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Dedection of crack via FRF
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<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/62634cb04f8811599e1e30c3/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <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://static.pudn.com/prod/directory_preview_static/62634cb04f8811599e1e30c3/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">IMAC VIII <span class="ls1 ws1"> <span class="ls2 ws2">January, 1990</span><span class="ws3"> </span></span></div><div class="t m0 x2 h3 y2 ff1 fs1 fc0 sc0 ls1 ws4"> </div><div class="t m0 x3 h2 y3 ff1 fs0 fc0 sc0 ls3 ws5">Page <span class="ls1 ws6">1<span class="ls4 ws7"> of </span>6<span class="ws3"> </span></span></div><div class="t m0 x4 h4 y4 ff2 fs2 fc0 sc0 ls5 ws8">Detection and Location of Structural Cracks using FRF Measurements<span class="ls1 ws9"> </span></div><div class="t m0 x1 h5 y5 ff2 fs0 fc0 sc0 ls1 wsa"> </div><div class="t m0 x5 h2 y6 ff1 fs0 fc0 sc0 ls6 ws6">by<span class="ls1 ws3"> </span></div><div class="t m0 x6 h2 y7 ff1 fs0 fc0 sc0 ls7 wsb">M.A. Mannan<span class="ls1 ws3"> </span></div><div class="t m0 x7 h2 y8 ff1 fs0 fc0 sc0 ls8 wsc">Royal Institute of Technology, Stockholm, Sweden<span class="ls1 ws3"> </span></div><div class="t m0 x8 h2 y9 ff1 fs0 fc0 sc0 ls9 ws6">And<span class="ls1 ws3"> </span></div><div class="t m0 x2 h2 ya ff1 fs0 fc0 sc0 ls1 ws3"> </div><div class="t m0 x9 h2 yb ff1 fs0 fc0 sc0 lsa wsd">Mark H. Richardson<span class="ls1 ws3"> </span></div><div class="t m0 xa h2 yc ff1 fs0 fc0 sc0 lsb wse">Structural Measurement Systems, Milpitas, California<span class="ls1 ws3"> </span></div><div class="t m0 x2 h5 yd ff2 fs0 fc0 sc0 ls1 wsa"> </div><div class="t m0 x2 h5 ye ff2 fs0 fc0 sc0 ls1 wsa"> </div><div class="t m0 x1 h5 yf ff2 fs0 fc0 sc0 lsc ws6">Abstract<span class="ls1 wsa"> </span></div><div class="t m0 x1 h5 y10 ff2 fs0 fc0 sc0 ls1 wsa"> </div><div class="t m0 x1 h2 y11 ff1 fs0 fc0 sc0 lsd wsf">This is follow<span class="lse ws6">-<span class="lsf ws10">on work to an IMAC <span class="ls10 ws11">paper given last year [1] </span></span></span></div><div class="t m0 x1 h2 y12 ff1 fs0 fc0 sc0 ls11 ws12">where it was shown that modal testing can be used to detect </div><div class="t m0 x1 h2 y13 ff1 fs0 fc0 sc0 ls12 ws6">&#8220;<span class="ls13">faults</span><span class="ws13">&#8221; <span class="ls14 ws14">in mechanical structures. By </span></span>&#8220;<span class="ls13">faults<span class="ls15 ws15">&#8221;, we mean any of </span></span></div><div class="t m0 x1 h2 y14 ff1 fs0 fc0 sc0 ls16 ws16">the following occurrences:<span class="ls1 ws3"> </span></div><div class="t m0 x1 h2 y15 ff1 fs0 fc0 sc0 ls1 ws3"> </div><div class="t m0 xb h6 y16 ff3 fs0 fc0 sc0 ls17 ws6">&#8226;<span class="ls1 ws17"> <span class="ff1 ls18 ws18">failure of the structural material, e.g. cracking, breaking, </span></span></div><div class="t m0 xc h2 y17 ff1 fs0 fc0 sc0 ls19 ws19">or delamination.