[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/21202#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/21202","headline":"Complex Creek -Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178","name":"Complex Creek -Wikipedia\u3001\u7121\u6599\u767e\u79d1\u4e8b\u5178","description":"before-content-x4 \u3068 \u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5 \u3053\u308c\u306f\u3001\u5358\u7d14\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306e\u7dda\u5f62\u30aa\u30fc\u30d0\u30fc\u30e9\u30c3\u30d7\u306e\u52d5\u304d\u3067\u3059\u3002\u5358\u7d14\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306f\u5e38\u306b\u65b0\u805e\u3067\u3059\u304c\u3001\u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306f\u5fc5\u305a\u3057\u3082\u65b0\u805e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u30d5\u30fc\u30ea\u30a8\u306e\u8abf\u548c\u306e\u3068\u308c\u305f\u5206\u6790\u306b\u3088\u3063\u3066\u5206\u6790\u3067\u304d\u307e\u3059\u3002\u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306f\u3001\u5468\u6ce2\u6570\u304c\u3059\u3079\u3066\u57fa\u672c\u5468\u6ce2\u6570\u306e\u5408\u7406\u7684\u306a\u500d\u6570\u3067\u3042\u308b\u5358\u7d14\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u3042\u308b\u5834\u5408\u306b\u306e\u307f\u65b0\u805e\u3067\u3059\u3002 after-content-x4 Table of Contents \u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306e\u904b\u52d5\u5b66 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u5468\u671f\u6027 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u52d5\u304d\u65b9\u7a0b\u5f0f [ \u7de8\u96c6\u3057\u307e\u3059 ]","datePublished":"2022-06-23","dateModified":"2022-06-23","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:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/0777b8a59a3b320bf6d6b7808e4c794c06301ec3","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/0777b8a59a3b320bf6d6b7808e4c794c06301ec3","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/21202","wordCount":10126,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u3068 \u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5 \u3053\u308c\u306f\u3001\u5358\u7d14\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306e\u7dda\u5f62\u30aa\u30fc\u30d0\u30fc\u30e9\u30c3\u30d7\u306e\u52d5\u304d\u3067\u3059\u3002\u5358\u7d14\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306f\u5e38\u306b\u65b0\u805e\u3067\u3059\u304c\u3001\u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306f\u5fc5\u305a\u3057\u3082\u65b0\u805e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u30d5\u30fc\u30ea\u30a8\u306e\u8abf\u548c\u306e\u3068\u308c\u305f\u5206\u6790\u306b\u3088\u3063\u3066\u5206\u6790\u3067\u304d\u307e\u3059\u3002\u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306f\u3001\u5468\u6ce2\u6570\u304c\u3059\u3079\u3066\u57fa\u672c\u5468\u6ce2\u6570\u306e\u5408\u7406\u7684\u306a\u500d\u6570\u3067\u3042\u308b\u5358\u7d14\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u3042\u308b\u5834\u5408\u306b\u306e\u307f\u65b0\u805e\u3067\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Table