Transcription of Response of MDOF systems - Chula
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Example: air traffic controller
Response of MDOF systems - Chula
Response of mdof systemsDegree of freedom (DOF): The minimum number of independent coordinates required to determine completely the positions of all parts of a system at any instant of time. Two DOF systemsThree DOF systemsThe normal mode analysis (EOM-1)Example: Response of 2 DOF systemm2mkkkx1x2 FBDm2mkx1k(x1-x2)kx2 EOM1211)(xmxxkkx&&= 22212)(xmkxxxk&&= In matrix form, EOM is = + 00222002121xxkkkkxxmm&&&&EOM -2 (example) = + 00222002121xxkkkkxxmm&&&&x EOMMKFx)()()()(ttttFKxxCxM=++&&&In general formMis the inertia of mass matrix (nx n)Cis the damping matrix (n x n)Kis the stiffness matrix (n x n)Fis the external force vector (n x 1)xis the position vector (n x 1)Synchronous motionFrom observations, free vibration of undamped MDOF system is a synchronous motion. All coordinates pass the equilibrium points at the same time All coordinates reach extreme positions at the same time Relative shape does not change with time=21xxconstanttimex1x2x1x2No phase diff.
Modal analysis • is a method for solving for both transient and steady state responses of free and forced MDOF systems through analytical approaches. • Uses the orthogonality property of the modes to “decouple” the EOM breaking EOM into independent SDOF equations, which can be solved for response separately. Introduction
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