Structures have natural frequency & time period based upon their mass, stiffness & damping distribution.

[1] Natural frequency and time period help in understanding the dynamic response of the structure towards a certain load.

F(t) = m.a(t) + c.v(t) + k.x(t) = 0

[2] The solution to the above mentioned equation gives the natural response of the structure.

[3] The mathematical solution yields to the displacement as

x = A cos(wt) + B sin(wt)

This gives a harmonic nature for displacement and attains maxima for multiple values of w.

[4] Hence this gives us multiple values for frequency corresponding to different modes.

[5] The participation of each of these modes make up the overall response of the structure, which is dependent on mass & stiffness of the structure.

This is a post on modal analysis & natural frequency.

Any comments or suggestions are welcomed.