tailieunhanh - Harris' Shock and Vibration Handbook Part 12

Tham khảo tài liệu 'harris' shock and vibration handbook part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | FINITE ELEMENT MODELS where LTMJ Ks l LTMf K p When the mode acceleration method is employed Eqs. and are combined to define the mode acceleration LTM relationship 5 LTM4 ặ LTM vlk LTMaf F where IITM. 1 - Kì K-1M l LTMv - K5 K-1B L ltmf K K- T In practice LTMv is generally ignored. Mode acceleration LTMs are used extensively in the aeronautical and space vehicle industries while their mode displacement and residual vector -based counterpart is rarely applied. APPLIED LOADS AND ENFORCED MOTIONS Dynamic excitation environments sometimes are described in terms of specified foundation or boundary motions for example in the study of structural dynamic response to seismic excitations see Chap. 24 . In such situations the physical displacement array is partitioned into two subsets as follows interior motions boundary motions The conventional linear structural dynamic formulation is expressed in partitioned form as Mtt Miblpil Mbi MbbjpbJ Bii Bib Bbi Bbb Kii Kdkl i Fii KbiKbb J ựb J Using the partitioned stiffness matrix the transformation from absolute to relative response displacements is Ui Ub Iii 0bi -K-Kb IfUiT 1 riii ib Ibb Ub 0bi Ibb Moreover this transformation may be expressed in modal form by substituting the lowest-frequency modes associated with the interior eigenvalue problem which follows the relationships already discussed in Eqs. through that is K J Mii i L Ui fcjfol CHAPTER TWENTY-EIGHT PART II By combining Eqs. and the modal reduction transformation is Ui Ub i ib 0bi Ibb Substitution of this transformation into the partitioned dynamic equation set Eq. results in In TTM Pbi M bb bj 2Zi i 0bi B0bl i q j 2 OiblUli QjFt 0bi K bb ub J hi F Fb The terms in the above equation set have the following significance 1. Pib is the modal participation factor matrix. Its terms express the degree of excitation delivered by individual foundation .