y26 ff2 fs8 fc0 sc0 ls9 ws6">Figura 04 \u2013 Rotor bomba Centrífuga </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/10beeb3d-54c0-4574-8724-997922c5239a/bg2.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls9 ws6"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls9 ws6">2 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls9 ws6"> </div></div><div class="t m0 x3 he y27 ff6 fs4 fc0 sc0 ls9 ws6">\u2022 <span class="_8 blank"> </span><span class="ff2 lsa">F<span class="fs5 ls9 ws7 v8">c</span><span class="ls9"> </span><span class="ffa">\uf0e0</span><span class="ls9"> a força de excitação por desbalanceamento, no SI é dada p<span class="_4 blank"></span>or N </span></span></div><div class="t m0 x4 h7 y28 ff2 fs4 fc0 sc0 ls9 ws6">(Newtons); </div><div class="t m0 x3 he y29 ff6 fs4 fc0 sc0 ls9 ws6">\u2022 <span class="_8 blank"> </span><span class="ff2 lsa">m<span class="fs5 lsb v8">o</span><span class="ls9"> </span><span class="ffa">\uf0e0</span><span class="ls9"> a massa desbalanceada, no SI é dada por kg (quilograma); </span></span></div><div class="t m0 x3 he y2a ff6 fs4 fc0 sc0 ls9 ws6">\u2022 <span class="_8 blank"> </span><span class="ff2">d <span class="ffa lsa">\uf0e0</span> a excentricidade, no SI é dada por m (metros) </span></div><div class="t m0 x3 he y2b ff6 fs4 fc0 sc0 ls9 ws6">\u2022 <span class="_8 blank"> </span><span class="ff5 ws1">\uf077</span><span class="ff2 lsc"> <span class="ffa lsa">\uf0e0</span><span class="ls9"> a velocidade angular no SI é dada por rad/s (radian<span class="_4 blank"></span>os por segundos); </span></span></div><div class="t m0 x3 he y2c ff6 fs4 fc0 sc0 ls9 ws6">\u2022 <span class="_8 blank"> </span><span class="ff2">T <span class="ffa lsa">\uf0e0</span> o tempo, no SI é dado por s (segundo). </span></div><div class="t m0 x1 h7 y2d ff2 fs4 fc0 sc0 ls9 ws6"> </div><div class="t m0 x1 h6 y2e ff3 fs3 fc1 sc0 ls9 ws6">Equação do Movimento para Desbalanceamento<span class="_0 blank"> </span> </div><div class="t m0 x1 h7 y2f ff2 fs4 fc0 sc0 ls9 ws6">Esse sistema pode ser representado pela figura<span class="_4 blank"></span> ao lado: </div><div class="t m0 x1 h7 y30 ff2 fs4 fc0 sc0 ls9 ws6">A equação do movimento ficará: </div><div class="t m0 xb ha y31 ff8 fs4 fc0 sc0 ls9 ws2">\ue893<span class="ffb lsc ws6"> </span>\ue89e</div><div class="t m0 xc ha yc ff8 fs4 fc0 sc0 lsd">\u0308<span class="ls9 ws8 v3">+ \ue889\ue89e</span></div><div class="t m0 xd hf yc ff8 fs4 fc0 sc0 lse">\u0307<span class="ls9 ws9 v3">+<span class="_1 blank"> </span>\ue891\ue89e = \ue893</span><span class="fs6 lsf v9">\ue895</span><span class="ls9 ws3 v3">. \ue88a. \ue8d3</span><span class="fs6 ls10 v1">\ueadb</span><span class="ls9 ws3 v3">. \ue899\ue88b\ue894</span><span class="ls9 ws2 v0">(<span class="ws3 v3">\ue8d3. \ue89a</span>)<span class="ff4 ws6 v3"> </span></span></div><div class="t m0 x1 h7 y32 ff2 fs4 fc0 sc0 ls9 ws6">Como vimos na aula anterior X<span class="fs5 ls11 v8">p</span> é: </div><div class="t m0 xe ha y33 ff8 fs4 fc0 sc0 ls9">\ue73a</div><div class="t m0 xf h10 y34 ff8 fs6 fc0 sc0 ls12">\uebe3<span