of Contents\u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306e\u904b\u52d5\u5b66 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u5468\u671f\u6027 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u52d5\u304d\u65b9\u7a0b\u5f0f [ \u7de8\u96c6\u3057\u307e\u3059 ] \u7d50\u5408\u632f\u52d5 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u72ec\u81ea\u306e\u5468\u6ce2\u6570\u3068\u30e2\u30fc\u30c9 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u81ea\u7531\u632f\u52d5\u306e\u554f\u984c\u306e\u89e3\u6c7a [ \u7de8\u96c6\u3057\u307e\u3059 ] \u5f37\u5236\u632f\u52d5\u306e\u554f\u984c\u306e\u89e3\u6c7a\u7b56\u304c\u7de9\u885d\u3055\u308c\u307e\u3057\u305f [ \u7de8\u96c6\u3057\u307e\u3059 ] \u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306e\u904b\u52d5\u5b66 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u8abf\u548c\u632f\u52d5\u3092\u63d0\u793a\u3059\u308b\u30b7\u30b9\u30c6\u30e0 n \u4e00\u822c\u7684\u306a\u81ea\u7531\u5ea6\u306b\u306f\u4f38\u3073\u304c\u3042\u308a\u307e\u3059 \u30d0\u30c4 \u79c1 o\u30d5\u30a9\u30fc\u30e0\u306e\u72ec\u7acb\u3057\u305f\u65b9\u5411\u5168\u4f53\u306e\u52d5\u304d\uff1a \uff08 1a \uff09\uff09 \u30d0\u30c4 \uff08 t \uff09\uff09 = \u2211 j=1nc jAjcos \u2061 \uff08 \u304a\u304a jt + \u03d5 j\uff09\uff09 {displaystyle mathbf {x}\uff08t\uff09= sum _ {j = 1}^{n} c_} mathbf {a} _ _ {j} cos\uff08omega _ {j} t+phi _ {j}\uff09}}  \u307e\u305f\u306f\u8a73\u7d30\uff1a        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\uff08 1b \uff09\uff09 (x1(t)\u22eexn(t))= (A11\u22efA1n\u22ee\u22f1\u22eeAn1\u22efAnn)(C1cos\u2061(\u03c91t+\u03d51)\u22eeCncos\u2061(\u03c9nt+\u03d5n))= \u2211 j(A1j\u22eeAnj)c jcos \u2061 \uff08 \u304a\u304a jt + \u03d5 j\uff09\uff09 {displaystyle {begin {pmatrix} x_ {1}\uff08t\uff09\\ vdots \\ x_ {n}\uff08t\uff09end {pmatrix}} = {begin {pmatrix} a_ {11}\uff06cdots\uff06a_ {1n} \\ vdots\uff06vdots\uff06vdots\uff06vdots\uff06a_ {n1} {pmatrix}} {begin {pmatrix} c_ {1} cos\uff08omega _ {1} t+phi _ {1}\uff09\\ vdots \\ c_ {n} cos\uff08omega _ {n} t+phi _ {n} _ {1j} \\ vdots \\ a_ {nj} end {pmatrix}} c_ {j} cos\uff08omega _ {j} t+phi _ {j}\uff09}  \u3069\u3053\u3001 { \u03c9i} \u79c1 = \u521d\u3081 \u3001 \u3002 \u3002 \u3002 \u3001 n {displaystyle leftlbrace omega _ {i} rightrbrace _ {i = 1\u3001…\u3001n}} \u3067\u3059 \u72ec\u81ea\u306e\u5468\u6ce2\u6570 \u30b7\u30b9\u30c6\u30e0\u306e\u3001 { \u03d5i} \u79c1 = \u521d\u3081 \u3001 \u3002 \u3002 \u3002 \u3001 n {displaystyle leftlbrace phi _ {i} rightrbrace _ {i = 1\u3001…\u3001n}}} \u521d\u671f\u30d5\u30a7\u30fc\u30ba\u3002\u5404\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u5217\u30d9\u30af\u30c8\u30eb