Related Resources: vibration

Angular Natural Frequency Geared System Equations and Calculator

Machine Design and Engineering

Angular Natural Frequency of Geared System with Masses Gears Equations and Calculator
Speed of Rotors 2 is n times Speed of Rotor 1.

Mass Spring Systems in Translation Equation and Calculator

ω_n = [ ( k_t1 k_t2 ( I₁ + n² I₂ ) / ( I₁ I₂ ( n² k_t2 + k_t1 ) ) ] ^1/2

Where:

k_{t1, t2} = Torsional Stiffness of Shaft ( lb-in/rad )
I_{1, 2} = Rotary Mass Moment of Inertia of Mass ( lb-in-sec² )
n = Rotor speed 2 n times faster than Rotor Speed 1
ω_n = Angular Natural Frequency ( rad/sec )

Reference Harris, Shock and Vibration Handbook