# Random Response of a MDOF System Using ode45

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EhsanZ 2017년 2월 1일
답변: Aadarsh Jain 2019년 5월 14일
Hi,
I want to calculate the random response of a MDOF system (Response of the system when it is being excited at some of its DOFS by a zero-mean random excitation). The system is a simple 5 DOF lumped mass-spring system. I derived the mass, damping, and stiffness matrices of the system. Next, I rewrote the governing differential equation of the system (Mx'' + Cx' + kx = f) in the from q' = f(q) in order to use ode45 to calculate the time domain response of the system. The code works well when the system is excited by lets say sin(2*pi*f*t) or step function or... . However, when I use a random number generator rand or randn to excite the system with a zero-mean random process, it takes the code too much to reach the answer. The time is too long (due to too short time intervals of the solution process in ode45). Can anybody say if there is another way to calculate the random response of an M,C,K model?

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### 채택된 답변

KSSV 2017년 2월 2일
편집: KSSV 2017년 2월 2일
There are other methods like Newmark beta method...You may refer Dynamic of structures - Clough and/or Finite element Procedures - Bathe

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### 추가 답변(1개)

Hey Ehsan Z,
I have been trying to write the ODE for MDOF system in matlab. I am finding it very difficult to input ground acceleration for given time range and finding the solution. Kindly help.
Thank you
ME17F09F006@geca.ac.in

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