Time response of multi degree of freedom systems undergoes f

This function provides a tool for free vibration time response of a multi degree of freedom (n-DOF) system.

This function provides a tool for free vibration time response of a multi degree of freedom (n-DOF) system. The inputs of the function are mass matrix, stiffness matrix and initial displacement and velocities.

The first step is to solve an eigenvalue analysis to obtain the natural frequencies and mode shapes.

The second step is obtaining the coefficients and phase delay of each mode based on the initial displacements and velocities.

After obtaining the coefficients, the last step is obtaining the displacements, velocities and accelerations of each degree of freedom by mode summation.

In fact, the concept behind the free vibration is that the time response of the vibrating system is a superposition of different modes but each of them with a weighting coefficient and a phase delay.

There are three sample files that show how to use this function.