Calculating the Natural Circular Frequency, Period, and Frequency of a Cantilevered Beam with a Concentrated Load at Any Point Along its Length

February 23, 2017 Abdul Siraj, P.E.

In this post, I will discuss the fourth example in our structural dynamics course covering undamped free vibration. The goal of this structural dynamics example is to calculateĀ the natural circular frequency, period, and frequency of a cantilevered beam with a concentrated load at any point along its length.


The problem statement states,


A fixed-fixed beam having a concentrated weight at its midspan is shown below.

Assume: Mass of beam negligible in comparison to mass of concentrated weight and neglect effects of damping.

Determine equation of motion, natural circular frequency, period, and natural frequency


Let W = 10 kips,
I = 200 in^4,
E = 29,000 ksi,
L = 20′



Abdul Siraj, P.E.