Glossary term
Natural Frequency
A frequency at which a system tends to oscillate when disturbed without continuing excitation.
Definition
quantityA frequency at which a system tends to oscillate when disturbed without continuing excitation.
Natural frequency is the frequency at which a system oscillates in free vibration after an initial disturbance. It depends primarily on mass, stiffness, boundary conditions, and mode shape, and it is central to resonance avoidance, modal testing, rotating machinery, vibration isolation, and structural dynamics.
Natural frequency describes the preferred free-vibration rate of a system. If a bracket, shaft, building floor, suspension, or control mechanism is displaced and released, it tends to oscillate near one or more natural frequencies. Each natural frequency belongs to a mode shape, so real structures usually have many natural frequencies rather than one.
For a simple single-degree-of-freedom mass-spring system, the undamped natural circular frequency is:
and the frequency in hertz is:
This equation shows the basic design levers: higher stiffness raises natural frequency, while higher effective mass lowers it. In distributed structures, equivalent mass and stiffness vary by mode, boundary condition, and deformation pattern.
Role in design
Natural frequency matters when a system is exposed to periodic or broadband excitation. A motor speed, gear-mesh frequency, blade-passing frequency, pump pulsation, road input, acoustic source, or control-loop command can excite a mode if it lies near a natural frequency. When that happens, response amplitude can increase sharply, especially if damping is low.
Engineers estimate natural frequencies with hand models, finite element modal analysis, impact testing, shaker testing, or operational vibration data. In early design, the goal is often to separate natural frequencies from expected forcing frequencies. In later validation, measured modes are compared with simulations to check stiffness, mass distribution, joints, and boundary conditions.
Damping and interpretation
Damping changes the peak response and the damped oscillation frequency, but it does not remove the need to understand the undamped natural frequencies. A lightly damped mode can create fatigue, noise, measurement error, or unstable control behaviour. A highly damped mode may still matter if excitation is strong or if isolation requirements are strict.
Natural frequencies are not fixed material constants. A bolted joint, filled tank, temperature change, preload, cracked member, boundary support, or attached sensor can shift them. In rotating machinery, gyroscopic effects and bearing stiffness can also make natural frequencies speed-dependent.
Common mistakes
A common mistake is to quote a natural frequency without the associated mode shape and boundary condition. Another is to compare a free-free laboratory test with a fixed-base service installation. A sound review states the configuration, mass loading, support conditions, damping estimate, excitation sources, frequency margin, and whether the mode was predicted, measured, or inferred from operating data.