<span class="ls1 ws3"> </span></div><div class="t m0 x1 h2 y18 ff1 fs0 fc0 sc0 ls1 ws3"> </div><div class="t m0 xb h6 y19 ff3 fs0 fc0 sc0 ls17 ws6">&#8226;<span class="ls1 ws17"> <span class="ff1 ls1a ws1a">loosening of assembled parts, e.g. loose bolts, rivets, or </span></span></div><div class="t m0 xc h2 y1a ff1 fs0 fc0 sc0 ls1b ws1b">glued joints.<span class="ls1 ws3"> </span></div><div class="t m0 x1 h2 y1b ff1 fs0 fc0 sc0 ls1 ws3"> </div><div class="t m0 xb h6 y1c ff3 fs0 fc0 sc0 ls17 ws6">&#8226;<span class="ls1 ws17"> <span class="ff1 ls1c ws1c">flaws, voids, cracks, thin spots, etc. caused during </span></span></div><div class="t m0 xc h2 y1d ff1 fs0 fc0 sc0 ls1d ws6">manufacturing.<span class="ls1 ws3"> </span></div><div class="t m0 x1 h2 y1e ff1 fs0 fc0 sc0 ls1 ws3"> </div><div class="t m0 xb h6 y1f ff3 fs0 fc0 sc0 ls17 ws6">&#8226;<span class="ls1 ws17"> <span class="ff1 ls1e ws1d">improper assembly of parts during manufacturing.<span class="ls1 ws3"> </span></span></span></div><div class="t m0 x1 h2 y20 ff1 fs0 fc0 sc0 ls1 ws3"> </div><div class="t m0 x1 h2 y21 ff1 fs0 fc0 sc0 ls1f ws1e">The underlying principle behind this fault detection method is </div><div class="t m0 x1 h2 y22 ff1 fs0 fc0 sc0 ls20 ws1f">that vibration is a sensitive indicator of the physical integrity </div><div class="t m0 x1 h2 y23 ff1 fs0 fc0 sc0 ls21 ws20">of any mechanical structure. Or, more specifically, if any of<span class="ls1 ws21"> </span></div><div class="t m0 x1 h2 y24 ff1 fs0 fc0 sc0 ls22 ws22">the mass, stiffness, of damping properties of the structure<span class="ls1 ws21"> </span></div><div class="t m0 x1 h2 y25 ff1 fs0 fc0 sc0 ls23 ws23">change due to a structural fault, then its vibrational response </div><div class="t m0 x1 h2 y26 ff1 fs0 fc0 sc0 ls24 ws6">will<span class="ls25 ws24"> change, and this change can be accurately measured using </span></div><div class="t m0 x1 h2 y27 ff1 fs0 fc0 sc0 ls26 ws25">standard modal testing methods.<span class="ls1 ws3"> </span></div><div class="t m0 x1 h2 y28 ff1 fs0 fc0 sc0 ls1 ws3"> </div><div class="t m0 x1 h2 y29 ff1 fs0 fc0 sc0 ls27 ws26">In this paper, we carry this approach one step farther, and<span class="ls1 ws21"> </span></div><div class="t m0 x1 h2 y2a ff1 fs0 fc0 sc0 ls28 ws27">discuss the problem of not only <span class="ff4 ls29 ws28">detecting, </span><span class="ls2a ws29">but also <span class="ff4 ls2b ws2a">locating, </span><span class="ls2c ws2b">or </span></span></div><div class="t m0 x1 h2 y2b ff1 fs0 fc0 sc0 ls2d ws2c">at least <span class="ff4 ls2e ws6">localizing</span><span class="ls2f ws2d">, a structural fault.