Response of MDOF structures to ground motion

1 Response of MDOF structures to ground motion ()()()1()gMxtC xtK xtMx t If damping is well-behaving, or can be approximated using equivalent viscous damping, we can decouple the equations of motion using modal decomposition: 1212()()()()Nqtqtxtqt ()Nqt and separate the system into its natural ()()()1()gMxtC xtK xtMx t becomesbecomes ()()()1()1, 2 ,,TTT TiiiiiiiiiigMqtCqtKqtMx tiN Tor when normalized with respect to modal mass TiiM 2() 2()()()1,2, ,iiiiii igqtwqt wqtx tiN 2() 2()()()1,2, ,iiiiii igqtwqt wqtx tiN 1TM where , called modal participation factorfor mode i. 1iiTiiMM 11 NTjjiijmM 21iTNiijjijMm 32() 2()()()1,2, ,iiiiii igqtwqt wqtx tiN For a lightly damped (underdamped) system that is initially at restFor a lightly damped (underdamped) system that is initially at rest, solution can be found using the convolution/Duhamel s integral from(),,0()( )sin()iitwtiigdidiqtx ew t dw Or using a numerical solution algorithm, once you compute you can find the contribution of the i-th mode to the respons

Response of MDOF structures to ground motion M xt C xt K xt M x t () () 1 () g If damping is well-behaving, or can be approximated using equivalent viscous damping, we can decouple the equations of motion using modal decomposition: 1 2 12 () ()N qt

Tags:

  Structure, Response, Ground, Motion, Modal, Ofdm, Response of mdof structures to ground motion

Information

Related search queries