class="fs4 ls9 ws6 v4">=<span class="_9 blank"> </span> <span class="_a blank"> </span></span><span class="ls13 va">\uebbf</span><span class="ls9 vb">\uebde</span></div><div class="t m0 x10 h11 y35 ff8 fs6 fc0 sc0 ls9">\ued57</div><div class="t m0 x11 h12 y36 ff8 fs6 fc0 sc0 ls14">\ueda5<span class="ls15 v0">(<span class="ls9 wsa v3">\ueb35\ueb3f\uebe5 </span><span class="fs9 ls16 v4">\uec2e</span>)<span class="fs9 ls16 v4">\uec2e</span><span class="ls9 wsb v3">\ueb3e</span>(<span class="ls9 wsc v3">\ueb36.\uec15.\uebe5 </span>)<span class="fs9 ls16 v4">\uec2e</span><span class="ff2 fs4 ls9 ws6 vc"> ou <span class="_0 blank"> </span> </span><span class="ls9 vd">\uebd1</span></span></div><div class="t m0 x12 h13 y37 ff8 fs9 fc0 sc0 ls9">\uecdb</div><div class="t m0 x13 h14 y38 ff8 fs6 fc0 sc0 ls17">\uebde<span class="fs4 ls9 ws6 vc">=<span class="_9 blank"> </span> <span class="_b blank"> </span></span><span class="ls18 va">\uebe0</span><span class="fs9 ls19 ve">\uecda</span><span class="ls9 wsd va">.\uebd7.\uec20 <span class="fs9 v2">\uec2e</span></span></div><div class="t m0 x14 h15 y36 ff8 fs6 fc0 sc0 ls9 wsb">\ueda5<span class="ls15 v0">(</span><span class="wsa v0">\ueb35\ueb3f\uebe5 <span class="fs9 ls16 v4">\uec2e</span><span class="ls15 v6">)</span><span class="fs9 ls1a v4">\uec2e</span><span class="wsb">\ueb3e<span class="v6">(</span><span class="wsc">\ueb36.\uec15.\uebe5 <span class="ls15 v6">)</span><span class="fs9 ls16 v4">\uec2e</span><span class="ff2 fs4 ws6 v5"> </span></span></span></span></div><div class="t m0 x1 h7 y39 ff2 fs4 fc0 sc0 ls9 ws6">Dividindo por m, vem: </div><div class="t m0 x15 h16 y3a ff1 fs4 fc0 sc0 ls6">\u039b<span class="ff2 ls9 ws6">(r, </span><span class="ls9 wse">\u03be<span class="ff2 ws6">) <span class="ff8 ls5">=<span class="fs6 ls9 wsb vf">\uebe0.\uebd1</span></span></span></span></div><div class="t m0 x16 h13 y3b ff8 fs9 fc0 sc0 ls9">\uecdb</div><div class="t m0 x17 h14 y3c ff8 fs6 fc0 sc0 ls18">\uebe0<span class="fs9 ls19 v10">\uecda</span><span class="ls9 wsf">.\uebd7 <span class="fs4 ws6 vc">=<span class="_9 blank"> </span> <span class="_c blank"> </span></span><span class="ls1b va">\uebe5</span><span class="fs9 v11">\uec2e</span></span></div><div class="t m0 x18 h15 y3d ff8 fs6 fc0 sc0 ls9 wsb">\ueda5<span class="ls15 v0">(</span><span class="wsa v0">\ueb35\ueb3f\uebe5 <span class="fs9 ls1a v4">\uec2e</span><span class="ls15 v6">)</span><span class="fs9 ls16 v4">\uec2e</span><span class="wsb">\ueb3e<span class="ls15 v6">(</span><span class="wsc">\ueb36.\uec15.\uebe5 <span class="ls15 v6">)</span><span class="fs9 ls1c v4">\uec2e</span><span class="ff2 fs4 ws6 v5"> </span></span></span></span></div><div class="t m0 x1 h7 y3e ff2 fs4 fc0 sc0 ls9 ws6">Acabamos de definir o <span class="fc1">fator de ampliação adimensional</span>, <span class="ff1 ls6">\u039b</span>(r, <span class="ff1 wse">\u03be</span>) </div><div class="t m0 x1 h6 y3f ff3 fs3 fc1 sc0 ls9 ws6">Representação Gráfica do Fator de Ampliação Adimensional pela </div><div class="t m0 x1 h6 y40 ff3 fs3 fc1 sc0 ls9 ws6">Razão r. </div><div