physics//mechanics//vibration

Vibration is the oscillation of a structure or a machine about its equilibrium, and engineers care about it because it wears bearings, loosens bolts, cracks welds and pollutes sensors. Every elastic structure has a set of preferred ways of vibrating, each with its own natural frequency and its own pattern of deformation, the mode shape; when something excites the structure near one of those frequencies the motion is amplified, which is resonance. A two-pole motor turning at about 49 Hz on a pump frame with a mode at 47 Hz shakes the bearings; on a drone, propellers spinning near the first bending mode of an arm shake the IMU, and the flight controller then estimates its attitude from vibration.

Vibration is the oscillation of a structure or a machine about its equilibrium, and engineers care about it because it wears bearings, loosens bolts, cracks welds and pollutes sensors. Every elastic structure has a set of preferred ways of vibrating, each with its own natural frequency and its own pattern of deformation, the mode shape; when something excites the structure near one of those frequencies the motion is amplified, which is resonance. A two-pole motor turning at about 49 Hz on a pump frame with a mode at 47 Hz shakes the bearings; on a drone, propellers spinning near the first bending mode of an arm shake the IMU, and the flight controller then estimates its attitude from vibration.

The three members of this branch answer three questions. Natural frequency says at what rate a mode oscillates on its own and what moves it (stiffness up, mass down). Resonance says what happens when an excitation sits near that rate and what can be done about it. Modal analysis computes or measures all the modes of a structure before it is built or while it is running. The mathematics underneath is one generalized eigenvalue problem, Kv=ω2MvKv=\omega^2MvKv=ω2Mv, on the mass and stiffness matrices (eigenvalue, modes).

The same physics is read in two directions. A designer keeps natural frequencies away from the speeds of motors, fans and propellers; a maintenance engineer reads the vibration of a running machine to learn what is failing inside it (vibration analysis).

On a drone the defence is layered: stiff arms and a soft mount for the flight controller, then notch filters that follow each motor's speed in software (notch filter).