[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/20994#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/20994","headline":"\u30d9\u30c3\u30bb\u30eb\u30dd\u30a4\u30f3\u30c8\u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"\u30d9\u30c3\u30bb\u30eb\u30dd\u30a4\u30f3\u30c8\u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u30d9\u30c3\u30bb\u30eb\u30c9\u30c3\u30c8 \u6b69\u9053\u306e\u5bfe\u79f0\u7684\u306b\u914d\u7f6e\u3055\u308c\u305f2\u3064\u306e\u30b9\u30c8\u30ec\u30fc\u30b8\u30dd\u30a4\u30f3\u30c8\u3067\u3042\u308a\u3001\u305d\u3053\u3067\u5f7c\u306f\u53ef\u80fd\u306a\u9650\u308a\u4f4e\u3044\u91cd\u529b\u95a2\u9023\u306e\u5909\u5f62\u3092\u7d4c\u9a13\u3057\u307e\u3059\u3002\u3053\u306e\u6700\u5c0f\u9650\u306e\u5909\u5f62\u306e\u6700\u9069\u306a\u6761\u4ef6\u306f\u3001\u7570\u306a\u308b\u57fa\u6e96\u306b\u5f93\u3063\u3066\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u70b9\u306f\u3001\u30d7\u30ed\u30a4\u30bb\u30f3\u6e2c\u5b9a\u30b7\u30b9\u30c6\u30e0\u306e\u5b9a\u7fa9\u306b\u304a\u3051\u308b\u9577\u3055\u306e\u5bf8\u6cd5\u306e\u6a19\u6e96\u5316\u306b\u95a2\u9023\u3057\u3066\u3001\u30d5\u30ea\u30fc\u30c9\u30ea\u30c3\u30d2\u30fb\u30a6\u30a3\u30eb\u30d8\u30eb\u30e0\u30fb\u30d9\u30c3\u30bb\u30eb\u306b\u3088\u3063\u3066\u521d\u3081\u3066\u8a08\u7b97\u3055\u308c\u307e\u3057\u305f\u3002 after-content-x4 \u30b5\u30dd\u30fc\u30c8\u30dd\u30b8\u30b7\u30e7\u30f3\u306e\u8a08\u7b97\u57fa\u6e96\u306f\u3001\u30d0\u30eb\u30b1\u30f3\u7406\u8ad6\uff08\u30d9\u30eb\u30cc\u30fc\u30ea\u30b7\u30e5\u306e\u4eee\u5b9a\u306b\u5f93\u3063\u3066\u3001\u30b9\u30e9\u30b9\u30c8\u304c\u91cd\u3044\u30d3\u30fc\u30e0\uff09\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u305f\u308f\u307f\u306e\u95a2\u6570\u306b\u3064\u306a\u304c\u308a\u307e\u3059 \u306e \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle w\uff08x\uff09} \u9577\u3055\u306e\u5ea7\u6a19\u306b\u5fdc\u3058\u3066\u30d0\u30fc\u306e \u30d0\u30c4 {displaystyle x} from -Bean Line\u3002 2\u3064\u306e\u30b5\u30dd\u30fc\u30c8\uff08\u30b9\u30dd\u30f3\u30b5\u30fc\u306e\u7d42\u308f\u308a\uff09\u306e\u9577\u3055L\u306e\u5747\u7b49\u306b\u30b9\u30c8\u30ec\u30b9\u306e\u3042\u308b\u5bfe\u79f0\u30d0\u30fc\u306e\u95a2\u9023\u3059\u308b\u30b1\u30fc\u30b9\u306b\u306f\u30013\u3064\u306e\u9818\u57df\u304c\u3042\u308a\u3001\u305d\u308c\u305e\u308c\u304c4\u5ea6\u306e\u591a\u9805\u5f0f\u95a2\u6570\u3067\u8aac\u660e\u3067\u304d\u307e\u3059\u3002\u6298\u308a\u7573\u307f\u30dc\u30c3\u30af\u30b9\u306b\u306f\u3001\u30bb\u30af\u30b7\u30e7\u30f3I\uff080\u2264x\u2264a\uff09\u304a\u3088\u3073II\uff08a\u2264x\u2264l -a\uff09\u306e\u5c0e\u51fa\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002","datePublished":"2020-07-07","dateModified":"2020-07-07","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/e\/e6\/Bessel_balken.png\/220px-Bessel_balken.