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## Structural Dynamics: Total response of a damped system

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Dynamic Analysis: Total response of a damped system

Updated 21 Dec 2019

This function determines total response of a damped system
Input:
Mass, Damping coefficient, Stiffness, Excitation force

Output:
The file calculates the total response of a damped system including the followings:
-Natural circular frequency
-Critical damping coefficient
-Relative critical viscous damping
-Damped circular frequency
-Total solution as sum of homogenous and particular solution
-Plotting displacement as a function of time

How to use the function:
- Step 1: Derive the equation of motion for the whole system in order to obtain total mass, damping, stiffness and excitation values.
- Step 2: Determine the particular solution of the system.
- Step 3: Determine the coefficients A & B in the homogenous solution according to the initial conditions, so that when (t=0) for u(t), coefficient A is obtained. Derive u(t) and set (t=0) and with help of A, the coefficient B could be obtained.
- Step 4: Determine the total solution as a sum of homogenous solution and particular solution.
- Step 5: Plot the result.

Extra information: Try to experiment on increasing/ decreasing the value of the damping coefficient in order to see the decaying of the vibration.

If the system is SDOF and free vibration wants to be plotted, ignore the exciting force & particular solution.

### Cite As

Benjamin Bondsman (2020). Structural Dynamics: Total response of a damped system (https://www.mathworks.com/matlabcentral/fileexchange/73751-structural-dynamics-total-response-of-a-damped-system), MATLAB Central File Exchange. Retrieved .