a \u547c\u3070\u308c\u3066\u3044\u307e\u3059 \u72ec\u81ea\u306e\u3084\u308a\u65b9 \u632f\u52d5\u306e\u3001\u305d\u3057\u3066 c \u79c1 \u305d\u308c\u3089\u306f\u3001\u5404\u7247\u65b9\u306e\u76f8\u5bfe\u7684\u306a\u632f\u5e45\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u306b\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 n = 1\u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306f\u3001\u5358\u306b\u5358\u7d14\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306e\u5408\u8a08\u3067\u3059\u3002 \u4e00\u822c\u7684\u306a\u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306e\u901f\u5ea6\u3068\u52a0\u901f\u306f\u3001\u6642\u9593\u306b\u95a2\u3057\u3066\u5c0e\u51fa\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u3001\u307e\u305f\u3001\u540c\u3058\u5468\u6ce2\u6570\u306e\u52d5\u304d\u306e\u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u306e\u52d5\u304d\u3067\u3042\u308b\u3053\u3068\u304c\u5224\u660e\u3057\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u5358\u7d14\u306a\u9ad8\u8abf\u6ce2\u306e\u52d5\u304d\u306e\u3088\u3046\u306b\u3001\u30bc\u30ed\u901f\u5ea6\u30dd\u30a4\u30f3\u30c8\u306f\u73fe\u5728\u3042\u308a\u307e\u305b\u3093\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u5468\u671f\u6027 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u904b\u52d5\u306f\u3001\u5b9a\u671f\u7684\u306b\u6642\u9593\u306e\u9593\u9694\u3067\u7e70\u308a\u8fd4\u3055\u308c\u308b\u3068\u65b0\u805e\u304c\u8a00\u308f\u308c\u3066\u3044\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u4e00\u5b9a\u306e\u6642\u9593\u9593\u9694\u306e\u5f8c\u3001\u540c\u3058\u4f4d\u7f6e\u3092\u901a\u308a\u3001\u540c\u3058\u901f\u5ea6\u3067\u623b\u308b\u5834\u5408\u3067\u3059\u3002\u5468\u671f\u6027\u306b\u306f\u3001\u4f4d\u7f6e\u30d9\u30af\u30c8\u30eb\u304c\u5fc5\u8981\u3067\u3059 \u30d0\u30c4 \uff08 t \uff09= \u30d0\u30c4 \uff08 t+t \uff09 \u3059\u3079\u3066\u306e\u305f\u3081\u306b t \u306e\u4fa1\u5024\u306e\u305f\u3081\u306b t \u3002\u6b21\u306e\u3088\u3046\u306a\u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306e\u5834\u5408 1a \uff09\u305d\u308c\u306f\u3059\u3079\u3066\u306e\u305f\u3081\u306b\u5fc5\u8981\u3067\u3059 \u79c1 \u3001 cos \u2061 \uff08 \u304a\u304a i\uff08 t + t \uff09\uff09 \uff09\uff09 = cos \u2061 \uff08 \u304a\u304a it \uff09\uff09 \u21d2 { \u2203k1,...kn} \u2282 \u3068 \uff1a t = 2\u03c0ki\u03c9i= \u3002 \u3002 \u3002 = 2\u03c0kn\u03c9n{displaystyle cos\uff08omega _ {i}\uff08t+t\uff09\uff09= cos\uff08omega _ {i} t\uff09rightarrow leftlbrace\u306fexists k_ {1}\u3001… k_ {n} rightrbrace Subset Mathbb {z}\uff1at = {frac {{i} {i}} {} {{} {i} {{i}} {{i}} {frac {2pi k_ {n}} {omega _ {n}}}}}  \u5468\u671f\u6027\u306f\u3001\u3069\u3093\u306a\u5468\u6ce2\u6570\u3067\u3082\u3001\u305d\u306e\u5546\u304c\u5408\u7406\u7684\u306a\u6570\u3067\u3042\u308b\u5834\u5408\u306b\u306e\u307f\u53ef\u80fd\u3067\u3059\u3002\u5408\u7406\u7684\u306a\u6570\u5024\u304c\u30bc\u30ed\u307e\u305f\u306f\u30cc\u30eb\u30bb\u30c3\u30c8\u30bb\u30c3\u30c8\u3067\u3042\u308b\u305f\u3081\u3001\u3059\u3079\u3066\u306e\u5468\u6ce2\u6570\u306e\u5546\u304c\u5408\u7406\u7684\u306a\u6570\u5024\u3067\u3042\u308b\u53ef\u80fd\u6027\u306f\u30bc\u30ed\u3067\u3042\u308b\u305f\u3081\u3001\u5b9f\u969b\u306e\u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u306e\u52d5\u304d\u306fQuasiperi\u00f3dicos\u3067\u3059\u304c\u3001\u65b0\u805e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u52d5\u304d\u65b9\u7a0b\u5f0f [ \u7de8\u96c6\u3057\u307e\u3059 ] \u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u305f\u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\uff08 1a \uff09o\uff08 1b \uff09\u3053\u308c\u306f\u3001\u30bf\u30a4\u30d7\u306e\u5c0f\u3055\u306a\u632f\u52d5\u306e\u554f\u984c\u306e\u65b9\u7a0b\u5f0f\u306b\u5bfe\u3059\u308b\u89e3\u6c7a\u7b56\u3067\u3059\u3002 m x\u00a8\uff08 t \uff09\uff09 + k \u30d0\u30c4 \uff08 t \uff09\uff09 = 0 {displaystyle mathbf {m} {ddot {mathbf {x}}}\uff08t\uff09+mathbf {k} mathbf {x}\uff08t\uff09= mathbf {0}}  \u3069\u3053\uff1a m {displaystyle mathbf {m}} \u3001\u30b7\u30b9\u30c6\u30e0\u306e\u6163\u6027\u3092\u8868\u3059So -Caled Mass Matrix\u3067\u3059\u3002 k {displaystyle mathbf {k}} \u3001\u56de\u5fa9\u529b\u306e\u5f37\u5ea6\u3092\u8868\u3059SO -COMLED\u306e\u525b\u6027\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3067\u3042\u308a\u3001\u3069\u3061\u3089\u3082\u30b7\u30b9\u30c6\u30e0\u304c\u3088\u308a\u525b\u6027\u306e\u65b9\u304c\u5927\u304d\u3044\u3053\u3068\u3067\u3059\u3002 \u7dda\u5f62\u6e1b\u8870\u3068\u5185\u90e8\u52b1\u8d77\u529b\u3092\u6301\u3064\u30b7\u30b9\u30c6\u30e0\u306e\u6700\u3082\u4e00\u822c\u7684\u306a\u30b1\u30fc\u30b9\u3067\u306f\u3001\u52d5\u304d\u306e\u65b9\u7a0b\u5f0f\u306f\u3088\u308a\u4e00\u822c\u7684\u3067\u3059\u3002 m x\u00a8\uff08 t \uff09\uff09 + c x\u02d9\uff08 t \uff09\uff09 + k \u30d0\u30c4 \uff08 t \uff09\uff09 = f \uff08 t \uff09\uff09 {displaystyle mathbf {m} {ddot {mathbf {x}}}\uff08t\uff09+mathbf {c}} {dot {mathbf {x}}}\uff08t\uff09+mathbf {k} mathbf {x}\uff08t\uff09= mathbf {f}\uff08t\uff09}  \u30de\u30c8\u30ea\u30c3\u30af\u30b9\u304c\u8ffd\u52a0\u3055\u308c\u305f\u5834\u6240 c {displaystyle mathbf {c}} \u305d\u308c\u306f\u6e1b\u8870\u3092\u5360\u3081\u3066\u3044\u307e\u3059\u3002 \u7d50\u5408\u632f\u52d5 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u8907\u96d1\u306a\u9ad8\u8abf\u6ce2\u904b\u52d5\u306e\u4e00\u822c\u7684\u306a\u30b1\u30fc\u30b9\u306f\u3001 \u7d50\u5408\u632f\u52d5 \u3002\u7d50\u5408\u3055\u308c\u305f\u632f\u52d5\u306e\u3053\u306e\u554f\u984c\u306f\u3001\u305f\u3068\u3048\u3070\u3001\u7d50\u6676\u306e\u71b1\u632f\u52d5\u3001\u5730\u9707\u3067\u306e\u5efa\u7269\u306e\u6c34\u5e73\u65b9\u5411\u306e\u52d5\u304d\u3001\u30c9\u30c3\u30af\u307e\u305f\u306f\u30b9\u30d7\u30ea\u30f3\u30b0\u306b\u3088\u308b\u5927\u898f\u6a21\u306a\u8cea\u91cf\u30b7\u30b9\u30c6\u30e0\u306e\u52d5\u304d\u306b\u73fe\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u554f\u984c\u306f\u3001\u6b21\u306e\u30bf\u30a4\u30d7\u306e\u65b9\u7a0b\u5f0f\u306e\u30b7\u30b9\u30c6\u30e0\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002 \uff08 2 \uff09\uff09  mix\u00a8i+ \u2211k=1Nkikxk= 0 {displaystyle m_ {i} {ddot {x}} _ {i}+sum _ {k = 1}^{n} k_ {ik} x_ {k} = 0} \u305d\u308c\u306f\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u65b9\u6cd5\u3067\u3001\u6b21\u306e\u3088\u3046\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \uff08 2 ‘ \uff09\uff09 (m10\u22ef00m2\u22ef0\u22ee\u22ee\u22f1\u22ee00\u22efmN)(x\u00a81x\u00a82\u22eex\u00a8N)+ (k11k12\u22efk1Nk21k22\u22efk2N\u22ee\u22ee\u22f1\u22eekN1kN2\u22efkNN)(x1x2\u22eexN)= 0 {displaystle {begin {pmatrix} m_ {1}\uff060\uff060\uff06cdots\uff060 \\ 0\uff06m_ {2}\uff06cdots\uff060 \\ vdots\uff06vdots\uff06dots\uff06vdots\uff06vdots \\ 0\uff060\uff060\uff06cdots\uff06m_ {n} end {pmatrix}} {{Pmatrix} {x} {x} {x} {x} {x}} _ {2} \\ vdots \\ {dot {x}} _ {n} end {pmatrix}}+{begin {pmatrix} k_ {11}\uff06k_ {12}\uff06k_ {1n} \\ k_ {21} {22} {22} {2n} {2n} {2n} {2n} {22} {2n} {2n} {2n} { \uff06vdots \\ k_ {n1}\uff06k_ {n2}\uff06cdots\uff06k_ {nn} end {pmatrix}}} {begin {pmatrix} x_ {1} \\ x_ {2} \\ vdots} end {pmatrix}}} = 0}}  \u554f\u984c\u306f\u3001\u901a\u5e38\u306e\u5ea7\u6a19\u307e\u305f\u306f\u632f\u5e45\u306b\u3064\u306a\u304c\u308b\u5909\u6570\u306e\u7279\u5b9a\u306e\u5909\u66f4\u306b\u3088\u3063\u3066\u89e3\u6c7a\u3067\u304d\u307e\u3059\u3002 \u72ec\u81ea\u306e\u30e2\u30fc\u30c9 \u5b9f\u969b\u3001\u5143\u306e\u6a5f\u68b0\u7684\u554f\u984c\u306e\u4e00\u822c\u5316\u3055\u308c\u305f\u5ea7\u6a19\u306e\u7279\u5b9a\u306e\u5f62\u614b\u3067\u3042\u308b\u632f\u52d5\u306e\u3002 \u72ec\u81ea\u306e\u5468\u6ce2\u6570\u3068\u30e2\u30fc\u30c9 [ \u7de8\u96c6\u3057\u307e\u3059 ] \u72ec\u81ea\u306e\u30e2\u30fc\u30c9\u306f\u554f\u984c\u89e3\u6c7a\u7b56\u3092\u63d0\u4f9b\u3057\u307e\u3059\uff08 2 ‘ \uff09 \u5f62 \uff08 \u521d\u3081 \uff09\u3002\u3053\u306e\u305f\u3081\u306b\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u308b\u30b7\u30b9\u30c6\u30e0\u306e\u4e00\u9023\u306e\u81ea\u7136\u5468\u6ce2\u6570\u3092\u6c7a\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 |k11\u2212\u03c9j2m1k12\u22efk1Nk21k22\u2212\u03c9j2m2\u22efk2N\u22ee\u22ee\u22f1\u22eekN1kN2\u22efkNN\u2212\u03c9j2mN|= 0 {displaystyle {begin {vmatrix} k_ {11} -omega _ {j}^{2} m_ {1}\uff06k_ {12}\uff06cdots\uff06k_ {1n} \\ vdots\uff06vdots\uff06ddots\uff06vdots \\ k_ {n1}\uff06k_ {n2}\uff06cdots\uff06k_ {nn} -omega _ {j}^{2} m_ {n} end {vmatrix}} = 