<span class="ls30 ws2e"> We present a method for </span></span></div><div class="t m0 x1 h2 y2c ff1 fs0 fc0 sc0 ls31 ws2f">determining the mass, stiffness, and damping properties of the </div><div class="t m0 x1 h2 y2d ff1 fs0 fc0 sc0 ls32 ws30">structure from measured Frequency Response Functions<span class="ls1 ws21"> </span></div><div class="t m0 x1 h2 y2e ff1 fs0 fc0 sc0 ls33 ws31">(FRFs), and show how changes in these parameters can be<span class="ls1 ws21"> </span></div><div class="t m0 x1 h2 y2f ff1 fs0 fc0 sc0 ls34 ws32">used to localize the fault.<span class="ls1 ws3"> </span></div><div class="t m0 x1 h2 y30 ff1 fs0 fc0 sc0 ls1 ws3"> </div><div class="t m0 x1 h5 y31 ff2 fs0 fc0 sc0 ls35 ws6">Introduction<span class="ls1 wsa"> </span></div><div class="t m0 x1 h5 y32 ff2 fs0 fc0 sc0 ls1 wsa"> </div><div class="t m0 x1 h2 y33 ff1 fs0 fc0 sc0 ls36 ws33">The linear dynam<span class="ls21 ws34">ics of structures are commonly represented </span></div><div class="t m0 x1 h2 y34 ff1 fs0 fc0 sc0 ls37 ws35">by the <span class="ls12 ws6">&#8220;<span class="ls38 ws36">force balance</span><span class="ws37">&#8221; <span class="ls39 ws38">shown in Figure 1. This equation<span class="ls1 ws21"> </span></span></span></span></div><div class="t m0 x1 h2 y35 ff1 fs0 fc0 sc0 ls3a ws39">balances the internal forces within a structure, which are<span class="ls1 ws21"> </span></div><div class="t m0 x1 h2 y36 ff1 fs0 fc0 sc0 ls3b ws3a">functions of its mass, damping and stiffness properties, with<span class="ls1 ws21"> </span></div><div class="t m0 x1 h2 y37 ff1 fs0 fc0 sc0 ls3c ws3b">any externally applied forces, which<span class="ls3d ws3c"> are written on the right </span></div><div class="t m0 x1 h2 y38 ff1 fs0 fc0 sc0 lsa wsd">hand side of the equation.<span class="ls1 ws3"> </span></div><div class="t m0 x1 h2 y39 ff1 fs0 fc0 sc0 ls1 ws3"> </div><div class="t m0 x1 h2 y3a ff1 fs0 fc0 sc0 ls3e ws3d">Structures begin to vibrate when external forces are applied to </div><div class="t m0 x1 h2 y3b ff1 fs0 fc0 sc0 ls3f ws3e">them and the resulting energy becomes trapped within the<span class="ls1 ws21"> </span></div><div class="t m0 x1 h2 y3c ff1 fs0 fc0 sc0 ls40 ws3f">their boundaries. This energy is then <span class="ls12 ws6">&#8220;<span class="ls41 ws40">traded back and forth</span><span class="ws41">&#8221; </span></span></div><div class="t m0 x1 h2 y3d ff1 fs0 fc0 sc0 ls42 ws42">between the inertia<span class="ls27 ws43">l (mass) properties and the restoring<span class="ls1 ws21"> </span></span></div><div class="t m0 xd h2 y3e ff1 fs0 fc0 sc0 ls43 ws44">(stiffness) properties.<span class="ls1 ws3"> </span></div><div class="t m0 xd h2 y3f ff1 fs0 fc0 sc0 ls1 ws3"> </div><div class="t m0 xd h2 y11 ff1 fs0 fc0 sc0 ls44 ws45">If the external forces are removed, the structure will continue </div><div class="t m0 xd h2 y12 ff1 fs0 fc0 sc0 ls45 ws46">to vibrate, but eventually, the dissipative (damping) properties </div><div class="t m0 xd h2 y13 ff1 fs0 fc0 sc0 ls46 ws47">will dissipate the energy, and the structure will stop vibrating<span class="ls47 ws6">.