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1、用复模态理论讨论状态矩阵对角化问题25/2684285???:???1????????(???7?????>)2008???K9???K1?,J.ChangchunInst.Tech.(Nat.Sci.Edi.),2008,Vol.9,No.1ISSN100928984CN2221323/N?[?.?o?2?4?????????2???-?????s?????7?b???,232(5,2),??(?z),?0?????:,???????D???u??????????????{5??{???1
2、,?????i2(1.???:???1?????4????,???:130012;2.???U???????o,???U518055)??{???:???>???????.?o?2?4??,?7?C?]?[???A?D?W?????????????r?w?????4???1???????????n??,?????????2???-?C?w?????????????????n???q????????{5???C?k?????2???-???????????n???????????A,?????
3、??????2???-?????????s{5???J?????w?????4???1?????7?C???O{5???R??:?.?o?2;???2???-;?????n????;???2?????=???4????:O151???R?(???2:A?????s??:100928984(2008)01200842020{??I???o?2?4???????R?w???{?o?2?w?????-???Y???????????(???????n????,?[?????a?o?2???(????{5?
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6、+C?u(t)+Ku(t)=0(1)?h?=:MVuVuVu?[??;CVuVuVu?D?W;KVuVuVu?N?????-;u(t)l)RNVuVuVu???z???(?n??;tl)R+VuVuVu????{5???a????(?J????)u(t)=uest=ueiwt(s=iw)????(1)?h??(s2Mu+sCu+Ku)est=0(2)???????1(2)???????Wsi?w?????N???hdet[s2M+sC+K]=0???k{5????N???r??????,???1(
7、2)?02N?M?>?.?????????????????Ws1,l?,sN,s31,l?,s3N?s???YS1,l?,S2N,???=s3i???Ysi??????(i=1,2,l?,N),???Y??????????{5?????????W?????p?????????n??,???N???r??????,?????????n??{ur}?w?.????????????,???Y?o?2?w???n??(?.?o?2?n??),?o?2???-?Y[U]={u1}l?{uN}{uN}3
8、{uN}3s1{u1}l?sN{uN}s31{u1}1l?s3N{u}N???=,{ur}3{ur}??????r=1,2,l?l?N,???0s2iMui+siCui+Kui=0{?(Πi=1,2,l?,N)???=,sil)C?w?Ki?M?????W,uil)CN?w?Ki?M?????n??,???.?????????????9?h,?????Y???7????(1)?????????n??{5?J?Z?????I???????????????n??,????s2ivTiM