0} = 0}  \u3053\u308c\u306f\u63d0\u4f9b\u3057\u307e\u3059 n \u56fa\u6709\u5468\u6ce2\u6570\u306e\u6b63\u65b9\u5f62\u306e\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u3002\u3053\u308c\u3089\u306e\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u306e\u305d\u308c\u305e\u308c\u306b\u3064\u3044\u3066\u3001\u30e6\u30cb\u30c3\u30c8\u30d9\u30af\u30c8\u30eb\u304c\u6c42\u3081\u3089\u308c\u3001\u547c\u3070\u308c\u307e\u3059 \u72ec\u81ea\u306e\u3084\u308a\u65b9 \u3001\u305d\u308c\u306f\u4e0d\u78ba\u5b9a\u306a\u4e92\u63db\u6027\u306e\u3042\u308b\u65b9\u7a0b\u5f0f\u3092\u6e80\u305f\u3057\u307e\u3059\uff1a (k11\u2212\u03c9j2m1k12\u22efk1Nk21k22\u2212\u03c9j2m2\u22efk2N\u22ee\u22ee\u22f1\u22eekN1kN2\u22efkNN\u2212\u03c9j2mN)(a1ja2j\u22eeaNj)= 0 {displaystyle {begin {pmatrix} k_ {11} -omega _ {j}^{2} m_ {1}\uff06k_ {12}\uff06cdots\uff06k_ {1n} vdots\uff06vdots\uff06ddots\uff06vdots \\ k_ {n1}\uff06k_ {n2}\uff06cdots\uff06k_ {nn} -omega _ {j}^{2} m_ {n} end {pmatrix}} {begin {pmatrix} a_ {a_ a_ {a_ \\ a_ \\ a_ {a_ \\ a_ \\ a_ {pmatrix} {pmatrix} } end {pmatrix}} = 0}  \u30b7\u30b9\u30c6\u30e0\u306e\u3055\u307e\u3056\u307e\u306a\u30e2\u30fc\u30c9\u3092\u8868\u3059\u3053\u308c\u3089\u306e\u30d9\u30af\u30c8\u30eb\u304c\u4e92\u3044\u306b\u76f4\u4ea4\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u305d\u308c\u3089\u3059\u3079\u3066\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u76f4\u4ea4\u884c\u5217\u3067\u3042\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3067\u304d\u307e\u3059\u3002 a = {aij}i=1…nj=1…n= (a11\u22efa1n\u22ee\u22f1\u22eean1\u22efann){displaystyle mathbf {a} = {leftlbrace a_ {ij} rightrbrace} _ {i = 1 … n}^{j = 1 … n} = {begin {pmatrix} a_ {11}\uff06cdots\uff06a_ {1n} \\ vdots\uff06ddots\uff06ddots\uff06vdots} End {pmatrix}}}   \u901a\u5e38\u306e\u5ea7\u6a19 \u3001\u72ec\u81ea\u306e\u30e2\u30fc\u30c9\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u3066\u304a\u308a\u3001\u5f93\u6765\u306e\u5ea7\u6a19\u304b\u3089\u306e\u7dda\u5f62\u5909\u5316\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u307e\u3059\u3002 (q1(t)\u22eeqN(t))= (b11\u22efb1n\u22ee\u22f1\u22eebn1\u22efbnn)(x1(t)\u22eexN(t)){displaystyle {begin {pmatrix} q_ {1}\uff08t\uff09\\ vdots \\ q_ {n}\uff08t\uff09end {pmatrix}} = {begin {pmatrix} {11}\uff06cdots\uff06b_ {1n} \\ vdots\uff06vdots\uff06vdots\uff06vdots\uff06vdots \\ b_ {n1} {pmatrix}} {begin {pmatrix} x_ {1}\uff08t\uff09\\ vdots \\ x_ {n}\uff08t\uff09end {pmatrix}}}}  \u3069\u3053 b = { b ij} = a t {displaystyle mathbf {b} = leftlbrace b_ {ij} rightrbrace = mathbf {a} ^{t}} \u3001\u305d\u308c\u3092\u6e80\u305f\u3057\u307e\u3059 b ‘ \u306e\u9006\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3067\u3059 a \uff08 a\u30fbb = b\u30fba = \u79c1 \uff09\u3002 \u81ea\u7531\u632f\u52d5\u306e\u554f\u984c\u306e\u89e3\u6c7a [ \u7de8\u96c6\u3057\u307e\u3059 ] \u4e00\u822c\u7684\u306a\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u306f\u3001\u901a\u5e38\u306e\u5ea7\u6a19\u3067\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u3053\u3068\u3067\u7c21\u5358\u306b\u53d6\u5f97\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u5ea7\u6a19\u3092\u4f7f\u7528\u3057\u3066\u3001\u305d\u308c\u3092\u8003\u616e\u3059\u308b\u3068\u7c21\u5358\u306b\u53d6\u5f97\u3067\u304d\u307e\u3059 \u30d0\u30c4 = a Q {displaystyle mathbf {x} = mathbf {a} mathbf {q}} \uff1a m x\u00a8+ k \u30d0\u30c4 = 0 \u21d2 q\u00a8+ [ ATM\u22121KA] Q = 0 {displaystyle mathbf {m} {ddt {xbf {x}}}+mathbf {k} mathbf {x} = 0qqquad rightarrow qud {ddot {q}}}+left [mathbf {a} ^{mathbf {a} mathbf {mathbf {-1bf {{-1bf {-1bf {-1bf {mathbf {{-1bf {{-1bf {-1bf} {a} right] mathbf {q} = 0}  \u3057\u304b\u3057\u3001\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u306b\u3088\u308b a {displaystyle mathbf {a}} \u62ec\u5f27\u5185\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306f\u659c\u3081\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3067\u3042\u308b\u3053\u3068\u304c\u5224\u660e\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u305d\u306e\u6700\u5f8c\u306e\u30b7\u30b9\u30c6\u30e0\u306e\u89e3\u306f\u89e3\u6c7a\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u307e\u3059 n \u578b\u65b9\u7a0b\u5f0f\u306e\u5404\u30bb\u30c3\u30c8\u306e\u65b9\u7a0b\u5f0f\uff1a q\u00a8j+ \u304a\u304a j2Q j= 0 \u21d2 Q j\uff08 t \uff09\uff09 = c jcos \u2061 \uff08 \u304a\u304a jt + \u03d5 j\uff09\uff09 {displaystyle {ddot {q}} _ {j}+omega _ {j}^{2} q_ {j} = 0qquad right arrow qquad q_ {j}\uff08t\uff09= c_ {j} cos _ {j} t+phi_ {j}}  \u901a\u5e38\u306e\u5ea7\u6a19\u3068\u72ec\u81ea\u306e\u30e2\u30fc\u30c9\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306b\u95a2\u3057\u3066\u306f\u3001\u30b7\u30b9\u30c6\u30e0\u306e\u4e00\u822c\u7684\u306a\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u304c\u66f8\u304b\u308c\u3066\u3044\u307e\u3059\u3002 (x1(t)\u22eexN(t))= (a11\u22efa1n\u22ee\u22f1\u22eean1\u22efann)(q1(t)\u22eeqN(t))= (a11\u22efa1n\u22ee\u22f1\u22eean1\u22efann)(C1cos\u2061(\u03c91t+\u03d51)\u22eeCncos\u2061(\u03c9nt+\u03d5n)){displaystyle {begin {pmatrix} x_ {1}\uff08t\uff09\\ vdots \\ x_ {n}\uff08t\uff09end {pmatrix}} = {begin {pmatrix} a_ {11}\uff06cdots\uff06a_ {1n} \\ vdots\uff06vdots\uff06vdots\uff06vdots\uff06a_ {n1} {pmatrix}} {begin {pmatrix} q_ {1}\uff08t\uff09\\ vdots \\ q_ {n}\uff08t\uff09end {pmatrix}} = {begin {pmatrix} a_ {11}\uff06cdots\uff06a_ {1n} \\ vdots\uff06ddots\uff06a_ a_ {n1} } end {pmatrix}}} {begin {pmatrix} c_ {1} cos\uff08omega _ {1} t+phi _ {1}\uff09\\ vdots \\ c_ {n}  \u5f37\u5236\u632f\u52d5\u306e\u554f\u984c\u306e\u89e3\u6c7a\u7b56\u304c\u7de9\u885d\u3055\u308c\u307e\u3057\u305f [ \u7de8\u96c6\u3057\u307e\u3059 ] \u4e00\u822c\u7684\u306a\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u306f\u3001\u901a\u5e38\u306e\u5ea7\u6a19\u3092\u4f7f\u7528\u3057\u3066\u524d\u3068\u540c\u69d8\u306b\u53d6\u5f97\u3055\u308c\u307e\u3059 \u30d0\u30c4 = a Q {displaystyle mathbf {x} = mathbf {a} mathbf {q}} \uff1a m x\u00a8+ c x\u02d9+ k \u30d0\u30c4 = f \u21d2 q\u00a8+ [ ATM\u22121CA] q\u02d9+ [ ATM\u22121KA] Q = [ ATM\u22121F] {Displaystyle Mathbf {m} {ddot {ddot {xbf {xbf {x} }+Mathbf {c} {dot {dot {dot {dot {xbf {x {x} }+mathbf {k} mathbf {f} Quad Rightarrow quad {ddf {Q} }+Left[ Mathbf {a} ^{t}mathbf {m} ^{1}mathbf {c} mathbf {a} right]{dot {a} right]{mathbf {Q} }+Left[mathbf {a} ^{t}mathbf {m} {-1}mathbf {k} mathbf {a} mathbf {a} mathbf {a} mathbf {a} mathbf =Left[mathbf {a} ^{t}mathbf {m} ^{-1}mathbf {f} right]}  \u4e57\u7b97\u3059\u308b\u76f4\u4ea4\u5ea7\u6a19\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u69cb\u7bc9\u306b\u3088\u308a q\u00a8{displaystyle scriptStyle {ddot {mathbf {q}}}}} \u3068 q\u02d9{displaystyle scriptStyle {dot {mathbf {q}}}}} \u305d\u308c\u3089\u306f\u5bfe\u89d2\u7dda\u3067\u3059\uff08\u3053\u308c\u306b\u306f\u8ffd\u52a0\u306e\u6761\u4ef6\u3068\u3057\u3066\u5fc5\u8981\u3067\u3059 k c = c k {displaystyle scriptStyle mathbf {kc} = mathbf {ck}} \uff09\u3001\u3057\u305f\u304c\u3063\u3066\u3001\u6700\u5f8c\u306e\u30b7\u30b9\u30c6\u30e0\u306f\u306b\u7e2e\u5c0f\u3055\u308c\u307e\u3059 n \u30bf\u30a4\u30d7\u306e\u72ec\u7acb\u3057\u305f\u65b9\u7a0b\u5f0f\uff1a q\u00a8j+ 2 n \u304a\u304a q\u02d9j+ \u304a\u304a j2Q j= 0 \u21d2 Q j\uff08 t \uff09\uff09 = c j\u222b 0t\u2212Qj\u03c9j1\u2212\u03bdj\u305d\u3046\u3067\u3059 \u2212\u03bdj\u03c9j(t\u2212\u03c4)\u7f6a \u2061 \uff08 \u304a\u304a j1\u2212\u03bdj\uff08 t  –  t \uff09\uff09 t + \u03d5 j\uff09\uff09  d t {displaystyle {ddot {q}} _ {j}+2nu omega {dot {q}} _ {j}+omega _ {j}^{2} q_ {j} = 0qquad rightarrow qqquad q_ {j}\uff08j}\uff08t\uff09= c_ {j} {j} {j} {-q_ {j}} {omega _ {j} {sqrt {1-nu _ {j}}}}} e^{ –  nu _ {j}} omega _ {j}\uff08t-tau\uff09} sin\uff08omega _ {j} {sqr} {x} {x} {x} {x} {j} {j} {j} {j}\uff09 t+phi _ {j}\uff09dtau}  \u3057\u305f\u304c\u3063\u3066\u3001\u89e3\u6c7a\u7b56\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 (x1(t)\u22eexN(t))= (a11\u22efa1n\u22ee\u22f1\u22eean1\u22efann)(q1(t)\u22eeqN(t)){displaystyle {begin {pmatrix} x_ {1}\uff08t\uff09\\ vdots \\ x_ {n}\uff08t\uff09end {pmatrix}} = {begin {pmatrix} a_ {11}\uff06cdots\uff06a_ {1n} \\ vdots\uff06vdots\uff06vdots\uff06vdots\uff06a_ {n1} {pmatrix}} {begin {pmatrix} q_ {1}\uff08t\uff09\\ vdots \\ q_ {n}\uff08t\uff09end {pmatrix}}}}  \u3064\u307e\u308a\u3001\u306e\u7dda\u5f62\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u3059 n \u5f37\u5236\u9ad8\u8abf\u6ce2\u904b\u52d5\u306f\u7de9\u548c\u3055\u308c\u307e\u3057\u305f\u3002          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