class="t m0 x1 h7 y41 ff2 fs4 fc0 sc0 ls9 ws6">Semelhantemente, ao que fizemos para a força de excitaçã<span class="_4 blank"></span>o harmônica convencional, </div><div class="t m0 x1 h7 y42 ff2 fs4 fc0 sc0 ls9 ws6">podemos representar um diagrama Fator de Ampliação Adimensional <span class="ff1 ls6">\u039b</span>(r, <span class="ff1 wse">\u03be</span>) pela </div><div class="t m0 x1 h7 y43 ff2 fs4 fc0 sc0 ls9 ws6">razão r, para diversos fatores de amortecimento. Como ilustrado na figura a seguir: </div><div class="t m0 x19 hd y44 ff2 fs8 fc0 sc0 ls9 ws6">Figura 05 \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/10beeb3d-54c0-4574-8724-997922c5239a/bg3.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls9 ws6"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls9 ws6">3 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls9 ws6"> </div></div><div class="t m0 x1a h9 y45 ff7 fs4 fc0 sc0 ls9 ws6"> </div><div class="t m0 x1b h9 y46 ff7 fs8 fc0 sc0 ls9 ws6">Figura 06: Gráfico <span class="_4 blank"></span>Fator de Ampliação Adi<span class="_4 blank"></span>mensional <span class="fs4">\u039b(r, \u03be) </span>X Razão r </div><div class="t m0 x1c h9 y47 ff7 fs4 fc0 sc0 ls9 ws6"> </div><div class="t m0 x1 h17 y48 ff2 fs4 fc0 sc0 ls9 ws6">Nota-se que para um <span class="ff8 ws10">\ue7e6<span class="_d blank"> </span>< <span class="ls1d v1">1</span><span class="ws2 v12">\u221a</span><span class="v13">2</span></span></div><div class="t m0 x15 h18 y49 ff8 fs4 fc0 sc0 ls1e">\ued57<span class="ff2 ls9 ws6 v14"> , o máximo valor de <span class="ff1 ls6">\u039b</span> é <span class="ff8 lsa">\ue8ab</span></span><span class="fs6 ls9 ws11 v8">\ue893\ue887\ue89e </span><span class="ls1f v14">=</span><span class="fs6 ls9 v15">\ueada</span></div><div class="t m0 x1d h19 y4a ff8 fs6 fc0 sc0 ls9 wsb">\ueadb.\ue8c8<span class="v6">\ueda5</span>\ueada\ueb3f\ue8c8<span class="fs9 ls20 v4">\ueadb</span><span class="ff3 fs4 ws6 v5"> <span class="ff2">e ocorre </span></span></div><div class="t m0 x1 h1a y4b ff2 fs4 fc0 sc0 ls9 ws6">quando <span class="ff8 ws2">\ue898<span class="fs6 ws12 v9">\ue8ab\ue893\ue887\ue89e </span><span class="ls21">=</span><span class="fs6 v5">\ueada</span></span></div><div class="t m0 x1e h15 y4c ff8 fs6 fc0 sc0 ls9 wsb">\ueda5<span class="v3">\ueada\ueb3f\ueadb.\ue8c8</span><span class="fs9 ls22 v4">\ueadb</span><span class="ff2 fs4 ws6 vc"> </span></div><div class="t m0 x1 h6 y4d ff3 fs3 fc1 sc0 ls9 ws6">Exemplo: </div><div class="t m0 x1 h7 y4e ff2 fs4 fc0 sc0 ls9 ws6">Um gerador composto por um motor de <span class="_1 blank"> </span>1 cil<span class="_4 blank"></span>indro tem massa m <span class="_1 blank"> </span>=<span class="_4 blank"></span> 1.100 kg está </div><div class="t m0 x1 h7 y4f ff2 fs4 fc0 sc0 ls9 ws6">montado <span class="_e blank"> </span>sobre <span class="_e blank"> </span>isoladores <span class="_e blank"> </span>com <span class="_e blank"> </span>uma <span class="_e blank"> </span>rigidez <span class="_e blank"> </span>equivalente <span class="_e blank"> </span>k<span class="_0 blank"> </span><span class="fs5 