LEADER 03639nam 22006014a 450 001 9910827653803321 005 20230607221509.0 010 $a981-277-762-8 035 $a(CKB)1000000000410461 035 $a(StDuBDS)AH24684744 035 $a(SSID)ssj0000151634 035 $a(PQKBManifestationID)11146918 035 $a(PQKBTitleCode)TC0000151634 035 $a(PQKBWorkID)10318322 035 $a(PQKB)10779641 035 $a(MiAaPQ)EBC1681563 035 $a(WSP)00004940 035 $a(Au-PeEL)EBL1681563 035 $a(CaPaEBR)ebr10201227 035 $a(CaONFJC)MIL505412 035 $a(OCoLC)879074411 035 $a(EXLCZ)991000000000410461 100 $a20020702d2002 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aExact analysis of bi-periodic structures$b[electronic resource] /$fC.W. Cai, J.K. Liu, H.C. Chan 210 $aNew Jersey $cWorld Scientific$dc2002 215 $a1 online resource (ix, 269 p. )$cill 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a981-02-4928-4 320 $aIncludes bibliographical references (p. 263-264) and index. 327 $aU-transformation and uncoupling of governing equations for systems with cyclic bi-periodicity; bi-periodic mass-spring systems; bi-periodic structures; structures with bi-periodicity in two directions; nearly periodic systems with non-linear disorders. 330 8 $aBy using the U-transformation method, it is possible to uncouple linear simultaneous equations with cyclic periodicity. This text discusses how to apply U-transformation twice to uncouple the two sets of unknown variables in a doubly periodic structure to achieve an analytical exact solution.$bBy using the U-transformation method, it is possible to uncouple linear simultaneous equations, either algebraic or differential, with cyclic periodicity. This text presents a procedure for applying the U-transformation technique twice to uncouple the two sets of unknown variables in a doubly periodic structure to achieve an analytical exact solution.;Explicit exact solutions for the static and dynamic analyses for certain engineering structures with doubly periodic properties - such as a continuous truss with any number of spans, cable network and grillwork on supports with periodicity, and grillwork with periodic stiffening members or equidistant line supports - can be found in the volume. The availability of these exact solutions not only helps with the checking of the convergence and accuracy of numerical solutions, but also provides a basis for optimization design for these types of structures.;The study of the force vibration and mode shape of periodic systems with non-linear disorder is yet another research area which has attained considerable success by the U-transformation method. This work illustrates the analytical approach and procedure for the problems of localization of the mode shape of nearly periodic systems together with the results. 606 $aStructural analysis (Engineering) 606 $aMechanics, Analytic 606 $aTransformation groups 615 0$aStructural analysis (Engineering) 615 0$aMechanics, Analytic. 615 0$aTransformation groups. 676 $a624.1/71 700 $aCai$b C. W$01672498 701 $aLiu$b J. K$01672499 701 $aChan$b H. C$g(Hon Chuen)$01672500 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910827653803321 996 $aExact analysis of bi-periodic structures$94035877 997 $aUNINA