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/e\/e6\/Bessel_balken.png\/220px-Bessel_balken.png","height":"121","width":"220"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/20994","wordCount":9394,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4  \u30d9\u30c3\u30bb\u30eb\u30c9\u30c3\u30c8 \u6b69\u9053\u306e\u5bfe\u79f0\u7684\u306b\u914d\u7f6e\u3055\u308c\u305f2\u3064\u306e\u30b9\u30c8\u30ec\u30fc\u30b8\u30dd\u30a4\u30f3\u30c8\u3067\u3042\u308a\u3001\u305d\u3053\u3067\u5f7c\u306f\u53ef\u80fd\u306a\u9650\u308a\u4f4e\u3044\u91cd\u529b\u95a2\u9023\u306e\u5909\u5f62\u3092\u7d4c\u9a13\u3057\u307e\u3059\u3002\u3053\u306e\u6700\u5c0f\u9650\u306e\u5909\u5f62\u306e\u6700\u9069\u306a\u6761\u4ef6\u306f\u3001\u7570\u306a\u308b\u57fa\u6e96\u306b\u5f93\u3063\u3066\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u70b9\u306f\u3001\u30d7\u30ed\u30a4\u30bb\u30f3\u6e2c\u5b9a\u30b7\u30b9\u30c6\u30e0\u306e\u5b9a\u7fa9\u306b\u304a\u3051\u308b\u9577\u3055\u306e\u5bf8\u6cd5\u306e\u6a19\u6e96\u5316\u306b\u95a2\u9023\u3057\u3066\u3001\u30d5\u30ea\u30fc\u30c9\u30ea\u30c3\u30d2\u30fb\u30a6\u30a3\u30eb\u30d8\u30eb\u30e0\u30fb\u30d9\u30c3\u30bb\u30eb\u306b\u3088\u3063\u3066\u521d\u3081\u3066\u8a08\u7b97\u3055\u308c\u307e\u3057\u305f\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30b5\u30dd\u30fc\u30c8\u30dd\u30b8\u30b7\u30e7\u30f3\u306e\u8a08\u7b97\u57fa\u6e96\u306f\u3001\u30d0\u30eb\u30b1\u30f3\u7406\u8ad6\uff08\u30d9\u30eb\u30cc\u30fc\u30ea\u30b7\u30e5\u306e\u4eee\u5b9a\u306b\u5f93\u3063\u3066\u3001\u30b9\u30e9\u30b9\u30c8\u304c\u91cd\u3044\u30d3\u30fc\u30e0\uff09\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u305f\u308f\u307f\u306e\u95a2\u6570\u306b\u3064\u306a\u304c\u308a\u307e\u3059 \u306e \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle w\uff08x\uff09} \u9577\u3055\u306e\u5ea7\u6a19\u306b\u5fdc\u3058\u3066\u30d0\u30fc\u306e \u30d0\u30c4 {displaystyle x} from -Bean Line\u3002 2\u3064\u306e\u30b5\u30dd\u30fc\u30c8\uff08\u30b9\u30dd\u30f3\u30b5\u30fc\u306e\u7d42\u308f\u308a\uff09\u306e\u9577\u3055L\u306e\u5747\u7b49\u306b\u30b9\u30c8\u30ec\u30b9\u306e\u3042\u308b\u5bfe\u79f0\u30d0\u30fc\u306e\u95a2\u9023\u3059\u308b\u30b1\u30fc\u30b9\u306b\u306f\u30013\u3064\u306e\u9818\u57df\u304c\u3042\u308a\u3001\u305d\u308c\u305e\u308c\u304c4\u5ea6\u306e\u591a\u9805\u5f0f\u95a2\u6570\u3067\u8aac\u660e\u3067\u304d\u307e\u3059\u3002\u6298\u308a\u7573\u307f\u30dc\u30c3\u30af\u30b9\u306b\u306f\u3001\u30bb\u30af\u30b7\u30e7\u30f3I\uff080\u2264x\u2264a\uff09\u304a\u3088\u3073II\uff08a\u2264x\u2264l -a\uff09\u306e\u5c0e\u51fa\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30bb\u30af\u30b7\u30e7\u30f3I\u304a\u3088\u3073II\u3067\u306e\u8c46\u30e9\u30a4\u30f3\u306e\u5c0e\u51fa w\u2033{displaystyle w”}\u2026\u66f2\u7387\u3001 w\u2032{displaystyle w’}\u2026\u30d4\u30c3\u30c1\u3001 w{displaystyle w}…\u504f\u5411\u3001        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4x{displaystyle x}\u2026l\u00e4ngenkoordinatedesbalkens\u3001 a{displaystyle a}…\u7e2b\u3044\u30d9\u30fc\u30eb\u306e\u7aef\u3078\u306e\u30b5\u30dd\u30fc\u30c8\u3092\u8ddd\u96e2\u3001 L{displaystyle L}…\u30d3\u30fc\u30e0\u306e\u9577\u3055\u3001 Mb{displaystyle M_{b}}\u2026\u4e8c\u91cd\u9020\u308a\u3001 qges{displaystyle q_{ges}}…\u30eb\u30fc\u30c8\u30ed\u30fc\u30c9\u3001 E{displaystyle E}\u2026\u5f3e\u529b\u6027\u306e\u30e2\u30b8\u30e5\u30e9\u30b9\u3001 Iy{displaystyle I_{y}}\u2026\u8ef8\u9762\u7a4d\u6163\u6027\u30c8\u30eb\u30af \u30bb\u30af\u30b7\u30e7\u30f3I\uff080\u2264x\u2264a\uff09 \u30bb\u30af\u30b7\u30e7\u30f3II\uff08a\u2264x\u2264l-a\uff09 Mb(0\u2264x\u2264a)=\u2212qges2x2{displaystyle M_{b}(0leq xleq a)=-{frac {q_{ges}}{2}}x^{2}}wI\u2033(x)=\u22121EIyMb(x)=1EIyqges2x2{displaystyle w”_{mathrm {I} }(x)=-{frac {1}{EI_{y}}}M_{b}(x)={frac {1}{EI_{y}}}{frac {q_{ges}}{2}}x^{2}}wI\u2032(x)=1EIy(qges6x3+C1){displaystyle w’_{mathrm {I} }(x)={frac {1}{EI_{y}}}left({frac {q_{ges}}{6}}x^{3}+C_{1}right),}wI(x)=1EIy(qges24x4+C1x+C2){displaystyle w_{mathrm {I} }(x)={frac {1}{EI_{y}}}left({frac {q_{ges}}{24}}x^{4}+C_{1}x+C_{2}right),}Mb(a\u2264x\u2264L\u2212a)=\u2212qges2x2+qgesL2(x\u2212a){displaystyle M_{b}(aleq xleq L-a)=-{frac {q_{ges}}{2}}x^{2}+{frac {q_{ges}L}{2}}(x-a)}wII\u2033(x)=1EIy(qges2x2\u2212qgesL2(x\u2212a)){displaystyle w”_{mathrm {II} }(x)={frac {1}{EI_{y}}}left({frac {q_{ges}}{2}}x^{2}-{frac {q_{ges}L}{2}}(x-a)right),}wII\u2032(x)=1EIy(qges2(13x3\u221212Lx2+Lax)+C3){displaystyle w’_{mathrm {II} }(x)={frac {1}{EI_{y}}}left({frac {q_{ges}}{2}}left({frac {1}{3}}x^{3}-{frac {1}{2}}Lx^{2}+Laxright)+C_{3}right),}wII(x)=1EIy(qges4(16x4\u221213Lx3+Lax3)+C3x+C4){displaystyle w_{mathrm {II} }(x)={frac {1}{EI_{y}}}left({frac {q_{ges}}{4}}left({frac {1}{6}}x^{4}-{frac {1}{3}}Lx^{3}+Lax^{3}right)!+C_{3}x+C_{4}right)}\u5bfe\u79f0\u6027\u3001\u4fdd\u7ba1\u3001\u304a\u3088\u3073\u79fb\u884c\u6761\u4ef6\uff1a SB-1\uff1a wII\u2032(L\/2)=0\u21d2C3=\u2212qges24L2(6a\u2212L){displaystyle w’_{mathrm {II} }(L\/2)=0Rightarrow C_{3}=-{frac {q_{ges}}{24}}L^{2}(6a-L)}LB-1\uff1a wII(a)=0\u21d2C4=qges24a(\u2212a3\u22124a2L+6aL2\u2212L3){displaystyle w_{mathrm {II} }(a)=0Rightarrow C_{4}={frac {q_{ges}}{24}}a(-a^{3}-4a^{2}L+6aL^{2}-L^{3})}\u00fcb-1\uff1a