ws7 v8">eq</span> <span class="_e blank"> </span>= <span class="_e blank"> </span>1,5 <span class="_e blank"> </span>MN/m. <span class="_e blank"> </span>O <span class="_e blank"> </span>pistão <span class="_e blank"> </span>e <span class="_e blank"> </span>a </div><div class="t m0 x1 h7 y50 ff2 fs4 fc0 sc0 ls9 ws6">parte <span class="_5 blank"> </span>da <span class="_e blank"> </span>biela <span class="_5 blank"> </span>equivalente <span class="_e blank"> </span>tem <span class="_5 blank"> </span>massa <span class="_e blank"> </span>de <span class="_5 blank"> </span>26 <span class="_5 blank"> </span>kg<span class="_4 blank"></span> <span class="_5 blank"> </span>e <span class="_e blank"> </span>movem<span class="_0 blank"> </span>-se <span class="_5 blank"> </span>de <span class="_e blank"> </span>forma <span class="_5 blank"> </span>harmônica <span class="_e blank"> </span>na </div><div class="t m0 x1 h7 y51 ff2 fs4 fc0 sc0 ls9 ws6">máquina no sentido vertical, com <span class="_0 blank"> </span>curso de 0,45 m a 500 RPM. O curso<span class="_0 blank"> </span> é definido como </div><div class="t m0 x1 h7 y52 ff2 fs4 fc0 sc0 ls9 ws6">curso = <span class="_1 blank"> </span>2 d. <span class="_1 blank"> </span>A partir <span class="_1 blank"> </span>de um <span class="_1 blank"> </span>teste experimental co<span class="_0 blank"> </span>nstatou<span class="_0 blank"> </span>-se <span class="_1 blank"> </span>que a amplitude <span class="_1 blank"> </span>de </div><div class="t m0 x1 h7 y53 ff2 fs4 fc0 sc0 ls9 ws6">vibração em regime <span class="_0 blank"> </span>permanente do motor, <span class="_0 blank"> </span>X<span class="_0 blank"> </span><span class="fs5 ls11 v8">p</span> é de <span class="_0 blank"> </span>0,01 m. <span class="_0 blank"> </span>Admitindo amortecimento </div><div class="t m0 x1 h7 y54 ff2 fs4 fc0 sc0 ls9 ws6">viscoso, calcular o coeficiente de amortecimento do sistema. </div><div class="t m0 x1 h7 y55 ff2 fs4 fc0 sc0 ls9 ws13">Solução:<span class="fs8 ws6"> </span></div><div class="t m0 x1 h7 y56 ff2 fs4 fc0 sc0 ls9 ws6">Podemos <span class="_f blank"> </span>representar <span class="_f blank"> </span>o <span class="_f blank"> </span>problema <span class="_f blank"> </span>por <span class="_f blank"> </span>meio <span class="_f blank"> </span>de <span class="_f blank"> </span>u<span class="_4 blank"></span>m <span class="_f blank"> </span>modelo, <span class="_f blank"> </span>como <span class="_f blank"> </span>o </div><div class="t m0 x1 h7 y57 ff2 fs4 fc0 sc0 ls9 ws6">indicado <span class="_e blank"> </span>na <span class="_e blank"> </span>figura <span class="_e blank"> </span>ao <span class="_5 blank"> </span>lado. <span class="_e blank"> </span> <span class="_e blank"> </span>Considerando <span class="_e blank"> </span>como <span class="_e blank"> </span>a <span class="_e blank"> </span>massa <span class="_5 blank"> </span>d<span class="_4 blank"></span>esbalanceada <span class="_e blank"> </span>a </div><div class="t m0 x1 h7 y58 ff2 fs4 fc0 sc0 ls9 ws6">massa <span class="_5 blank"> </span>equi<span class="_4 