<span class="ls1 ws3"> </span></span></div><div class="t m0 xd h2 y14 ff1 fs0 fc0 sc0 ls1 ws3"> </div><div class="t m0 xd h2 y15 ff1 fs0 fc0 sc0 ls48 ws48">The structural faults listed above will all have an effect on the </div><div class="t m0 xd h2 y40 ff1 fs0 fc0 sc0 ls49 ws49">mass, damping, and stiffness properties of a structure. All of </div><div class="t m0 xd h2 y41 ff1 fs0 fc0 sc0 ls4a ws4a">them should cause a decrease in the structure&#8217;s stiffness, and </div><div class="t m0 xd h2 y42 ff1 fs0 fc0 sc0 ls4b ws4b">some will also affect its mass and damping properties.<span class="ls1 ws21"> </span></div><div class="t m0 xd h2 y43 ff1 fs0 fc0 sc0 ls4c ws6">Theref<span class="ls4d ws4c">ore, structural faults should <span class="ff4 ls4e ws4d">always, at a sufficient level </span></span></div><div class="t m0 xd h2 y44 ff4 fs0 fc0 sc0 ls4f ws4e">of severity, <span class="ff1 ls50 ws4f">cause a change in a structure&#8217;s vibrational<span class="ls1 ws21"> </span></span></div><div class="t m0 xd h2 y45 ff1 fs0 fc0 sc0 ls51 ws6">behavior.<span class="ls1 ws3"> </span></div><div class="t m0 xd h5 y46 ff2 fs0 fc0 sc0 ls1 wsa"> </div><div class="t m0 xd h5 y47 ff2 fs0 fc0 sc0 ls52 ws50">Equivalent Forms of Structural Dynamics<span class="ls1 wsa"> </span></div><div class="t m0 xd h5 y48 ff2 fs0 fc0 sc0 ls1 wsa"> </div><div class="t m0 xd h2 y49 ff1 fs0 fc0 sc0 ls53 ws51">In addition to its differential equations of motion, a structure&#8217;s </div><div class="t m0 xd h2 y4a ff1 fs0 fc0 sc0 ls40 ws52">linear dynamics can <span class="ls54 ws53">be represented in several other equivalent </span></div><div class="t m0 xd h2 y4b ff1 fs0 fc0 sc0 ls55 ws54">forms, as shown in Figure 2. FRFs, Impulse Responses, or </div><div class="t m0 xd h2 y4c ff1 fs0 fc0 sc0 ls56 ws55">modal parameters each fully represent the linear dynamic </div><div class="t m0 xd h2 y4d ff1 fs0 fc0 sc0 ls57 ws56">properties of a structure. Consequently, if any of the mass, </div><div class="t m0 xd h2 y4e ff1 fs0 fc0 sc0 ls58 ws57">damping or stiffness properties of a s<span class="ls59 ws58">tructure should change, </span></div><div class="t m0 xd h2 y4f ff1 fs0 fc0 sc0 ls5a ws59">we should expect its dynamic response, and also its FRFs, </div><div class="t m0 xd h2 y50 ff1 fs0 fc0 sc0 ls5b ws5a">Impulse Responses, and modal parameters to change. <span class="ls1 ws3"> </span></div><div class="t m0 xd h2 y51 ff1 fs0 fc0 sc0 ls1 ws3"> </div><div class="t m0 xe h2 y52 ff1 fs0 fc0 sc0 ls1 ws3"> </div><div class="t m0 xf h7 y53 ff4 fs0 fc0 sc0 ls5c ws5b">Figure 1<span class="ls1 ws5c"> </span></div><div class="t m0 xd h2 y54 ff1 fs0 fc0 sc0 ls1 ws3"> </div></div><div class="pi" data-data='{"ctm":[1.568627,0.000000,0.000000,1.568627,0.000000,0.000000]}'></div></div> </body> </html>
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