wI\u2032(a)=wII\u2032(a)\u21d2C1=qges24L(6a2\u22126aL+L2){displaystyle w’_{mathrm {I} }(a)=w’_{mathrm {II} }(a)Rightarrow C_{1}={frac {q_{ges}}{24}}L(6a^{2}-6aL+L^{2})}LB-2\uff1a wI(a)=0\u21d2C2=\u2212qges24a(a3+6a2L\u22126aL2+L3){displaystyle w_{mathrm {I} }(a)=0Rightarrow C_{2}=-{frac {q_{ges}}{24}}a(a^{3}+6a^{2}L-6aL^{2}+L^{3})}\u30d3\u30fc\u30b2\u30ea\u30f3 w(x){displaystyle w(x)}\uff1a wI(0\u2264x\u2264a)=qges24EIy(x4+(6a2L\u22126aL2+L3)x\u2212a4\u22126a3L+6a2L2\u2212aL3){displaystyle w_{mathrm {I} }(0leq xleq a)={frac {q_{ges}}{24EI_{y}}}(x^{4}+(6a^{2}L-6aL^{2}+L^{3})x-a^{4}-6a^{3}L+6a^{2}L^{2}-aL^{3})}\u3001 wII(a\u2264x\u2264L\u2212a)=qges24EIy(x4\u22122Lx3+6aLx2\u2212(6aL2\u2212L3)x\u2212a4\u22124a3L+6a2L2\u2212aL3){displaystyle w_{mathrm {II} }(aleq xleq L-a)={frac {q_{ges}}{24EI_{y}}}(x^{4}-2Lx^{3}+6aLx^{2}-(6aL^{2}-L^{3})x-a^{4}-4a^{3}L+6a^{2}L^{2}-aL^{3})}\u3002 \u3055\u307e\u3056\u307e\u306a\u5b9a\u7fa9\u306b\u5fdc\u3058\u305f\u6700\u9069\u306a\u4f4d\u7f6e\u6c7a\u3081\u30dd\u30a4\u30f3\u30c8 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ]  \u30d9\u30c3\u30bb\u30eb\u30c9\u30c3\u30c8\u4e0a\u306e\u30d0\u30fc\u306e\u4fdd\u7ba1\uff1a\u4f4e\u3044\u30d0\u30fc\u306e\u524a\u6e1b\uff08\u30cb\u30e5\u30fc\u30c8\u30e9\u30eb\u30ec\u30d9\u30eb\u306e\u30ec\u30d9\u30eb\u3067\u30d0\u30fc\u306e\u7aef\u3067\u6e2c\u5b9a\uff09  \u98a8\u901a\u3057\u306e\u826f\u3044\u30dd\u30a4\u30f3\u30c8\u4e0a\u306e\u30d0\u30fc\u306e\u4fdd\u7ba1\uff1a\u5e73\u884c\u30d3\u30fc\u30e0\u7aef\u9762  \u6c34\u5e73\u7dda\u306e\u4f8b\uff1a\u7c73\u56fd\u306e1889\u5e74\u306e\u5143\u306e\u30e1\u30fc\u30bf\u30fc\u306e\u30b3\u30d4\u30fcNo. 27 \u5747\u8cea\u3067\u5747\u7b49\u306b\u6c5a\u67d3\u3055\u308c\u305f\u30d7\u30ea\u30ba\u30e0\u30d3\u30fc\u30e0\u304c2\u3064\u306e\u30b5\u30dd\u30fc\u30c8\u30b5\u30a4\u30c8\u306b\u4fdd\u5b58\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u305d\u308c\u306f\u91cd\u529b\u95a2\u9023\u306e\u5909\u5f62\u306e\u5f71\u97ff\u3092\u53d7\u3051\u307e\u3059\u3002 [\u521d\u3081] 2\u3064\u306e\u30b5\u30dd\u30fc\u30c8\u30b5\u30a4\u30c8\u3067\u306e\u30b9\u30c8\u30ec\u30fc\u30b8\u306e\u6700\u3082\u5358\u7d14\u306a\u30b1\u30fc\u30b9\u306e\u5834\u5408\u3001\u305d\u308c\u305e\u308c\u304c\u540c\u3058\u8ddd\u96e2 a {displaystyle a} \u5168\u9577\u306e\u30ad\u30e3\u30ea\u30a2\u306e\u7aef\u304b\u3089 l {displaystyle l} \u6700\u521d\u306e\u9806\u5e8f\u30d0\u30eb\u30b1\u30f3\u7406\u8ad6\u306b\u5f93\u3063\u3066\u6bd4\u7387\u5024\u3092\u6301\u3063\u3066\u3044\u308b a \/ l {displaystyle a\/l} \u7570\u306a\u308b\u57fa\u6e96\u306b\u5f93\u3063\u3066\u6700\u9069\u306a\u5009\u5eab\u4f4d\u7f6e\u306b\u3064\u3044\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\uff08\u8868\u3092\u53c2\u7167\uff09\u3002 \u6700\u9069\u5316\u57fa\u6e96 \u8aac\u660e a\/L\u2212{displaystyle a\/l-} \u5024\uff08\u6570\u5024\uff09 \u30d3\u30fc\u30b2\u30ea\u30cb\u30fc\u306e\u6761\u4ef6\u3068\u3001\u5fc5\u8981\u306b\u5fdc\u3058\u3066\u3001\u6b63\u78ba\u306a\u89e3\u6c7a\u7b56 \u9577\u3055\u306e\u6700\u5c0f\u9650\u306e\u77ed\u7e2e\uff08\u30cb\u30e5\u30fc\u30c8\u30e9\u30eb\u30d5\u30a1\u30a4\u30d0\u30fc\u306e\u7aef\uff09   Friedrich Wilhelm Bessel\u306f\u3001 \u4e2d\u9818\u57df\u306e\u30ad\u30e3\u30ea\u30a2\u306e\u9577\u3055\u306e\u308f\u305a\u304b\u306a\u77ed\u7e2e \u3001\u30cb\u30e5\u30fc\u30c8\u30e9\u30eb\u30ec\u30d9\u30eb\u3002\u9577\u3055\u306e\u57fa\u6e96\u306f\u3001\u30d9\u30c3\u30bb\u30eb\u306b\u3068\u3063\u3066\u91cd\u8981\u3067\u3057\u305f\u3002\u306a\u305c\u306a\u3089\u3001\u5f7c\u306f\u30d7\u30ed\u30a4\u30bb\u30f3\u306e\u9577\u3055\u306e\u6b63\u5e38\u3068\u6bd4\u8f03\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u6e2c\u5b9a\u6975\u306e\u4fdd\u7ba1\u3092\u6271\u3063\u305f\u305f\u3081\u3067\u3059\u3002 [2] \u6c34\u5e73\u306e\u5834\u5408 \u6b6a\u307f \u305d\u306e\u3088\u3046\u306a\u305f\u3068\u3048\u3070\u30011889\u5e74\u306e\u539f\u59cb\u30e1\u30fc\u30bf\u30fc\uff08\u30cb\u30e5\u30fc\u30c8\u30e9\u30eb\u30ec\u30d9\u30eb\u306e\u30e9\u30a4\u30f3\u30de\u30fc\u30ad\u30f3\u30b0\u3092\u5099\u3048\u305fX\u5b57\u578b\u306e\u65ad\u9762\uff09\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306eA\/L\u69cb\u6210\u3067\u306f\u3001\u53ef\u80fd\u306a\u9650\u308a\u6700\u5927\u306e\u7cbe\u5ea6\u3092\u5b9f\u73fe\u3067\u304d\u307e\u3059\u3002 \u22480,22031{displaystyle amptox 0 {\u3001} 22031}  ddx(\u222b0L(w\u2032)2dx)=0{displaystyle {frac {mathrm {d}} {mathrm {d} x}}\u5de6\uff08int _ {0}^{l}\uff08w ‘\uff09^{2}\u3001mathrm {d} xright\uff09= 0}  \u9577\u3055\u306e\u6700\u5c0f\u9650\u306e\u77ed\u7e2e\uff08\u30a8\u30c3\u30b8\u30d5\u30a1\u30a4\u30d0\u30fc\u306e\u7d42\u4e86\uff09   \u540c\u3058\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u3067\u3001\u306e\u4f4d\u7f6e\u306e\u4f4d\u7f6e \u8868\u9762\u306e\u9577\u3055\u306e\u6700\u4f4e\u5909\u5316 \u6e2c\u5b9a\u30ed\u30c3\u30c9\u306e\u30b9\u30b1\u30fc\u30eb\u304c\u523b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u30ad\u30e3\u30ea\u30a2\u306e\u7aef\u9762\u306f\u4e92\u3044\u306b\u5e73\u884c\u3067\u3059\u3002 H.