blank"></span>valente <span class="_5 blank"> </span>d<span class="_4 blank"></span>o <span class="_5 blank"> </span>conjunto <span class="_e blank"> </span>pisto <span class="_5 blank"> </span>e <span class="_10 blank"> </span>biela, <span class="_e blank"> </span>no <span class="_5 blank"> </span>caso, <span class="_10 blank"> </span>em <span class="_10 blank"> </span>questão, <span class="_10 blank"> </span>26 <span class="_10 blank"> </span>kg, </div><div class="t m0 x1 h7 y59 ff2 fs4 fc0 sc0 ls9 ws6">temos. </div><div class="t m0 x1 h7 y5a ff2 fs4 fc0 sc0 ls9 ws6">Calculando a Frequência da Máquina, <span class="ff5 ws1">\uf077</span>: </div><div class="t m0 x1f h1a y5b ff8 fs4 fc0 sc0 ls9 ws3">\ue7f1<span class="_d blank"> </span>=<span class="_9 blank"> </span>2. \ue7e8. \ue742<span class="_d blank"> </span>=<span class="_9 blank"> </span>2. \ue7e8<span class="_0 blank"> </span>. <span class="fs6 wsb v5">\ueb39\ueb34\ueb34</span></div><div class="t m0 x20 h1b y5c ff8 fs6 fc0 sc0 ls9 ws14">\ueb3a\ueb34 <span class="ff2 fs4 ws6 vc"> <span class="ff3 fs3">= 52,3(rad/s)</span> </span></div><div class="t m0 x1 h7 y5d ff2 fs4 fc0 sc0 ls9 ws6">Calculando a frequência angular natural, <span class="ff5">\uf077</span></div><div class="t m0 x21 h1c y5e ff2 fs5 fc0 sc0 ls9 ws7">n<span class="fs4 ws6 v16">: </span></div><div class="t m0 x22 ha y5f ff8 fs4 fc0 sc0 ls9">\ue7f1</div><div class="t m0 x23 h1d y60 ff8 fs6 fc0 sc0 ls23">\uebe1<span class="fs4 ls9 ws6 v4">=<span class="_9 blank"> </span> <span class="ws2 v17">\ueda7<span class="v1">\ue747</span></span></span><span class="ls9 ws15 vf">\uebd8\uebe4 <span class="fs4 v18">\ue749</span></span></div><div class="t m0 x24 h1e y61 ff8 fs4 fc0 sc0 ls24">\ued57<span class="ls9 ws6 v19">=<span class="_9 blank"> </span> </span><span class="ls9 ws2 v3">\ueda7</span><span class="ls9 ws3 v1">(1,5. 10</span><span class="fs6 ls25 vf">\ueb3a</span><span class="ls26 v1">)</span><span class="ls9 ws2 v1a">1100</span></div><div class="t m0 x25 ha y62 ff8 fs4 fc0 sc0 ls27">\ued57<span class="ls28 v8">=<span class="ff3 fs3 ls9 ws6"> 36,9 (rad/s)<span class="ff2 fs4"> </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="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/10beeb3d-54c0-4574-8724-997922c5239a/bg4.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls9 ws6"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls9 ws6">4 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls9 ws6"> </div></div><div class="t m0 x1 h7 y27 ff2 fs4 fc0 sc0 ls9 ws6">Calculando a razão entre as frequências, r: </div><div class="t m0 x26 h1a y63 ff8 fs4 fc0 sc0 ls9 ws9">\ue74e<span class="_d blank"> </span>= <span class="ff9 lse ws6"> </span><span class="fs6 v5">\uec20</span></div><div class="t m0 x27 h1f y64 ff8 fs6 fc0 sc0 ls9 wsb">\uec20<span class="fs9 ls29 v10">\uecd9</span><span class="ff9 fs4 ws6 vc"> <span class="ff8 ls5">=<span class="ff9 ls2a"> </span></span></span><span class="va">\ueb39\ueb36,\ueb37</span></div><div class="t m0 x28 h20 y64 ff8 fs6 fc0 sc0 ls9 wsb">\ueb37\ueb3a,\ueb3d\ueb36<span class="ff9 fs4 ws6 