Fundamental Frequency - Mechanical Systems

Mechanical Systems

Consider a beam, fixed at one end and having a mass attached to the other; this would be a single degree of freedom (SDoF) oscillator. Once set into motion it will oscillate at its natural frequency. For a single degree of freedom oscillator, a system in which the motion can be described by a single coordinate, the natural frequency depends on two system properties: mass and stiffness; (providing the system is undamped). The radian frequency, ω_n, can be found using the following equation:

Where:
k = stiffness of the beam
m = mass of weight
ω_n = radian frequency (radians per second)

From the radian frequency, the natural frequency, f_n, can be found by simply dividing ω_n by 2π. Without first finding the radian frequency, the natural frequency can be found directly using:

Where:
f_n = natural frequency in hertz (cycles/second)
k = stiffness of the beam (Newtons/meter or N/m)
m = mass at the end (kg)
while doing the modal analysis of structures and mechanical equipments, the frequency of 1st mode is called fundamental frequency.