\u7aef\u306e\u89d2\u5ea6\u306e\u5909\u5316\u3082\u6700\u5c0f\u9650\u306b\u6291\u3048\u3089\u308c\u307e\u3059\u3002 [3] 1795\u5e74\u30681799\u5e74\u306e\u5143\u306e\u30e1\u30fc\u30bf\u30fc\u306a\u3069\u306e\u7aef\u672b\u306e\u5bf8\u6cd5\u306f\u3001\u6700\u7d42\u9818\u57df\u9593\u306e\u8ddd\u96e2\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u5408\u8a08\u9577\u3055\u306f\u3001\u3053\u306e\u5009\u5eab\u306e\u8ddd\u96e2\u3067\u30b5\u30dd\u30fc\u30c8\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u3053\u306e\u554f\u984c\u306b\u5bfe\u51e6\u3057\u305f\u30b8\u30e7\u30fc\u30b8\u30fb\u30d3\u30c7\u30eb\u30fb\u30a8\u30a2\u30ea\u30fc\u306b\u656c\u610f\u3092\u8868\u3057\u3066\u3001\u6587\u732e\u306e\u3053\u308c\u3089\u306e\u7acb\u5834\u306f\u300c\u98a8\u901a\u3057\u306e\u826f\u3044\u70b9\u300d\u3068\u547c\u3070\u308c\u3066\u3044\u307e\u3059\u3002 [4] \u22480,211325{displaystyle amptox 0 {\u3001} 211325}  w\u2032(0)=w\u2032(L\u2212a)=0\u21d2a\/L=12\u2212123{displaystyle w ‘\uff080\uff09= w’\uff08l-a\uff09= 0quad rightarrow\u3001a\/l = {tfrac {1} {2}}  –  {tfrac {1} {2 {sqrt {3}}}}}}}  \u7fd2\u5f97\u306e\u6700\u5c0f\u5024   \u4e00 \u6700\u5c0f\u9650\u306e\u30d9\u30f3\u30c9 \u30d3\u30fc\u30e0\u306e\u4e2d\u592e\u3068\u7aef\u306e\u305f\u308f\u307f\u304c\u540c\u4e00\u306b\u306a\u308b\u3068\u3001\u30ad\u30e3\u30ea\u30a2\u306e\u5168\u9577\u306b\u308f\u305f\u3063\u3066\u5230\u9054\u3055\u308c\u307e\u3059\u3002 [\u521d\u3081] \u22480,223149{displaystyle amptox 0 {\u3001} 223149}  w(0)=w(L\/2)=w(L){displaystyle w\uff080\uff09= w\uff08l\/2\uff09= w\uff08l\uff09}  \u30d3\u30fc\u30e0\u306e\u4e2d\u592e\u3067\u30bc\u30ed\u66f2\u304c\u308a\u307e\u3059   \u3053\u306e\u30b9\u30c8\u30ec\u30fc\u30b8\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u30d3\u30fc\u30e0\u306e\u4e2d\u592e\u306b\u3042\u308b\u504f\u5411\u304c\u50240\u3092\u60f3\u5b9a\u3057\u307e\u3059\u3002 [\u521d\u3081] \u22480,238613{displaystyle amptox 0 {\u3001} 238613}  w(L\/2)=0\u21d2a\/L=152\u221252{displaystyle w\uff08l\/2\uff09= 0quad rightarrow\u3001a\/l = {sqrac {15} {2}}}  –  {tfrac {5} {2}}}}}  \u30d0\u30fc\u306e\u7aef\u3067\u30bc\u30ed\u66f2\u304c\u308a\u307e\u3059   \u30d3\u30fc\u30e0\u306e\u7aef\u304c\u30b5\u30dd\u30fc\u30c8\u30dd\u30a4\u30f3\u30c8\u306e\u30ec\u30d9\u30eb\u3068\u6bd4\u8f03\u3057\u3066\u66f2\u304c\u3063\u3066\u3044\u306a\u3044\u5834\u5408\u3001\u3053\u306e\u30b9\u30c8\u30ec\u30fc\u30b8\u306f\u9069\u7528\u3055\u308c\u307e\u3059\u3002 \u22480,214175{displaystyle amptox 0 {\u3001} 214175}  w(0)=w(L)=0{displaystyle w\uff080\uff09= w\uff08l\uff09= 0}  \u6700\u5c0f\u9650\u306e\u57f9\u5730\u30b5\u30a4\u30ba\u306e\u305f\u308f\u307f   \u6700\u5c0f\u9650 \u5168\u9577\u306b\u308f\u305f\u308b\u4e2d\u7a0b\u5ea6\u306e\u305f\u308f\u307f \u6700\u5c0f\u9650\u306e\u5909\u5316\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u57fa\u6e96\u3092\u4e57\u308a\u8d8a\u3048\u307e\u3059\u3002 [5] \u30b5\u30dd\u30fc\u30c8\u306b\u306f\u6c34\u5e73\u65b9\u5411\u306e\u63a5\u7dda\u304c\u3042\u308a\u307e\u3059\uff08\u305d\u3053\u306b\u4f5c\u7528\u3059\u308b\u66f2\u3052\u77ac\u9593\u306e\u5e73\u7b49\uff09\u3002 \u22480,224745{displaystyle amptox 0 {\u3001} 224745}  w\u2032(a)=w\u2032(L\u2212a)=0\u21d2a\/L=32\u22121{displaystyle w ‘\uff08a\uff09= w’\uff08l-a\uff09= 0quad rightarrow\u3001a\/l = {sqrac {3} {2}}}}  –  1}  \u6700\u5c0f\u9650\u306e\u66f2\u3052\u5fdc\u529b\u6700\u5927   \u306e\u305f\u3081\u306b \u6700\u4f4e\u6700\u5927\u66f2\u3052\u96fb\u5727 \u30eb\u30fc\u30c8\u8377\u91cd\u306e\u3042\u308b\u30ad\u30e3\u30ea\u30a2\u306e qges{displaystyle q_ {ges}} \u30b5\u30dd\u30fc\u30c8\u30b5\u30a4\u30c8\u3067\u306e\u66f2\u3052\u77ac\u9593\u3067\u3059 Mb(a){displaystyle m_ {b}\uff08a\uff09} \u3068 Mb(L\u2212a){displaystyle m_ {b}\uff08l-a\uff09} \u540c\u3058\u91cf\u306e\u66f2\u3052\u30e2\u30fc\u30e1\u30f3\u30c8\u3067 Mb(L\/2){displaystyle m_ {b}\uff08l\/2\uff09} \u30ad\u30e3\u30ea\u30a2\u306e\u771f\u3093\u4e2d\u306b\u3002 \u22480,207107{displaystyle amptox 0 {\u3001} 207107}  |Mb(a)|=|Mb(L\u2212a)|=|Mb(L\/2)|\u21d2a\/L=12\u221212{displaystyle | m_ {b}\uff08a\uff09| = | m_ {b}\uff08l-a\uff09| = | m_ {b}\uff08l\/2\uff09| quad rightarrow\u3001a\/l = {tfrac {1} {sqrt {2}}}  –  {tfrac {1} {2}}}}  \u30d3\u30fc\u30e0\u306e\u9577\u3055\u306e\u534a\u5206\u306e\u9818\u57df\u306e\u30bc\u30ed\u66f2\u7387   \u3053\u306e\u30bf\u30a4\u30d7\u306e\u30b9\u30c8\u30ec\u30fc\u30b8\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u7740\u7528\u8005\u306e\u8c46\u30e9\u30a4\u30f3\u306e\u904e\u7a0b\u3067\u9818\u57df\u304c\u5f62\u6210\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30ad\u30e3\u30ea\u30a2\u306e\u4e2d\u592e\u306b\u63a5\u89e6\u9762\u304c\u5fc5\u8981\u306a\u5834\u5408\u306b\u8208\u5473\u6df1\u3044\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002 =0,25{displaystyle = 0 {\u3001} 25}  w\u2033(L\/2)=0\u21d2a\/L=14{displaystyle W ”\uff08l\/2\uff09= 0Quad rightArrow\u3001a\/l = {tfrac {1} {4}}}}  \u300c\u6700\u3082\u9577\u3044\u6e2c\u5b9a\u6280\u8853\u306e\u57fa\u6e96\u3067\u306f\u3001\u30d9\u30c3\u30bb\u30eb\u30dd\u30a4\u30f3\u30c8\u306f\u3001\u898b\u672c\u5e02\u30ec\u30d9\u30eb\u3067\u306e\u66f2\u7dda\u5b9a\u898f\u306e\u9577\u3055\u306e\u5909\u5316\u3092\u6700\u5c0f\u9650\u306b\u6291\u3048\u308b\u30b5\u30dd\u30fc\u30c8\u30dd\u30a4\u30f3\u30c8\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u300d 6\u3064\u306e\u78e8\u304b\u308c\u305f\u7cbe\u5ea6\u6e2c\u5b9a\u30d7\u30ec\u30fc\u30c8\uff08\u82b1\u5d17\u5ca9\u306a\u3069\u306e\u786c\u3044\u5ca9\u3067\u4f5c\u3089\u308c\u3066\u3044\u308b\uff09\u306f\u3001\u5236\u5fa1\u3001\u7d44\u307f\u7acb\u3066\u3001\u5b9f\u9a13\u76ee\u7684\u306e\u57fa\u790e\u3068\u3057\u3066\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u305d\u306e\u9ad8\u3044\u91cd\u91cf\u306b\u3088\u308b\u504f\u5411\u306f\u305d\u3046\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 \u30d9\u30c3\u30bb\u30eb3\u30dd\u30a4\u30f3\u30c8\u30b9\u30c8\u30ec\u30fc\u30b8 \u6700\u5c0f\u5316\u3055\u308c\u307e\u3059\u3002\u7c21\u7d20\u5316\u3055\u308c\u305f\u6761\u7d04\u306f\u3001\u9577\u3055\u306e22\uff05\u3001\u304a\u3088\u3073\u5916\u5074\u306e\u30a8\u30c3\u30b8\u304b\u3089\u306e\u5e45\u306e22\uff05\u306b\u3088\u3063\u30662\u3064\u306e\u6577\u8a2d\u30dd\u30a4\u30f3\u30c8\u304c\u5fc5\u8981\u3067\u3042\u308b\u3053\u3068\u3092\u9069\u7528\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u3068\u6bd4\u8f03\u3057\u3066\u30013\u756a\u76ee\u306e\u30dd\u30a4\u30f3\u30c8\u306f\u3001\u5e45\u306e50\uff05\u3068\u9577\u3055\u306e22\uff05\u306e\u8ddd\u96e2\u306b\u3042\u308b\u305d\u308c\u305e\u308c\u306e\u30a8\u30c3\u30b8\u306b\u3088\u3063\u3066\u914d\u7f6e\u3055\u308c\u308b\u3053\u3068\u3067\u3059\u3002 Gert-Jan Nijsse\uff1a \u7dda\u5f62\u904b\u52d5\u30b7\u30b9\u30c6\u30e0;\u307e\u3063\u3059\u3050\u306a\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3092\u6539\u5584\u3059\u308b\u305f\u3081\u306e\u30e2\u30b8\u30e5\u30e9\u30fc\u30a2\u30d7\u30ed\u30fc\u30c1\u3002 Delft University Press\u3001Delft 2001\u3001ISBN 90-407-2187-4\uff08 repository.tidelft.nl \uff09\u3002 R.\u30ea\u30fc\u30c9\uff1a \u54c1\u8cea\u5236\u5fa1\u6e2c\u5b9a\u306e\u305f\u3081\u306e\u30ac\u30e9\u30b9\u57fa\u6e96\u8868\u9762 \u3002 International Journal of Mechanical Sciences 8\uff081966\uff09\u3001703\u2013715\u3002 \u2191 a b c  Gert-Jan Nijsse\uff1a \u7dda\u5f62\u904b\u52d5\u30b7\u30b9\u30c6\u30e0;\u307e\u3063\u3059\u3050\u306a\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3092\u6539\u5584\u3059\u308b\u305f\u3081\u306e\u30e2\u30b8\u30e5\u30e9\u30fc\u30a2\u30d7\u30ed\u30fc\u30c1\u3002 Delft 2001\u3001S\u300239f\u3002  \u2191  F. W.\u30d9\u30c3\u30bb\u30eb\uff1a 1835\u5e74\u304b\u30891838\u5e74\u306b\u306f\u3001\u30d7\u30ed\u30a4\u30bb\u30f3\u306e\u9577\u3055\u306e\u7d71\u4e00\u306b\u3088\u3063\u3066\u5f15\u304d\u8d77\u3053\u3055\u308c\u305f\u8a66\u9a13\u3068\u5bfe\u7b56\u306e\u8868\u73fe\u3002 I.\u30b5\u30d7\u30ea\u30e1\u30f3\u30c8I \u540c\u3058\u9ad8\u3055\u306e2\u3064\u306e\u70b9\u306b\u3042\u308b\u30ed\u30c3\u30c9\u306e\u56f3\u306b\u5bfe\u3059\u308b\u91cd\u75c7\u5ea6\u306e\u5f71\u97ff\u3002 \u30d9\u30eb\u30ea\u30f31839\u3001S\u3002132\uff08 \u3042\u306a\u305f \uff09\u3002  \u2191  F. W.\u30d9\u30c3\u30bb\u30eb\u3001\u30d9\u30eb\u30ea\u30f31839\u3001S\u3002135\u3002  \u2191  G. 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