vc"> <span class="ff4 fs3">= 1,41</span> </span></div><div class="t m0 x1 h7 y65 ff2 fs4 fc0 sc0 ls9 ws6">Calculando a excentricidade, d: </div><div class="t m0 x29 h7 y66 ff2 fs4 fc0 sc0 ls9 ws6">Curso = 2.d </div><div class="t m0 x1 h7 y67 ff2 fs4 fc0 sc0 ls9 ws6">Calculando o fator de amortecimento, <span class="ff1 wse">\u03be</span>: </div><div class="t m0 x1 h16 y68 ff2 fs4 fc0 sc0 ls9 ws6">Temos: <span class="_11 blank"> </span><span class="ff8 fs6 wsb vf">\uebe0.\uebd1</span></div><div class="t m0 x2a h13 y69 ff8 fs9 fc0 sc0 ls9">\uecdb</div><div class="t m0 x2b h14 y6a ff8 fs6 fc0 sc0 ls18">\uebe0<span class="fs9 ls19 v10">\uecda</span><span class="ls9 wsf">.\uebd7 <span class="fs4 ls2b vc">=</span><span class="ls1b va">\uebe5</span><span class="fs9 v11">\uec2e</span></span></div><div class="t m0 x2c h15 y6b ff8 fs6 fc0 sc0 ls9 wsb">\ueda5<span class="ls15 v0">(</span><span class="wsa v0">\ueb35\ueb3f\uebe5 <span class="fs9 ls1a v4">\uec2e</span></span><span class="v0">)<span class="fs9 ls1a v4">\uec2e</span><span class="v3">\ueb3e</span><span class="ls15">(</span><span class="wsc v3">\ueb36.\uec15.\uebe5 </span><span class="ls15">)<span class="fs9 ls1c v4">\uec2e</span></span><span class="ff2 fs4 ws6 vc"> </span></span></div><div class="t m0 x2d h11 y6c ff8 fs6 fc0 sc0 ls9 ws6">\ueb35\ueb35\ueb34\ueb34 \ueb76 \ueb34,\ueb34\ueb35</div><div class="t m0 x2e h1f y6d ff8 fs6 fc0 sc0 ls9 ws6">\ueb36\ueb3a \ueb76 \ueb34,\ueb36\ueb36\ueb39<span class="_12 blank"> </span><span class="fs4 ls2c vc">=</span><span class="wsb va">\ueb35,\ueb38\ueb35</span></div><div class="t m0 x14 h13 y6e ff8 fs9 fc0 sc0 ls9">\uec2e</div><div class="t m0 x2f h21 y6f ff8 fs6 fc0 sc0 ls14">\ueda5<span class="ls15 v0">(<span class="ls9 wsb v3">\ueb35\ueb3f\ueb35,\ueb38\ueb35</span></span></div><div class="t m0 x16 h22 y70 ff8 fs9 fc0 sc0 ls16">\uec2e<span class="fs6 ls15 v19">)</span>\uec2e<span class="fs6 ls9 wsb v9">\ueb3e<span class="ls15 v6">(</span><span class="ws6">\ueb36 \ueb76 \ueb9e \ueb76 \ueb35,\ueb38\ueb35<span class="ls15 v6">)</span></span></span><span class="ls1c">\uec2e<span class="ff2 fs4 ls9 ws6 v1"> <span class="ffa lsa">\uf0e0</span> <span class="ffc fs3 ls2d">\u03be<span class="ff3 ls9"> = 0,133</span></span> </span></span></div><div class="t m0 x1 h7 y71 ff2 fs4 fc0 sc0 ls9 ws6">Calculando o coeficiente de amortecimento vi<span class="_4 blank"></span>scoso, c: </div><div class="t m0 x4 ha y72 ff8 fs4 fc0 sc0 ls9 ws3">\ue73f<span class="_d blank"> </span>=<span class="_9 blank"> </span>2. \ue749. \ue7e6<span class="_e blank"> </span>. \ue7f1</div><div class="t m0 x1f h23 y73 ff8 fs6 fc0 sc0 ls23">\uebe1<span class="fs4 ls9 ws6 v4">=<span class="_9 blank"> </span> <span class="ff2">2 x 1100 x 0,133 x 36,92<span class="ff8 fs3"> =<span class="_d blank"> </span> <span class="ff3">10.559,1 (N.s/<span class="_0 blank"> </span>m)</span></span> </span></span></div><div class="t m0 x1 h7 y47 ff2 fs4 fc0 sc0 ls9 ws6">Chegando assim a resposta desejada. </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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